On the Bipartite Unique Perfect Matching Problem
نویسندگان
چکیده
In this note, we give tighter bounds on the complexity of the bipartite unique perfect matching problem, bipartite-UPM. We show that the problem is in C=L and in NL , both subclasses of NC. We also consider the (unary) weighted version of the problem. We show that testing uniqueness of the minimum-weight perfect matching problem for bipartite graphs is in L= and in NL. Furthermore, we show that bipartite-UPM is hard for NL.
منابع مشابه
On the inverse maximum perfect matching problem under the bottleneck-type Hamming distance
Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...
متن کاملPerfect Bipartite Matching in Pseudo-Deterministic RNC
In this paper we present a pseudo-deterministic RNC algorithm for finding perfect matchings in bipartite graphs. Specifically, our algorithm is a randomized parallel algorithm which uses poly(n) processors, poly(log n) depth, poly(log n) random bits, and outputs for each bipartite input graph a unique perfect matching with high probability. That is, it returns the same matching for almost all r...
متن کاملDerandomizing Isolation Lemma for K3, 3-free and K5-free Bipartite Graphs
The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph, ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs, i.e. we give a d...
متن کاملThe labeled perfect matching in bipartite graphs
In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V,E) with |V | = 2n vertices such that E contains a perfect matching (of size n), together with a color (or label) function L : E → {c1, . . . , cq}, the labeled perfect matching problem consists in finding a perfect matching on G that us...
متن کاملNC Algorithms for Comparability Graphs Interval Graphs and Unique Perfect Matchings
Laszlo Lovasz recently posed the following problem Is there an NC algorithm for testing if a given graph has a unique perfect match ing We present such an algorithm for bipartite graphs We also give NC algorithms for obtaining a transitive orientation of a com parability graph and an interval representation of an interval graph These enable us to obtain an NC algorithm for nding a maximum match...
متن کامل