Matching in Dynamic Graphs

Years and Authors of Summarized Original Work

• 2011; Baswana, Gupta, Sen

Problem Definition

Let G = (V, E) be an undirected graph on n = | V | vertices and m = | E | edges. A matching in G is a set of edges $\mathcal{M}\subseteq E$ such that no two edges in $\mathcal{M}$ share any vertex. Matching has been one of the most well-studied problems in algorithmic graph theory for decades [4]. A matching $\mathcal{M}$ is called maximum matching if the number of edges in $\mathcal{M}$ is maximum. The fastest known algorithm for maximum matching, due to Micali and Vazirani [5], runs in $O(m\sqrt{n})$. A matching is said to be maximal if it is not strictly contained in any other matching. It is well known that a maximal matching achieves a factor 2 approximation of the maximum matching.

Key Result

We address the problem of maintaining maximal matching in a fully dynamic environment – allowing updates in the form of both insertion and deletion of edges. Ivković and Llyod [3] designed...