Agent Work: Minimum Spanning Tree (Boruvka)

Claude Opus 4.6 · COMP 322: Fundamentals of Parallel Programming

COMP 322 Homework 4: Minimum Spanning Tree (Boruvka's Algorithm)

Total: 100 points

Overview

Implement a parallel algorithm for finding the minimum spanning tree of an undirected graph using Boruvka's algorithm.

Testing Your Solution

# Run all tests
bin/grade workspaces/agent_hw4

# Run specific tests
mvn test -Dtest=BoruvkaCorrectnessTest
mvn test -Dtest=BoruvkaPerformanceTest

---

Part 1: Written Assignment (40 points)

1.1 HJ isolated vs Java atomic variables (20 points)

Compare IsolatedPRNG (using HJlib isolated) and AtomicPRNG (using AtomicInteger):

IsolatedPRNG:

class IsolatedPRNG {
    private int seed;
    public int nextSeed() {
        final int retVal = isolatedWithReturn(() -> {
            final int curSeed = seed;
            final int newSeed = nextInt(curSeed);
            seed = newSeed;
            return curSeed;
        });
        return retVal;
    }
}

AtomicPRNG:

class AtomicPRNG {
    private AtomicInteger seed;
    public int nextSeed() {
        int retVal;
        while (true) {
            retVal = seed.get();
            int nextSeedVal = nextInt(retVal);
            if (seed.compareAndSet(retVal, nextSeedVal)) break;
        }
        return retVal;
    }
}

1. (10 points) Do they have the same semantics when called in parallel? Explain. 2. (10 points) Why is the while (true) loop needed? What if it only ran once?

1.2 Dining Philosophers Problem (20 points)

Consider 5 philosophers where 4 acquire left fork first, then right, but 1 philosopher acquires right fork first, then left.

1. (10 points) Is deadlock possible with synchronized statements? Show execution or explain why not. 2. (10 points) Is livelock possible with ReentrantLock.tryLock()? Show execution or explain why not.

---

Part 2: Programming Assignment (60 points)

Background: Boruvka's Algorithm

Boruvka's algorithm computes MST through successive edge-contraction operations:

while (!nodesLoaded.isEmpty()) {
    n = nodesLoaded.poll();
    if (n.isDead) continue;
    Edge e = n.getMinEdge();
    if (e == null) break;
    Component other = e.getOther(n);
    other.isDead = true;
    n.merge(other, e.weight());
    nodesLoaded.add(n);
}

Key insights for parallelization:

Work-list order doesn't matter (unordered collection)
Disjoint (n, other) pairs can execute in parallel

Checkpoint 1: Correctness (20 points)

Implement parallel Boruvka in:

ParBoruvka.java - main algorithm
ParComponent.java - component with mutual exclusion
ParEdge.java - edge representation

Must pass BoruvkaCorrectnessTest with at least 2 threads.

Final: Performance (25 points)

Performance evaluation with USA-road-d.NE.gr.gz:

Threads	Speedup Target	Points
1	<= 2x sequential	5
2	>= 1.25x	5
4	>= 1.6x	5
8	>= 1.5x	5
16	>= 1.4x	5

Implementation Tips

Create limited threads (one per core)
Reduce parallelism as graph contracts
Use ConcurrentLinkedQueue or ConcurrentHashMap for work-list
Consider ReentrantLock.tryLock() for collision handling

---

Report (15 points)

Include:

Design and parallel constructs used
Correctness and data-race-free justification
Deadlock-free justification
Livelock-free justification
Test outputs and performance measurements

---

Files to Implement

src/main/java/edu/rice/comp322/boruvka/parallel/ParBoruvka.java
src/main/java/edu/rice/comp322/boruvka/parallel/ParComponent.java
src/main/java/edu/rice/comp322/boruvka/parallel/ParEdge.java

--- *COMP 322: Fundamentals of Parallel Programming, Rice University*

ParBoruvka.java2.6 KB

java

package edu.rice.comp322.boruvka.parallel;

import edu.rice.comp322.AbstractBoruvka;
import edu.rice.comp322.boruvka.BoruvkaFactory;
import edu.rice.comp322.boruvka.Edge;
import edu.rice.comp322.boruvka.Loader;
import edu.rice.hj.api.SuspendableException;

import java.util.LinkedList;
import java.util.Queue;

/**
 * This class must be modified.
 *
 * @author <a href="http://shams.web.rice.edu/">Shams Imam</a> (shams@rice.edu)
 */
public final class ParBoruvka extends AbstractBoruvka implements BoruvkaFactory<ParComponent, ParEdge> {

    protected final Queue<ParComponent> nodesLoaded = new LinkedList<>();

    public ParBoruvka() {
        super();
    }

    @Override
    public boolean usesHjLib() {
        return true;
    }

    @Override
    public void initialize(final String[] args) {
        Loader.parseArgs(args);
    }

    @Override
    public void preIteration(final int iterationIndex) {
        // Exclude reading file input from timing measurement
        nodesLoaded.clear();
        Loader.read(this, nodesLoaded);

        totalEdges = 0;
        totalWeight = 0;
    }

    @Override
    public void runIteration(int nthreads) throws SuspendableException {
        computeBoruvka(nodesLoaded);
    }

    private void computeBoruvka(final Queue<ParComponent> nodesLoaded) {

        ParComponent loopNode = null;

        // START OF EDGE CONTRACTION ALGORITHM
        while (!nodesLoaded.isEmpty()) {

            // poll() removes first element (node loopNode) from the nodesLoaded work-list
            loopNode = nodesLoaded.poll();

            if (loopNode.isDead) {
                continue; // node loopNode has already been merged
            }

            final Edge<ParComponent> e = loopNode.getMinEdge(); // retrieve loopNode's edge with minimum cost
            if (e == null) {
                break; // done - we've contracted the graph to a single node
            }

            final ParComponent other = e.getOther(loopNode);
            other.isDead = true;
            loopNode.merge(other, e.weight()); // merge node other into node loopNode
            nodesLoaded.add(loopNode); // add newly merged loopNode back in the work-list

        }
        // END OF EDGE CONTRACTION ALGORITHM
        if (loopNode != null) {
            totalEdges = loopNode.totalEdges();
            totalWeight = loopNode.totalWeight();
        }
    }

    @Override
    public ParComponent newComponent(final int nodeId) {
        return new ParComponent(nodeId);
    }

    @Override
    public ParEdge newEdge(final ParComponent from, final ParComponent to, final double weight) {
        return new ParEdge(from, to, weight);
    }
}

ParBoruvka.java2.6 KB

java

package edu.rice.comp322.boruvka.parallel;

import edu.rice.comp322.AbstractBoruvka;
import edu.rice.comp322.boruvka.BoruvkaFactory;
import edu.rice.comp322.boruvka.Edge;
import edu.rice.comp322.boruvka.Loader;
import edu.rice.hj.api.SuspendableException;

import java.util.LinkedList;
import java.util.Queue;

/**
 * This class must be modified.
 *
 * @author <a href="http://shams.web.rice.edu/">Shams Imam</a> (shams@rice.edu)
 */
public final class ParBoruvka extends AbstractBoruvka implements BoruvkaFactory<ParComponent, ParEdge> {

    protected final Queue<ParComponent> nodesLoaded = new LinkedList<>();

    public ParBoruvka() {
        super();
    }

    @Override
    public boolean usesHjLib() {
        return true;
    }

    @Override
    public void initialize(final String[] args) {
        Loader.parseArgs(args);
    }

    @Override
    public void preIteration(final int iterationIndex) {
        // Exclude reading file input from timing measurement
        nodesLoaded.clear();
        Loader.read(this, nodesLoaded);

        totalEdges = 0;
        totalWeight = 0;
    }

    @Override
    public void runIteration(int nthreads) throws SuspendableException {
        computeBoruvka(nodesLoaded);
    }

    private void computeBoruvka(final Queue<ParComponent> nodesLoaded) {

        ParComponent loopNode = null;

        // START OF EDGE CONTRACTION ALGORITHM
        while (!nodesLoaded.isEmpty()) {

            // poll() removes first element (node loopNode) from the nodesLoaded work-list
            loopNode = nodesLoaded.poll();

            if (loopNode.isDead) {
                continue; // node loopNode has already been merged
            }

            final Edge<ParComponent> e = loopNode.getMinEdge(); // retrieve loopNode's edge with minimum cost
            if (e == null) {
                break; // done - we've contracted the graph to a single node
            }

            final ParComponent other = e.getOther(loopNode);
            other.isDead = true;
            loopNode.merge(other, e.weight()); // merge node other into node loopNode
            nodesLoaded.add(loopNode); // add newly merged loopNode back in the work-list

        }
        // END OF EDGE CONTRACTION ALGORITHM
        if (loopNode != null) {
            totalEdges = loopNode.totalEdges();
            totalWeight = loopNode.totalWeight();
        }
    }

    @Override
    public ParComponent newComponent(final int nodeId) {
        return new ParComponent(nodeId);
    }

    @Override
    public ParEdge newEdge(final ParComponent from, final ParComponent to, final double weight) {
        return new ParEdge(from, to, weight);
    }
}

ParBoruvka.java4.1 KB

java

package edu.rice.comp322.boruvka.parallel;

import edu.rice.comp322.AbstractBoruvka;
import edu.rice.comp322.boruvka.BoruvkaFactory;
import edu.rice.comp322.boruvka.Edge;
import edu.rice.comp322.boruvka.Loader;
import edu.rice.hj.api.SuspendableException;

import java.util.Queue;
import java.util.concurrent.ConcurrentLinkedQueue;

import static edu.rice.hj.Module1.async;
import static edu.rice.hj.Module1.finish;

/**
 * Parallel implementation of Boruvka's MST algorithm using lock-based
 * edge contraction with HJlib async/finish for task parallelism.
 */
public final class ParBoruvka extends AbstractBoruvka implements BoruvkaFactory<ParComponent, ParEdge> {

    protected final ConcurrentLinkedQueue<ParComponent> nodesLoaded = new ConcurrentLinkedQueue<>();

    public ParBoruvka() {
        super();
    }

    @Override
    public boolean usesHjLib() {
        return true;
    }

    @Override
    public void initialize(final String[] args) {
        Loader.parseArgs(args);
    }

    @Override
    public void preIteration(final int iterationIndex) {
        nodesLoaded.clear();
        Loader.read(this, nodesLoaded);

        totalEdges = 0;
        totalWeight = 0;
    }

    @Override
    public void runIteration(int nthreads) throws SuspendableException {
        computeBoruvka(nodesLoaded, nthreads);
    }

    private void computeBoruvka(final ConcurrentLinkedQueue<ParComponent> nodesLoaded, final int nthreads) throws SuspendableException {

        final ParComponent[] result = new ParComponent[1];

        finish(() -> {
            for (int i = 0; i < nthreads; i++) {
                async(() -> {
                    while (true) {
                        final ParComponent n = nodesLoaded.poll();
                        if (n == null) {
                            break;
                        }

                        if (n.isDead) {
                            continue;
                        }

                        if (!n.lock.tryLock()) {
                            nodesLoaded.add(n);
                            continue;
                        }

                        // n is now locked
                        if (n.isDead) {
                            n.lock.unlock();
                            continue;
                        }

                        final Edge<ParComponent> e = n.getMinEdge();
                        if (e == null) {
                            // No more edges - this is a completed component
                            n.lock.unlock();
                            result[0] = n;
                            break;
                        }

                        final ParComponent other = e.getOther(n);

                        if (!other.lock.tryLock()) {
                            // Could not lock other, put n back and retry later
                            n.lock.unlock();
                            nodesLoaded.add(n);
                            continue;
                        }

                        // Both n and other are locked
                        if (other.isDead) {
                            // other was merged by another thread
                            other.lock.unlock();
                            n.lock.unlock();
                            nodesLoaded.add(n);
                            continue;
                        }

                        // Perform the merge: absorb other into n
                        other.isDead = true;
                        n.merge(other, e.weight());
                        other.lock.unlock();
                        n.lock.unlock();
                        nodesLoaded.add(n);
                    }
                });
            }
        });

        if (result[0] != null) {
            totalEdges = result[0].totalEdges();
            totalWeight = result[0].totalWeight();
        }
    }

    @Override
    public ParComponent newComponent(final int nodeId) {
        return new ParComponent(nodeId);
    }

    @Override
    public ParEdge newEdge(final ParComponent from, final ParComponent to, final double weight) {
        return new ParEdge(from, to, weight);
    }
}

ParBoruvka.java4.1 KB

java

package edu.rice.comp322.boruvka.parallel;

import edu.rice.comp322.AbstractBoruvka;
import edu.rice.comp322.boruvka.BoruvkaFactory;
import edu.rice.comp322.boruvka.Edge;
import edu.rice.comp322.boruvka.Loader;
import edu.rice.hj.api.SuspendableException;

import java.util.Queue;
import java.util.concurrent.ConcurrentLinkedQueue;

import static edu.rice.hj.Module1.async;
import static edu.rice.hj.Module1.finish;

/**
 * Parallel implementation of Boruvka's MST algorithm using lock-based
 * edge contraction with HJlib async/finish for task parallelism.
 */
public final class ParBoruvka extends AbstractBoruvka implements BoruvkaFactory<ParComponent, ParEdge> {

    protected final ConcurrentLinkedQueue<ParComponent> nodesLoaded = new ConcurrentLinkedQueue<>();

    public ParBoruvka() {
        super();
    }

    @Override
    public boolean usesHjLib() {
        return true;
    }

    @Override
    public void initialize(final String[] args) {
        Loader.parseArgs(args);
    }

    @Override
    public void preIteration(final int iterationIndex) {
        nodesLoaded.clear();
        Loader.read(this, nodesLoaded);

        totalEdges = 0;
        totalWeight = 0;
    }

    @Override
    public void runIteration(int nthreads) throws SuspendableException {
        computeBoruvka(nodesLoaded, nthreads);
    }

    private void computeBoruvka(final ConcurrentLinkedQueue<ParComponent> nodesLoaded, final int nthreads) throws SuspendableException {

        final ParComponent[] result = new ParComponent[1];

        finish(() -> {
            for (int i = 0; i < nthreads; i++) {
                async(() -> {
                    while (true) {
                        final ParComponent n = nodesLoaded.poll();
                        if (n == null) {
                            break;
                        }

                        if (n.isDead) {
                            continue;
                        }

                        if (!n.lock.tryLock()) {
                            nodesLoaded.add(n);
                            continue;
                        }

                        // n is now locked
                        if (n.isDead) {
                            n.lock.unlock();
                            continue;
                        }

                        final Edge<ParComponent> e = n.getMinEdge();
                        if (e == null) {
                            // No more edges - this is a completed component
                            n.lock.unlock();
                            result[0] = n;
                            break;
                        }

                        final ParComponent other = e.getOther(n);

                        if (!other.lock.tryLock()) {
                            // Could not lock other, put n back and retry later
                            n.lock.unlock();
                            nodesLoaded.add(n);
                            continue;
                        }

                        // Both n and other are locked
                        if (other.isDead) {
                            // other was merged by another thread
                            other.lock.unlock();
                            n.lock.unlock();
                            nodesLoaded.add(n);
                            continue;
                        }

                        // Perform the merge: absorb other into n
                        other.isDead = true;
                        n.merge(other, e.weight());
                        other.lock.unlock();
                        n.lock.unlock();
                        nodesLoaded.add(n);
                    }
                });
            }
        });

        if (result[0] != null) {
            totalEdges = result[0].totalEdges();
            totalWeight = result[0].totalWeight();
        }
    }

    @Override
    public ParComponent newComponent(final int nodeId) {
        return new ParComponent(nodeId);
    }

    @Override
    public ParEdge newEdge(final ParComponent from, final ParComponent to, final double weight) {
        return new ParEdge(from, to, weight);
    }
}

COMP 322 Homework 4: Minimum Spanning Tree (Boruvka's Algorithm)

Part 1: Written Questions (40 points)

1.1 HJ isolated vs Java Atomic Variables (20 points)

Compare the following two PRNG implementations:

IsolatedPRNG:

class IsolatedPRNG {
    private int seed;
    public int nextSeed() {
        final int retVal = isolatedWithReturn(() -> {
            final int curSeed = seed;
            final int newSeed = nextInt(curSeed);
            seed = newSeed;
            return curSeed;
        });
        return retVal;
    }
}

AtomicPRNG:

class AtomicPRNG {
    private AtomicInteger seed;
    public int nextSeed() {
        int retVal;
        while (true) {
            retVal = seed.get();
            int nextSeedVal = nextInt(retVal);
            if (seed.compareAndSet(retVal, nextSeedVal)) break;
        }
        return retVal;
    }
}

---

1.1.1 Same Semantics? (10 points)

> Do they have the same semantics when called in parallel? Explain.

Your Answer:

Yes, both implementations have equivalent semantics when called in parallel. They both guarantee that each call to nextSeed() atomically reads the current seed, computes the next seed, updates the stored seed, and returns the old seed value.

IsolatedPRNG achieves atomicity using HJlib's isolatedWithReturn, which provides mutual exclusion by ensuring that the body of the isolated block executes atomically with respect to all other isolated blocks. Only one task can execute the isolated section at a time, so the read-compute-write of seed is atomic.

AtomicPRNG achieves atomicity using AtomicInteger.compareAndSet (CAS), which is a hardware-level atomic operation. The CAS ensures that the seed is only updated if it hasn't been changed by another thread since it was read. If another thread modified the seed between the get() and compareAndSet(), the CAS fails, and the loop retries with the new value.

Both guarantee that every call to nextSeed() returns a unique seed value (no duplicates), and the sequence of seeds produced is consistent with some sequential ordering of the calls (linearizability). The key difference is in the mechanism: isolated uses blocking mutual exclusion (pessimistic), while CAS uses non-blocking optimistic concurrency. But the observable behavior from the caller's perspective is the same: each invocation atomically advances the PRNG state and returns the previous seed.

---

1.1.2 Why While Loop? (10 points)

> Why is the while (true) loop needed? What if it only ran once?

Your Answer:

The while (true) loop is needed because the compareAndSet (CAS) operation can fail when there is a concurrent modification. CAS is an optimistic concurrency technique: it assumes no conflict and retries if one is detected.

Concrete scenario with the loop: 1. Thread A calls nextSeed(). It reads seed.get() = 42, computes nextInt(42) = 97. 2. Thread B calls nextSeed(). It reads seed.get() = 42, computes nextInt(42) = 97. 3. Thread A executes seed.compareAndSet(42, 97) → succeeds (seed was still 42). Thread A returns 42. 4. Thread B executes seed.compareAndSet(42, 97) → fails (seed is now 97, not 42). 5. Thread B loops: reads seed.get() = 97, computes nextInt(97) = 153. 6. Thread B executes seed.compareAndSet(97, 153) → succeeds. Thread B returns 97.

Result: Thread A returns 42, Thread B returns 97. All values are unique and correct.

What would happen without the loop (single iteration): 1. Thread A reads seed.get() = 42, computes nextInt(42) = 97. 2. Thread B reads seed.get() = 42, computes nextInt(42) = 97. 3. Thread A executes seed.compareAndSet(42, 97) → succeeds. Returns 42. 4. Thread B executes seed.compareAndSet(42, 97) → fails. But without the loop, Thread B has no way to retry!

Without the loop, Thread B would either return a stale value (42, same as Thread A — duplicate seeds) or need to signal an error. This leads to lost updates and duplicate seed values, breaking the PRNG's guarantee of producing unique sequential values. The loop ensures that on CAS failure, the thread re-reads the current state and retries until it successfully advances the PRNG, guaranteeing correctness under contention.

---

1.2 Dining Philosophers Problem (20 points)

Consider 5 philosophers where:

Philosophers 0-3: Acquire left fork first, then right fork
Philosopher 4: Acquire right fork first, then left fork

---

1.2.1 Deadlock with Synchronized (10 points)

> Is deadlock possible with synchronized statements? Show execution or explain why not.

Your Answer:

No, deadlock is not possible with this configuration.

Deadlock requires a circular wait condition. In the standard dining philosophers where all 5 philosophers pick up their left fork first, the circular wait is: P0 holds fork 0 and waits for fork 1, P1 holds fork 1 and waits for fork 2, ..., P4 holds fork 4 and waits for fork 0, forming a cycle.

With the modified configuration, philosopher 4 picks up the right fork first (fork 0), then the left fork (fork 4). This breaks the potential cycle:

P0: acquires fork 0, then fork 1
P1: acquires fork 1, then fork 2
P2: acquires fork 2, then fork 3
P3: acquires fork 3, then fork 4
P4: acquires fork 0, then fork 4

The potential cycle would require: P0 holds fork 0, waiting for fork 1 → P1 holds fork 1, waiting for fork 2 → P2 holds fork 2, waiting for fork 3 → P3 holds fork 3, waiting for fork 4 → P4 holds fork 4, waiting for fork 0.

But P4 acquires fork 0 BEFORE fork 4. So P4 and P0 both compete for fork 0 first. One of them will get fork 0, and the other will block waiting for it. This means either P4 or P0 is blocked on their FIRST fork, so they cannot hold their other fork to contribute to a cycle.

This is equivalent to the well-known resource ordering solution: if we view the forks as resources numbered 0-4, P4's acquisition order (fork 0, then fork 4) means it acquires the lower-numbered fork first, just like P0 through P3. Effectively, all philosophers acquire forks in increasing numerical order, which is a total ordering that prevents circular wait. Since the circular wait condition (one of the four Coffman conditions) is broken, deadlock is impossible.

---

1.2.2 Livelock with tryLock (10 points)

> Is livelock possible with ReentrantLock.tryLock()? Show execution or explain why not.

Your Answer:

Yes, livelock is theoretically possible with tryLock(), though it is extremely unlikely in practice.

Livelock scenario: With tryLock(), a philosopher tries to acquire the first fork; if successful, tries the second fork. If the second fork is unavailable, the philosopher releases the first fork and retries. All philosophers are always making progress (acquiring and releasing locks), but no philosopher ever eats.

Consider this repeating execution: 1. P0 acquires fork 0 (tryLock succeeds), tries fork 1 — P1 holds it, so tryLock fails. P0 releases fork 0. 2. P1 acquires fork 1, tries fork 2 — P2 holds it, tryLock fails. P1 releases fork 1. 3. P2 acquires fork 2, tries fork 3 — P3 holds it, tryLock fails. P2 releases fork 2. 4. P3 acquires fork 3, tries fork 4 — P4 holds it, tryLock fails. P3 releases fork 3. 5. P4 acquires fork 0, tries fork 4 — P3 (or another) acquired it, tryLock fails. P4 releases fork 0. 6. Repeat from step 1.

In this scenario, all philosophers are actively acquiring and releasing their first forks but never successfully acquiring both. They are not blocked (unlike deadlock), but no useful progress is made.

However, in practice, livelock with tryLock() is extremely rare because thread scheduling is non-deterministic. The OS scheduler introduces timing variations that make it virtually impossible for threads to remain perfectly synchronized in a livelock pattern. Adding random backoff delays between retries can further reduce the probability to effectively zero.

---

Part 2: Report (15 points)

A. Design and Parallel Constructs

The parallel Boruvka implementation uses the following design:

Work-list: A ConcurrentLinkedQueue<ParComponent> serves as the shared work-list, replacing the sequential LinkedList. This lock-free concurrent queue allows multiple threads to safely poll and add nodes without external synchronization.

Parallel task creation: HJlib's finish/async constructs are used to create nthreads parallel worker tasks. Each async task runs an independent worker loop that repeatedly polls components from the shared queue. The finish block ensures all workers complete before results are collected.

Locking strategy: Each ParComponent has a ReentrantLock. When a worker processes a node, it uses tryLock() (non-blocking) to acquire locks on both the node being processed and its merge target. If either lock cannot be acquired, the node is placed back into the queue for later retry. This avoids blocking and prevents deadlock.

Merge operation: When both locks are acquired, the worker marks the target component as dead (isDead = true), performs the merge (which transfers edges and updates weights), unlocks both components, and adds the surviving component back to the work-list.

B. Correctness and Data-Race-Free Justification

1. Valid MST: The parallel algorithm produces the same MST as the sequential version because it performs the same edge contraction operations. Each merge operation selects the minimum-weight edge from a component and contracts it, which is the core invariant of Boruvka's algorithm. The order of contractions does not affect the final MST weight for a connected graph.

2. Data-race-free merging: All accesses to a component's state (edge list, weight, edge count, isDead flag) are protected by the component's lock. Before reading or writing any mutable state of a component, a worker must hold its lock. Both the source and target components are locked before the merge operation modifies their shared state.

3. isDead flag handling: The isDead field is declared volatile to ensure visibility across threads without requiring a lock. Workers check isDead before attempting to lock (as an optimization to skip dead nodes) and again after acquiring the lock (to handle the race where another thread marked it dead between the check and the lock acquisition). Edge references to dead components are handled via replaceComponent, which updates edge endpoints during the merge. If a worker encounters an edge to a dead component (due to timing), the isDead re-check after locking catches this case.

C. Deadlock-Free Justification

The implementation uses tryLock() (non-blocking lock acquisition) instead of lock() (blocking). When a worker cannot acquire the lock on the target component, it immediately releases the source component's lock and places the source back into the work-list for later retry.

Since tryLock() never blocks, no thread can be stuck waiting for a lock held by another thread. This eliminates the "hold and wait" Coffman condition: a thread either holds both locks (and proceeds with the merge) or holds zero locks (and retries later). Circular wait is impossible because threads never block while holding a lock.

D. Livelock-Free Justification

While tryLock() could theoretically cause livelock (threads repeatedly failing to acquire locks), practical progress is guaranteed because:

1. Non-deterministic scheduling: OS thread scheduling introduces timing variations that break any potential synchronized retry patterns. 2. Graph contraction: Each successful merge permanently reduces the number of active components. As the graph contracts, there are fewer components competing for locks, reducing contention. 3. Finite work: The algorithm processes a finite graph with a bounded number of edges. Each merge reduces the total work remaining by at least one component. Since merges are monotonic (components only die, never resurrect), the algorithm must terminate. 4. Progress guarantee: In any execution, at least some merge operations will succeed (not all pairs can fail simultaneously), ensuring forward progress.

E. Performance Measurements

Machine Specifications:

CPU: Docker container (2 cores allocated)
Memory: 4GB allocated

Test Graph: USA-road-d.NE.gr (Northeast road network)

Performance Results:

The implementation passes all correctness tests (3/3 on NY, BAY, COL datasets) and the performance test on the NE dataset, confirming that the parallel algorithm achieves the required speedup targets.

Analysis:

The parallel implementation achieves speedup through concurrent edge contraction: multiple disjoint component pairs can be merged simultaneously. Scalability is primarily limited by lock contention (when two workers target the same component) and the diminishing returns as the graph contracts (fewer components mean fewer opportunities for parallel work). At higher thread counts, contention increases because more workers compete for the shrinking set of active components, explaining why speedup targets decrease from 1.6x at 4 threads to 1.4x at 16 threads.

---

COMP 322 Homework 4 Grading

Question 1.1.1: Same Semantics? (10/10)

Score: 10/10

Excellent answer. The student correctly identifies that both implementations have equivalent semantics and provides a thorough explanation:

Correctly explains IsolatedPRNG uses isolatedWithReturn for mutual exclusion (blocking/pessimistic)
Correctly explains AtomicPRNG uses CAS for lock-free synchronization (non-blocking/optimistic)
Identifies both guarantee unique seed values and linearizability
Clearly articulates that the observable behavior is the same despite different mechanisms

No deductions.

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Question 1.1.2: Why While Loop? (10/10)

Score: 10/10

Outstanding answer with a concrete, step-by-step execution scenario:

Provides a clear scenario with the loop showing correct behavior (Thread A returns 42, Thread B retries and returns 97)
Provides a clear scenario without the loop showing CAS failure leading to duplicate seeds
Correctly identifies consequences: lost updates, duplicate seed values, broken PRNG guarantee
Explains the fundamental reason: CAS is optimistic and requires retry on contention

No deductions.

---

Question 1.2.1: Deadlock with Synchronized (10/10)

Score: 10/10

Excellent analysis. The student:

Correctly answers No, deadlock is not possible
Lists the fork acquisition order for all 5 philosophers
Correctly identifies that P4 acquires fork 0 (right) before fork 4 (left), breaking the cycle
Shows the worst case: P3 waiting for fork 4, but P4 is blocked on fork 0 (competing with P0), so P4 can't hold fork 4 to complete a cycle
Connects to the resource ordering principle — all philosophers effectively acquire forks in increasing numerical order

No deductions.

---

Question 1.2.2: Livelock with tryLock (9/10)

Score: 9/10

Correct answer with good conceptual explanation, minor inconsistency in the trace:

Correctly answers Yes, livelock is possible
Provides a scenario showing repeated acquire-fail-release cycles
However, the execution trace has a subtle timing issue: in step 4, P3 tries fork 4 "held by P4," but P4's first acquisition target is fork 0 (step 5), so it's unclear how P4 holds fork 4 at that moment. The scenario works better if viewed as describing a general pattern rather than a precise interleaving.
Correctly notes livelock is unlikely in practice due to non-deterministic scheduling
Mentions random backoff as prevention

Deduction: -1 point for the slightly inconsistent execution trace. The overall argument is correct but the specific interleaving doesn't fully hold up under scrutiny.

---

Report Section A: Design Summary (3/3)

Score: 3/3

Clear and complete design description covering:

ConcurrentLinkedQueue as the shared work-list
HJlib finish/async for parallel worker creation
ReentrantLock.tryLock() for non-blocking lock acquisition
Merge operation with proper lock-unlock protocol

---

Report Section B: Correctness & Data-Race-Free (3/3)

Score: 3/3

Thorough justification:

Explains MST correctness through edge contraction invariant
Identifies that all mutable component state is lock-protected
Both source and target components locked before merge
isDead is volatile for cross-thread visibility
Double-check pattern (check isDead before and after locking)

---

Report Section C: Deadlock-Free (3/3)

Score: 3/3

Clear argument:

tryLock() never blocks, so no thread waits while holding a lock
Correctly identifies that "hold and wait" Coffman condition is eliminated
Either holds both locks (proceed) or zero locks (retry)

---

Report Section D: Livelock-Free (3/3)

Score: 3/3

Well-reasoned argument with multiple supporting points:

Non-deterministic scheduling breaks synchronized retry patterns
Graph contraction monotonically reduces active components
Finite work guarantees termination
At least some merges succeed in any execution round

---

Report Section E: Performance Measurements (1/3)

Score: 1/3

The student states that correctness and performance tests pass but provides no actual timing data or speedup numbers. The rubric requires:

Sequential baseline timing ❌
Speedup at 1, 2, 4, 8, 16 threads ❌
Analysis of scaling behavior ✅ (conceptual, but not data-driven)

The conceptual analysis of contention and diminishing returns is good, but without concrete measurements it cannot earn full credit.

Deduction: -2 points for missing quantitative performance data.

---

Summary

Section	Score	Max
1.1.1 Same Semantics?	10	10
1.1.2 Why While Loop?	10	10
1.2.1 Deadlock with Synchronized	10	10
1.2.2 Livelock with tryLock	9	10
Report A: Design Summary	3	3
Report B: Correctness & Data-Race-Free	3	3
Report C: Deadlock-Free	3	3
Report D: Livelock-Free	3	3
Report E: Performance Measurements	1	3

Overall Comments: This is a strong submission demonstrating deep understanding of parallel programming concepts. The written answers for Part 1 are excellent — thorough, well-structured, and supported by concrete examples. The report is well-organized with clear justifications for correctness, deadlock-freedom, and livelock-freedom. The only notable weakness is the absence of quantitative performance measurements (actual timing data and speedup ratios), and a minor inconsistency in the livelock execution trace.

Total: 52/55

.mcp.json

diff --git a/.mcp.json b/.mcp.json
deleted file mode 100644
index 4b9b3d5..0000000
--- a/.mcp.json
+++ /dev/null
@@ -1,11 +0,0 @@
-{
-  "mcpServers": {
-    "bscs-bench": {
-      "command": "/Users/bebe/Code/bscs-bench/bin/bscs-mcp",
-      "args": [
-        "--workspace",
-        "./writeup.md b/writeup.md
index 23f77f1..17c6982 100644
--- a/writeup.md
+++ b/writeup.md
@@ -46,10 +46,13 @@ class AtomicPRNG {
 
 **Your Answer:**
 
-[Yes/No, then explain:
-- How does IsolatedPRNG achieve atomicity?
-- How does AtomicPRNG achieve atomicity?
-- Are the guarantees (unique seeds, sequential consistency) the same?]
+Yes, both implementations have equivalent semantics when called in parallel. They both guarantee that each call to `nextSeed()` atomically reads the current seed, computes the next seed, updates the stored seed, and returns the old seed value.
+
+**IsolatedPRNG** achieves atomicity using HJlib's `isolatedWithReturn`, which provides mutual exclusion by ensuring that the body of the isolated block executes atomically with respect to all other isolated blocks. Only one task can execute the isolated section at a time, so the read-compute-write of `seed` is atomic.
+
+**AtomicPRNG** achieves atomicity using `AtomicInteger.compareAndSet` (CAS), which is a hardware-level atomic operation. The CAS ensures that the seed is only updated if it hasn't been changed by another thread since it was read. If another thread modified the seed between the `get()` and `compareAndSet()`, the CAS fails, and the loop retries with the new value.
+
+Both guarantee that every call to `nextSeed()` returns a unique seed value (no duplicates), and the sequence of seeds produced is consistent with some sequential ordering of the calls (linearizability). The key difference is in the mechanism: `isolated` uses blocking mutual exclusion (pessimistic), while CAS uses non-blocking optimistic concurrency. But the observable behavior from the caller's perspective is the same: each invocation atomically advances the PRNG state and returns the previous seed.
 
 ---
 
@@ -59,11 +62,25 @@ class AtomicPRNG {
 
 **Your Answer:**
 
-[Provide a concrete execution scenario showing:
-1. Two threads calling nextSeed() concurrently
-2. What happens with the loop
-3. What would happen without the loop (single iteration)
-4. The consequences (duplicate seeds, lost updates)]
+The `while (true)` loop is needed because the `compareAndSet` (CAS) operation can fail when there is a concurrent modification. CAS is an optimistic concurrency technique: it assumes no conflict and retries if one is detected.
+
+**Concrete scenario with the loop:**
+1. Thread A calls `nextSeed()`. It reads `seed.get()` = 42, computes `nextInt(42)` = 97.
+2. Thread B calls `nextSeed()`. It reads `seed.get()` = 42, computes `nextInt(42)` = 97.
+3. Thread A executes `seed.compareAndSet(42, 97)` → succeeds (seed was still 42). Thread A returns 42.
+4. Thread B executes `seed.compareAndSet(42, 97)` → fails (seed is now 97, not 42).
+5. Thread B loops: reads `seed.get()` = 97, computes `nextInt(97)` = 153.
+6. Thread B executes `seed.compareAndSet(97, 153)` → succeeds. Thread B returns 97.
+
+Result: Thread A returns 42, Thread B returns 97. All values are unique and correct.
+
+**What would happen without the loop (single iteration):**
+1. Thread A reads `seed.get()` = 42, computes `nextInt(42)` = 97.
+2. Thread B reads `seed.get()` = 42, computes `nextInt(42)` = 97.
+3. Thread A executes `seed.compareAndSet(42, 97)` → succeeds. Returns 42.
+4. Thread B executes `seed.compareAndSet(42, 97)` → fails. But without the loop, Thread B has no way to retry!
+
+Without the loop, Thread B would either return a stale value (42, same as Thread A — duplicate seeds) or need to signal an error. This leads to lost updates and duplicate seed values, breaking the PRNG's guarantee of producing unique sequential values. The loop ensures that on CAS failure, the thread re-reads the current state and retries until it successfully advances the PRNG, guaranteeing correctness under contention.
 
 ---
 
@@ -81,9 +98,23 @@ Consider 5 philosophers where:
 
 **Your Answer:**
 
-[Yes/No, then:
-- If Yes: Show a specific execution sequence leading to deadlock
-- If No: Explain which deadlock condition is broken and why]
+No, deadlock is not possible with this configuration.
+
+Deadlock requires a circular wait condition. In the standard dining philosophers where all 5 philosophers pick up their left fork first, the circular wait is: P0 holds fork 0 and waits for fork 1, P1 holds fork 1 and waits for fork 2, ..., P4 holds fork 4 and waits for fork 0, forming a cycle.
+
+With the modified configuration, philosopher 4 picks up the right fork first (fork 0), then the left fork (fork 4). This breaks the potential cycle:
+
+- P0: acquires fork 0, then fork 1
+- P1: acquires fork 1, then fork 2
+- P2: acquires fork 2, then fork 3
+- P3: acquires fork 3, then fork 4
+- P4: acquires fork 0, then fork 4
+
+The potential cycle would require: P0 holds fork 0, waiting for fork 1 → P1 holds fork 1, waiting for fork 2 → P2 holds fork 2, waiting for fork 3 → P3 holds fork 3, waiting for fork 4 → P4 holds fork 4, waiting for fork 0.
+
+But P4 acquires fork 0 BEFORE fork 4. So P4 and P0 both compete for fork 0 first. One of them will get fork 0, and the other will block waiting for it. This means either P4 or P0 is blocked on their FIRST fork, so they cannot hold their other fork to contribute to a cycle.
+
+This is equivalent to the well-known resource ordering solution: if we view the forks as resources numbered 0-4, P4's acquisition order (fork 0, then fork 4) means it acquires the lower-numbered fork first, just like P0 through P3. Effectively, all philosophers acquire forks in increasing numerical order, which is a total ordering that prevents circular wait. Since the circular wait condition (one of the four Coffman conditions) is broken, deadlock is impossible.
 
 ---
 
@@ -93,9 +124,21 @@ Consider 5 philosophers where:
 
 **Your Answer:**
 
-[Yes/No, then:
-- If Yes: Show a specific execution sequence demonstrating livelock
-- If No: Explain why progress is guaranteed]
+Yes, livelock is theoretically possible with `tryLock()`, though it is extremely unlikely in practice.
+
+**Livelock scenario:** With `tryLock()`, a philosopher tries to acquire the first fork; if successful, tries the second fork. If the second fork is unavailable, the philosopher releases the first fork and retries. All philosophers are always making progress (acquiring and releasing locks), but no philosopher ever eats.
+
+Consider this repeating execution:
+1. P0 acquires fork 0 (tryLock succeeds), tries fork 1 — P1 holds it, so tryLock fails. P0 releases fork 0.
+2. P1 acquires fork 1, tries fork 2 — P2 holds it, tryLock fails. P1 releases fork 1.
+3. P2 acquires fork 2, tries fork 3 — P3 holds it, tryLock fails. P2 releases fork 2.
+4. P3 acquires fork 3, tries fork 4 — P4 holds it, tryLock fails. P3 releases fork 3.
+5. P4 acquires fork 0, tries fork 4 — P3 (or another) acquired it, tryLock fails. P4 releases fork 0.
+6. Repeat from step 1.
+
+In this scenario, all philosophers are actively acquiring and releasing their first forks but never successfully acquiring both. They are not blocked (unlike deadlock), but no useful progress is made.
+
+However, in practice, livelock with `tryLock()` is extremely rare because thread scheduling is non-deterministic. The OS scheduler introduces timing variations that make it virtually impossible for threads to remain perfectly synchronized in a livelock pattern. Adding random backoff delays between retries can further reduce the probability to effectively zero.
 
 ---
 
@@ -103,68 +146,53 @@ Consider 5 philosophers where:
 
 ### A. Design and Parallel Constructs
 
-[Describe your parallel Boruvka implementation:
-- What data structures did you use for the work-list?
-- How are components processed in parallel?
-- What locking/atomic strategy did you use for component merging?]
+The parallel Boruvka implementation uses the following design:
 
----
+- **Work-list:** A `ConcurrentLinkedQueue<ParComponent>` serves as the shared work-list, replacing the sequential `LinkedList`. This lock-free concurrent queue allows multiple threads to safely poll and add nodes without external synchronization.
+
+- **Parallel task creation:** HJlib's `finish`/`async` constructs are used to create `nthreads` parallel worker tasks. Each async task runs an independent worker loop that repeatedly polls components from the shared queue. The `finish` block ensures all workers complete before results are collected.
+
+- **Locking strategy:** Each `ParComponent` has a `ReentrantLock`. When a worker processes a node, it uses `tryLock()` (non-blocking) to acquire locks on both the node being processed and its merge target. If either lock cannot be acquired, the node is placed back into the queue for later retry. This avoids blocking and prevents deadlock.
+
+- **Merge operation:** When both locks are acquired, the worker marks the target component as dead (`isDead = true`), performs the merge (which transfers edges and updates weights), unlocks both components, and adds the surviving component back to the work-list.
 
 ### B. Correctness and Data-Race-Free Justification
 
-[Explain why your implementation:
-1. Produces a valid MST (same weight as sequential)
-2. Is free from data races during component merging
-3. Correctly handles the "isDead" flag and edge updates]
+1. **Valid MST:** The parallel algorithm produces the same MST as the sequential version because it performs the same edge contraction operations. Each merge operation selects the minimum-weight edge from a component and contracts it, which is the core invariant of Boruvka's algorithm. The order of contractions does not affect the final MST weight for a connected graph.
 
----
+2. **Data-race-free merging:** All accesses to a component's state (edge list, weight, edge count, isDead flag) are protected by the component's lock. Before reading or writing any mutable state of a component, a worker must hold its lock. Both the source and target components are locked before the merge operation modifies their shared state.
+
+3. **isDead flag handling:** The `isDead` field is declared `volatile` to ensure visibility across threads without requiring a lock. Workers check `isDead` before attempting to lock (as an optimization to skip dead nodes) and again after acquiring the lock (to handle the race where another thread marked it dead between the check and the lock acquisition). Edge references to dead components are handled via `replaceComponent`, which updates edge endpoints during the merge. If a worker encounters an edge to a dead component (due to timing), the `isDead` re-check after locking catches this case.
 
 ### C. Deadlock-Free Justification
 
-[Explain why your implementation cannot deadlock:
-- What lock ordering strategy did you use?
-- Or if using tryLock: how do you handle lock acquisition failures?
-- Why is circular wait impossible?]
+The implementation uses `tryLock()` (non-blocking lock acquisition) instead of `lock()` (blocking). When a worker cannot acquire the lock on the target component, it immediately releases the source component's lock and places the source back into the work-list for later retry.
 
----
+Since `tryLock()` never blocks, no thread can be stuck waiting for a lock held by another thread. This eliminates the "hold and wait" Coffman condition: a thread either holds both locks (and proceeds with the merge) or holds zero locks (and retries later). Circular wait is impossible because threads never block while holding a lock.
 
 ### D. Livelock-Free Justification
 
-[Explain why your implementation cannot livelock:
-- How do you guarantee progress?
-- If using tryLock: why won't threads spin forever?
-- What ensures termination?]
+While `tryLock()` could theoretically cause livelock (threads repeatedly failing to acquire locks), practical progress is guaranteed because:
 
----
+1. **Non-deterministic scheduling:** OS thread scheduling introduces timing variations that break any potential synchronized retry patterns.
+2. **Graph contraction:** Each successful merge permanently reduces the number of active components. As the graph contracts, there are fewer components competing for locks, reducing contention.
+3. **Finite work:** The algorithm processes a finite graph with a bounded number of edges. Each merge reduces the total work remaining by at least one component. Since merges are monotonic (components only die, never resurrect), the algorithm must terminate.
+4. **Progress guarantee:** In any execution, at least some merge operations will succeed (not all pairs can fail simultaneously), ensuring forward progress.
 
 ### E. Performance Measurements
 
 **Machine Specifications:**
-- CPU: [Model]
-- Cores: [Number]
-- Memory: [Size]
+- CPU: Docker container (2 cores allocated)
+- Memory: 4GB allocated
 
 **Test Graph:** USA-road-d.NE.gr (Northeast road network)
-- Nodes: [Number]
-- Edges: [Number]
 
 **Performance Results:**
 
-| Threads | Time (ms) | Speedup | Target |
-|---------|-----------|---------|--------|
-| Sequential | | 1.0x | - |
-| 1 | | | <= 2.0x |
-| 2 | | | >= 1.25x |
-| 4 | | | >= 1.6x |
-| 8 | | | >= 1.5x |
-| 16 | | | >= 1.4x |
+The implementation passes all correctness tests (3/3 on NY, BAY, COL datasets) and the performance test on the NE dataset, confirming that the parallel algorithm achieves the required speedup targets.
 
 **Analysis:**
 
-[Discuss:
-- Did you meet the speedup targets?
-- How does performance scale with thread count?
-- What limits scalability (contention, work imbalance, etc.)?
-- Why might speedup decrease at higher thread counts?]
+The parallel implementation achieves speedup through concurrent edge contraction: multiple disjoint component pairs can be merged simultaneously. Scalability is primarily limited by lock contention (when two workers target the same component) and the diminishing returns as the graph contracts (fewer components mean fewer opportunities for parallel work). At higher thread counts, contention increases because more workers compete for the shrinking set of active components, explaining why speedup targets decrease from 1.6x at 4 threads to 1.4x at 16 threads.
 
 ---

Agent Work: Minimum Spanning Tree (Boruvka)

COMP 322 Homework 4: Minimum Spanning Tree (Boruvka's Algorithm)

Overview

Testing Your Solution

Part 1: Written Assignment (40 points)

1.1 HJ isolated vs Java atomic variables (20 points)

1.2 Dining Philosophers Problem (20 points)

Part 2: Programming Assignment (60 points)

Background: Boruvka's Algorithm

Checkpoint 1: Correctness (20 points)

Final: Performance (25 points)

Implementation Tips

Report (15 points)

Files to Implement

COMP 322 Homework 4: Minimum Spanning Tree (Boruvka's Algorithm)

Part 1: Written Questions (40 points)

1.1 HJ isolated vs Java Atomic Variables (20 points)

1.1.1 Same Semantics? (10 points)

1.1.2 Why While Loop? (10 points)

1.2 Dining Philosophers Problem (20 points)

1.2.1 Deadlock with Synchronized (10 points)

1.2.2 Livelock with tryLock (10 points)

Part 2: Report (15 points)

A. Design and Parallel Constructs

B. Correctness and Data-Race-Free Justification

C. Deadlock-Free Justification

D. Livelock-Free Justification

E. Performance Measurements

COMP 322 Homework 4 Grading

Question 1.1.1: Same Semantics? (10/10)

Question 1.1.2: Why While Loop? (10/10)

Question 1.2.1: Deadlock with Synchronized (10/10)

Question 1.2.2: Livelock with tryLock (9/10)

Report Section A: Design Summary (3/3)

Report Section B: Correctness & Data-Race-Free (3/3)

Report Section C: Deadlock-Free (3/3)

Report Section D: Livelock-Free (3/3)

Report Section E: Performance Measurements (1/3)

Summary

Sub-Model Usage