Fast Parallel Matching in Expander Graphs

  title={Fast Parallel Matching in Expander Graphs},
  author={Pierre Kelsen},
Let H be a bipartite graph with bipartition (A, B) where IAI = n and every subset X of A with at most a n elements has at least blXl neighbors (a ~ 1, b > 1). We consider the problem of computing a matching from a given subset X ~ A of size at most a n into l?. By Hall’s theorem such a matchhg doea indeed exist. We propose two algorithms for this problem. The first algorithm is in NC for b ~ d’ for a constant e > O; here d denotes the maximum degree of a vertex in A. The second algorithm uses… CONTINUE READING