Faster Deterministic and Randomized Algorithms on the Homogeneous Set Sandwich Problem

A homogeneous set is a non-trivial, proper subset of a graph’s vertices such that all its elements present exactly the same outer neighborhood. Given two graphs, G1(V, E1), G2(V, E2), we consider the problem of finding a sandwich graph Gs(V, ES), with E1 ⊆ ES ⊆ E2, which contains a homogeneous set, in case such a graph exists. This is called the Homogeneous Set Sandwich Problem (HSSP). We give an O(n3.5 ) deterministic algorithm, which updates the known upper bounds for this problem, and an O(n3 ) Monte Carlo algorithm as well. Both algorithms, which share the same underlying idea, are quite easy to be implemented on the computer.

• Type: Conference
• Year: 2004
• Where: WEA
• Authors: Celina M. Herrera de Figueiredo, Guilherme Dias da Fonseca, Vinícius G. P. de Sá, Jeremy Spinrad
• Keywords: Algorithms, Graph’s Vertices, Homogeneous Set, Homogeneous Set Sandwich, WEA 2004