/**
* Random walks a chain from altruistic Vertex alt, sampling hops based on our weighting scheme.
*
* @param alt Starting altruist for the chain
* @param matchedVerts Set of off-limits vertices for this chain
* @param maxChainSize Chain cap (will sample a chain <= maxChainSize)
* @param usingFailureProbabilities True if the chain's weight should be discounted, false if raw
* @return A chain starting at alt of size <= maxChainSize that random walks from alt through the
* legal remaining vertices in the pool, sampling neighbors inversely proportional to the
* number of cycles containing those neighbors. Weight is discounted
* (usingFailureProbabilities=True) or raw (=False)
*/
protected Cycle sampleAChain(
Vertex alt, Set<Vertex> matchedVerts, int maxChainSize, boolean usingFailureProbabilities) {
if (null == alt) {
throw new IllegalArgumentException("Altruist cannot be null.");
}
if (null == matchedVerts) {
throw new IllegalArgumentException("Set of matched vertices cannot be null.");
}
if (maxChainSize < 2) {
throw new IllegalArgumentException(
"Cannot sample chains if maxChainSize<2 (maxChainSize=" + maxChainSize);
}
if (pool.outgoingEdgesOf(alt).size() < 1) {
throw new IllegalArgumentException(
"Altruist " + alt + " has no outgoing edges. Cannot call sampleAChain.");
}
// Accumulate our chain's edges
Deque<Edge> path = new ArrayDeque<Edge>();
Set<Vertex> inPath = new HashSet<Vertex>();
double pathSuccProb = 1.0;
double discountedPathWeight = 0.0;
double rawPathWeight = 0.0;
Vertex currentV = alt;
do {
// Want to choose next hop inversely proportional to #cycles/chains containing it
WeightedRandomSample<Edge> neighborSet = new WeightedRandomSample<Edge>();
for (Edge edge : pool.outgoingEdgesOf(currentV)) {
Vertex candidateV = pool.getEdgeTarget(edge);
// If this neighbor has already been matched (or is in our chain), skip
if (matchedVerts.contains(candidateV) || inPath.contains(candidateV)) {
continue;
}
// If this neighbor is an altruist who isn't the starting altruist, skip
if (candidateV.isAltruist() && !candidateV.equals(alt)) {
continue;
}
// Never want to sample vertices that are not in any cycles (no chance of matching)
double cycleCount = membership.getMembershipSet(candidateV).size();
if (cycleCount == 0) {
continue;
}
// Not worrying about overflow for now, since we won't be using this on big |cycle| counts
double weight = (double) cycles.size() / cycleCount;
neighborSet.add(weight, edge);
}
// Get our next hop in the chain, based on the weights computed above
Edge nextE = null;
if (path.size() >= maxChainSize - 1 || neighborSet.size() < 1) {
// If we're at the last step of the chain due to a chain cap, or if no vertices
// are both neighbors of this vertex AND unmatched, then try to hop back to the
// starting altruist
nextE = pool.getEdge(currentV, alt);
if (null == nextE) {
return null;
// throw new RuntimeException("Starting with altruist " + alt + ", found a vertex that did
// not connect (dummy edge or otherwise) back to the altruist.\n" +
// "Vertex: " + currentV + ", neighbors: " + pool.outgoingEdgesOf(currentV));
}
} else {
nextE = neighborSet.sampleWithoutReplacement();
}
path.push(nextE);
Vertex nextV = pool.getEdgeTarget(nextE);
inPath.add(nextV);
// If we're ending the chain, make a formal Cycle and return
if (nextV.isAltruist() && nextV.equals(alt)) {
// Add the discounted weight from this chain executing in its entirety
discountedPathWeight +=
((1.0 - nextE.getFailureProbability()) * pathSuccProb * rawPathWeight);
break;
} else {
// Add discounted utility of chain goings to EXACTLY this edge and then failing (so \sum
// weights * \prod success * (1-failure of this edge))
discountedPathWeight += (rawPathWeight * pathSuccProb * nextE.getFailureProbability());
// Probability of chain executing to very end (and maybe continuing)
pathSuccProb *= (1.0 - nextE.getFailureProbability());
// We assume the chain gets this far, add edge to raw weight
rawPathWeight += pool.getEdgeWeight(nextE);
// We've hopped!
currentV = nextV;
}
} while (true);
// Construct a formal Cycle from the sampled path, and weight it accordingly
if (!usingFailureProbabilities) {
return Cycle.makeCycle(path, rawPathWeight);
} else {
return Cycle.makeCycle(path, discountedPathWeight);
}
}
