An Improved Approximation Algorithm for the Matching Augmentation Problem
Copyright policy )An Improved Approximation Algorithm for the Matching Augmentation Problem
We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning subgraph (2-ECSS) of minimum cost. A $\frac74$-approximation algorithm for the same problem was presented recently, see Cheriyan, et al., "The matching augmentation problem: a $\frac{7}{4}$-approximation algorithm," {\em Math. Program.}, 182(1):315--354, 2020; arXiv:1810.07816. Our improvement is based on new algorithmic techniques, and some of these may lead to advances on related problems.
30 pages, 6 figures
FOS: Computer and information sciences, Combinatorial optimization, connectivity augmentation, Discrete Mathematics (cs.DM), network design, forest augmentation problem, matching augmentation problem, Graph algorithms (graph-theoretic aspects), Computer Science - Data Structures and Algorithms, Data Structures and Algorithms (cs.DS), approximation algorithms, Connectivity, 68W25, 90C59, 90C27, 68R10, 05C85, 2-edge connected graph, Approximation methods and heuristics in mathematical programming, Approximation algorithms, 004, Graph theory (including graph drawing) in computer science, 2-Edge connected graph, 2-edge covers, Computer Science - Discrete Mathematics, ddc: ddc:004
FOS: Computer and information sciences, Combinatorial optimization, connectivity augmentation, Discrete Mathematics (cs.DM), network design, forest augmentation problem, matching augmentation problem, Graph algorithms (graph-theoretic aspects), Computer Science - Data Structures and Algorithms, Data Structures and Algorithms (cs.DS), approximation algorithms, Connectivity, 68W25, 90C59, 90C27, 68R10, 05C85, 2-edge connected graph, Approximation methods and heuristics in mathematical programming, Approximation algorithms, 004, Graph theory (including graph drawing) in computer science, 2-Edge connected graph, 2-edge covers, Computer Science - Discrete Mathematics, ddc: ddc:004
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