The pair completion algorithm for the homogeneous set sandwich problem

Authors:
Claudson Bornstein;Celina M. H. de Figueiredo;Vinícius G. P. de Sá
Affiliations:
Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil;Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil;Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil
Venue:
Information Processing Letters
Year:
2006

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Abstract

A homogeneous set is a non-trivial module of a graph, i.e., a non-empty, non-unitary, proper vertex subset such that all its elements present the same outer neighborhood. Given two graphsG1 (V, E1) and G2(V, E2), the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a graph GS(V, ES), E1 ⊆ ES ⊆ E2, which has a homogeneous set. This paper presents an algorithm that uses the concept of bias graph [S. Tang, F. Yeh, Y. Wang, An efficient algorithm for solving the homogeneous set sandwich problem, Inform. Process. Lett. 77 (2001) 17-22] to solve the problem in O(n min{|E1|,|E2|} log n) time, thus outperforming the other known HSSP deterministic algorithms for inputs where max{|E1|, |E2|} = Ω (n log n).