Moderately exponential time algorithms for the maximum induced matching problem

Chang, Mau Song; Chen, Li-Hsuan; Hung, Ling-Ju

doi:10.1007/s11590-014-0813-z

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…Hung and Miau also gave an O(1.4786 n ) time algorithm to solve MIM [3] and using polynomial space as well. Chang, Chen and Hung then gave an algorithm running in O * (1.4658 n ) time to solve MIM and later improved it to O * (1.4321 n ) time in the same paper [2]. Furthermore, Xiao and Tan gave first an algorithm running in O * (1.4391 n ) [20] and then improved in a further paper [21] by giving two algorithms, one that runs in O * (1.4231 n ) time using polynomial space, the other using O(1.3752 n ) time and exponential space.…”

Section: Introductionmentioning

confidence: 99%

An Exact Algorithm for finding Maximum Induced Matching in Subcubic Graphs

Hoi¹,

Sabili²,

Stephan³

2022

Preprint

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The Maximum Induced Matching problem asks to find the maximum k such that, given a graph G = (V, E), can we find a subset of vertices S of size k for which every vertices v in the induced graph G[S] has exactly degree 1. In this paper, we design an exact algorithm running in O(1.2630 n ) time and polynomial space to solve the Maximum Induced Matching problem for graphs where each vertex has degree at most 3. Prior work solved the problem by finding the Maximum Independent Set using polynomial space in the line graph L(G 2 ); this method uses O(1.3139 n ) time.

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Section: Introductionmentioning

confidence: 99%

An Exact Algorithm for finding Maximum Induced Matching in Subcubic Graphs

Hoi¹,

Sabili²,

Stephan³

2022

Preprint

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“…The problem is proved to be NP-hard in general graphs [7]. Some exponential time algorithms for the MIM problem in general graphs are proposed recently by Chang et al [8] and Xiao et al [9]. Besides, it is known for polynomial-time maximum induced matching on special graph classes such as co-comparability graphs (including circular-arc graphs [10], interval graphs [11], etc.…”

Section: Introductionmentioning

confidence: 99%

“…A permutation graph G (a) and one of its corresponding permutation representation (b), which has π =(5,7,2,1,4,8,11,10,3,6,12,9). A trapezoid model of the trapezoid graph L(G) 2 , partially shown in (c), can be constructed from the permutation representation of G. A maximum induced matching for G is M = {(1, 5),(6,8),(9,12)}, also seen as a maximum independent set of L(G)2 . A trapezoid graph G (a) and one of its corresponding trapezoid representations (b).…”

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confidence: 99%

Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs

Nguyen,

Pham,

2021

Preprint

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We first design an O(n 2 ) 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(n 2 ) 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.

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