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Fixed-Parameter Tractability for Branchwidth of the Maximum-Weight Edge-Colored Subgraph Problem

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Advanced Information Networking and Applications (AINA 2024)

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 204))

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Abstract

A k-edge-coloring of a(n undirected) graph is an assignment of one of k possible colors to each of the edges of the graph such that different colors are assigned to any two adjacent (but different) edges. Given a weight function on colored edges of a graph G, a maximum-weight k-edge-coloring of G is a k-edge-coloring of a subgraph of G whose total weight of colored edges is maximum. The Maximum Weight Edge-Colored Subgraph asks, for a graph G, an integer k, and a weight function w for k-colored edges of G, to find a maximum-weight k-edge-colored subgraph of G. We propose a fixed-parameter tractable algorithm for the Maximum Weight Edge-Colored Subgraph problem with respect to two parameters: the branchwidth of the graph and the number k of colors. This result can be transferred to the treewidth.

This work is partially supported by the project ’Soluzioni innovative per il problema della copertura nelle multi-interfacce e relative varianti’, UNINT, and by the Italian National Group for Scientific Computation (GNCS-INdAM).

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Authors and Affiliations

  1. Dipartimento di Scienze Umanistiche e Sociali Internazionali, Università degli Studi Internazionali di Roma, Roma, Italy

    Alessandro Aloisio

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  1. Alessandro Aloisio
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Correspondence to Alessandro Aloisio .

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  1. Department of Information and Communication Engineering, Fukuoka Institute of Technology, Fukuoka, Japan

    Leonard Barolli

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Aloisio, A. (2024). Fixed-Parameter Tractability for Branchwidth of the Maximum-Weight Edge-Colored Subgraph Problem. In: Barolli, L. (eds) Advanced Information Networking and Applications. AINA 2024. Lecture Notes on Data Engineering and Communications Technologies, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-031-57942-4_10

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