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

Article type: Research Article

Authors: Nguyen, Viet Dung | Pham, Ba Thai | Do, Phan Thuan^{; *}

Affiliations: Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Ha Noi, Viet Nam. [email protected], [email protected], [email protected]

Correspondence: [*] Address for correspondence: Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Ha Noi, Viet Nam.

Abstract: 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.

Keywords: permutation graph, trapezoid graph, induced matching, sweep line, disjoint set

DOI: 10.3233/FI-2021-2073

Journal: Fundamenta Informaticae, vol. 182, no. 3, pp. 257-283, 2021