Quadratic time algorithm for maximum induced matching problem in trapezoid graphs

2019 ◽  
Author(s):  
Viet-Dung Nguyen ◽  
Phan-Thuan Do
Keyword(s):  
Time Algorithm ◽  
Matching Problem ◽  
Induced Matching ◽  
Maximum Induced Matching ◽  
Trapezoid Graphs

scholarly journals Efficient Algorithms for Maximum Induced Matching Problem in Permutation and Trapezoid Graphs

2021 ◽  
Vol 182 (3) ◽  
pp. 257-283
Author(s):  
Viet Dung Nguyen ◽  
Ba Thai Pham ◽  
Phan Thuan Do
Keyword(s):  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Matching Problem ◽  
Induced Matching ◽  
Graph Classes ◽  
Permutation Models ◽  
Maximum Induced Matching ◽  
Sweep Line ◽  
Trapezoid Graphs ◽  
Better Than

We first design an 𝒪(n2) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to 𝒪(m+n). Consequently, we extend this result to give an 𝒪(m+n) algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and 𝒪(n2) time, respectively. Our results are far better than the best known 𝒪(mn) algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.

scholarly journals On the induced matching problem in hamiltonian bipartite graphs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yinglei Song
Keyword(s):  
Bipartite Graph ◽  
Parameterized Complexity ◽  
Bipartite Graphs ◽  
Matching Problem ◽  
Induced Matching ◽  
Subexponential Time ◽  
Maximum Induced Matching

Abstract In this paper, we study the parameterized complexity of the induced matching problem in hamiltonian bipartite graphs and the inapproximability of the maximum induced matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian bipartite graph, the induced matching problem is W[1]-hard and cannot be solved in time n o ⁢ ( k ) {n^{o(\sqrt{k})}} , where n is the number of vertices in the graph, unless the 3SAT problem can be solved in subexponential time. In addition, we show that unless NP = P {\operatorname{NP}=\operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of n 1 / 4 - ϵ {n^{1/4-\epsilon}} , where n is the number of vertices in the graph.

scholarly journals Maximum induced matching problem on hhd-free graphs

2012 ◽  
Vol 160 (3) ◽  
pp. 224-230 ◽  
Author(s):  
Chandra Mohan Krishnamurthy ◽  
R. Sritharan
Keyword(s):  
Matching Problem ◽  
Induced Matching ◽  
Maximum Induced Matching
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