Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks

• Published in: European journal of operational research Vol. 316; no. 2; pp. 519 - 538
• Main Authors: Ponce, Diego, Puerto, Justo, Temprano, Francisco
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.07.2024
• Subjects: Community detection; Complex networks; Image segmentation; Mathematical programming; Normalized cuts; Image segmentation; 90C30; 91C20; 90C35; 05C82; Complex networks; Community detection; 90C27; Normalized cuts; Mathematical programming
• ISSN: 0377-2217; 1872-6860; 1872-6860
• DOI: 10.1016/j.ejor.2024.02.033

This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate large-scale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology. •MILP formulations for the k-way normalized cut problem in complex networks.•A branch-and-price algorithm for this problem which scales better.•A heuristic algorithm that provides good quality solutions for large scale problems.•Extensive computational experiments to compare the different algorithms.