Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-5

Date: Latest Version

Matching in Dynamic Graphs

  • Surender BaswanaAffiliated withDepartment of Computer Science and Engineering, IIT Kanpur Email author 
  • , Manoj GuptaAffiliated withIIT Delhi
  • , Sandeep SenAffiliated withIIT Delhi

Keywords

Matching Maximum matching Maximal matching Dynamic graph Randomized algorithms

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 ...

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