Erratum to: Greedy Matching: Guarantees and Limitations

Robust Guarantees of Stochastic Greedy Algorithms

In this paper we analyze the robustness of stochastic variants of the greedy algorithm for submodular maximization. Our main result shows that for maximizing a monotone submodular function under a cardinality constraint, iteratively selecting an element whose marginal contribution is approximately maximal in expectation is a sufficient condition to obtain the optimal approximation guarantee wit...

Greedy algorithms for max sat and maximum matching: their power and limitations

Randomized Greedy Matching II

Abstra t We onsider the following randomized algorithm for nding a mat hingM in an arbitrary graph G = (V;E). Repeatedly, hoose a random vertex u, then a random neighbour v of u. Add edge fu; vg to M and delete verti es u; v from G along with any verti es that be ome isolated. Our main result is that there exists a positive onstant su h that the expe ted ratio of the size of the mat hing produ ...

Max-Min Greedy Matching

A bipartite graph G(U, V ;E) that admits a perfect matching is given. One player imposes a permutation π over V , the other player imposes a permutation σ over U . In the greedy matching algorithm, vertices of U arrive in order σ and each vertex is matched to the lowest (under π) yet unmatched neighbor in V (or left unmatched, if all its neighbors are already matched). The obtained matching is ...

Randomized Greedy Matching

We consider a randomized version of the usual greedy algorithm for finding a large matching in a graph. We assume that the next edge is randomly chosen from those remaining at any stage. We analyse the expected performance of this algorithm when the input graph is fixed. We show that there are graphs for which this Randomized Greedy Algorithm (RGA) usually only obtains a matching close in size ...