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The Stable Set Problem: Clique and Nodal Inequalities Revisited

Adam N. Letchford (a.n.letchford***at***lancaster.ac.uk)
Fabrizio Rossi (fabrizio.rossi***at***univaq.it)
Stefano Smriglio (stefano.smriglio***at***univaq.it)

Abstract: The stable set problem is a fundamental combinatorial optimisation problem, that is known to be very difficult in both theory and practice. Some of the solution algorithms in the literature are based on 0-1 linear programming formulations. We examine an entire family of such formulations, based on so-called clique and nodal inequalities. As well as proving some theoretical results, we conduct extensive computational experiments. This enables us to derive guidelines on how to choose the right formulation for a given instance.

Keywords: stable set problem

Category 1: Combinatorial Optimization

Category 2: Integer Programming

Citation: Published as: A.N. Letchford, F. Rossi & S. Smriglio (2020) The stable set problem: clique and nodal inequalities revisited. Computers & Operations Research, vol. 123, article no. 105024.

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Entry Submitted: 05/07/2018
Entry Accepted: 05/07/2018
Entry Last Modified: 02/18/2021

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