Work

Efficient branch-and-bound algorithms for finding triangle-constrained 2-clubs

Year: 2024

Type: article

Abstract: In the Vertex Triangle 2-Club problem, we are given an undirected graph G and aim to find a maximum-vertex subgraph of G that has diameter at most 2 and in which every vertex is contained in at least $$\ell $$ ℓ triangles in the subgraph. So far, the only algorithm for solving Vertex Triangle 2-Club relies on an ILP formulation (Almeida and Brás in Comput Oper Res 111:258–270, 2019). In this work, we develop a combinatorial branch-and-bound algorithm that, coupled with a set of data reduction rules, outperforms the existing implementation and is able to find optimal solutions on sparse real-world graphs with more than 100,000 vertices in a few minutes. We also extend our algorithm to the Edge Triangle 2-Club problem where the triangle constraint is imposed on all edges of the subgraph.

Source: Journal of Combinatorial Optimization

DOI: 10.1007/s10878-024-01204-z

Authors: Niels Grüttemeier, Philipp Heinrich Keßler, Christian Komusiewicz, Frank Sommer

Institutions: Philipps University of Marburg, Friedrich Schiller University Jena, TU Wien

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Technische Universität Wien