In the matching problem, each node maintains a pointer to one of its neighbor or to null, and a maximal matching is computed when each node points either to a neighbor that itself points to it (they are then called married), or to null, in which case no neighbor can also point to null. This paper presents a self-stabilizing distributed algorithm to compute a maximal matching in the link-registe...

In the matching problem, each node maintains a pointer to one of its neighbor or to null, and a maximal matching is computed when each node points either to a neighbor that itself points to it (they are then called married), or to null, in which case no neighbor can also point to null. This paper presents a self-stabilizing distributed algorithm to compute a maximal matching in the link-registe...

We consider two models of computation: local centralized algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design improved local centralized algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum matching over bounded degree grap...

iSLIP and parallel hierarchical matching (PHM) are distributed maximal size matching schedulers for input-buffered switches. Previous research has analyzed the hardware cost of those schedulers and their performance after a small number of iterations. In this letter, we formulate an upper bound for the number of iterations required by PHM to converge. Then, we compare the number of iterations r...

Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal common subtrees. We then solve the problem using simple payoff-monotonic dynamics from evolutionary game theory. We illustrate the power of the...

Let G = (V, E) be a graph. A set M of edges is called a matching in G if each vertex in G belongs to at most one edge from M , and M is a maximal matching if any edgeset M ′, such that M ⊂ M ′, is not a matching in G. If all maximal matchings in G have the same cardinality then G is an equimatchable graph. In this paper we characterize the equimatchable graphs of girth at least five. As a conse...

An induced matching in a graph is a set of edges whose endpoints induce a 1-regular subgraph. It is known that every n-vertex graph has at most 10 ≈ 1.5849 maximal induced matchings, and this bound is best possible. We prove that every n-vertex triangle-free graph has at most 3 ≈ 1.4423 maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipar...