Cse525: Randomized Algorithms and Probabilistic Analysis Lecture 8 1.1 Ranking Algorithm

1 Online bipartite matching Recall from last time we introduced the online bipartite matching problem and gave an algorithm to solve a fractional version of the problem with competitive ratio 1− 1/e. In the online bipartite matching problem, we are given a bipartite graph G = (L,R,E), where the vertices in R are revealed to us one at a time along with the edges from that vertex to L. Once each vertex in R is revealed, we must immediately select an edge to that vertex to be a part of a matching M or permanently discard all the revealed edges, with the goal of maximizing the size of M . The fractional version of the problem is obtained by taking the linear relaxation of the integer program that corresponds to this problem.