Perfect Matching Preservers

Perfect Matching Preservers

For two bipartite graphs G and G , a bijection ψ : E(G) → E(G) is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if ψ(M) is a perfect matching in G. We characterize bipartite graphs G and G which are related by a matching preserver and the matching preservers between them.

Perfect Matching Disclosure Attacks

Traffic analysis is the best known approach to uncover relationships amongst users of anonymous communication systems, such as mix networks. Surprisingly, all previously published techniques require very specific user behavior to break the anonymity provided by mixes. At the same time, it is also well known that none of the considered user models reflects realistic behavior which casts some dou...

Srikumar 1 Perfect Matching and Matching Polytopes

Csc5160: Combinatorial Optimization and Approximation Algorithms Topic: Perfect Matching Polytope 12.1 Formulation of General Perfect Matching

In this lecture, the focus is on general perfect matching problem where the goal is to prove that it can be solved in polynomial time by linear programming. Based on the LP formulation for bipartite matching studied in Lecture 10, we add some valid inequalities to establish a new formulation. Then we prove that for general perfect matching, all vertex solutions of the linear program are integra...

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...