Efficient Branch-and-Bound Algorithms for Finding Triangle-Constrained 2-Clubs

11/03/2022
by   Niels Grüttemeier, et al.
0

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 ℓ triangles in the subgraph. So far, the only algorithm for solving Vertex Triangle 2-Club relies on an ILP formulation [Almeida and Brás, Comput. Oper. Res. 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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset