A $(2 - c \frac{\log {n}}{n})$ Approximation Algorithm for the Minimum Maximal Matching Problem

An approximation algorithm dependent on edge-coloring number for minimum maximal matching problem

“…For any simple graph, it was unknown whether there exists a non-trivial approximation algorithm whose approximation ratio is less than 2. Recently, Z. Gotthilf, M. Lewenstein, and E. Rainshmidt [5] presented a (2 − c log |V | |V | )-approximation algorithm, where c is an arbitrary constant. This algorithm is based on the local search technique.…”

“…Recently, Z. Gotthilf et al (2008) where c is an arbitrary constant.In this paper, we present a (2 − 1 χ (G) )-approximation algorithm based on an LP relaxation, where χ (G) is the edge-coloring number of G. Our algorithm is the first non-trivial approximation algorithm whose approximation ratio is independent of |V |. Moreover, it is known that the minimum maximal matching problem is equivalent to the edge dominating set problem.…”

“…Recently, Z. Gotthilf et al (2008) [5] presented a (2 − c log |V | |V | )-approximation algorithm, where c is an arbitrary constant.…”

Decomposition algorithms for solving the minimum weight maximal matching problem

“…Note that (15) simplifies to y j ≥ 1 for each vertex i having N(i) = {j}, which is equivalent to (16) as y-variables are binary.…”

“…Examples include trees [24], block graphs [18], series-parallel graphs [26], bipartite permutation graphs, and co-triangulated graphs [29]. Various approximation algorithms for MMM and MWMM have been proposed in the literature (see for instance [4,9,13,14,16,23,28]). Another line of research on MMM and MWMM considers the development of exponential time exact combinatorial algorithms [12,32].…”