Work

Conceptual clique sampling frameworks to design solution algorithms for the Edge Clique Cover Problem

Year: 2024

Type: article

Abstract: Given a graph G = (V, E), the Edge Clique Cover Problem (ECCP) asks for a minimum number of cliques so that every edge e ∈ E belongs to at least one of the subgraphs induced by the selected cliques. Rather than fine tuned ECCP algorithms, exact or heuristic, we investigate conceptual frameworks for designing them. In particular we focus on frameworks that are based on the formulation of ECCP as a Set Covering Problem (SCP). This formulation typically contains an exponential number of variables that are in a one-to-one relation with the distinct maximal cliques of G. Our frameworks firstly generate reduced SCP formulations that contain a conveniently small number of variables and then solve them to obtain feasible solutions to ECCP. Variables for these formulations are selected via two distinct clique sampling criteria. One of them relies on random considerations for selecting the cliques (variables) while the other is based on Linear Programming reduced costs. The latter one, in particular, is further refined here into a procedure that implements local search within a column generation environment and is straightforward to adapt to numerous other problems.

Source: RAIRO - Operations Research

DOI: 10.1051/ro/2024229

Authors: Douglas Picciani, Abilio Lucena

Institution: Universidade Federal do Rio de Janeiro

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G321761023, G847940474