Maximizing Minimum Cycle Bases Intersection
Dimitri Watel (SAMOVAR, ENSIIE), Marc-Antoine Weisser (GALaC),, Dominique Barth (UVSQ, DAVID), Yl\`ene Aboulfath (UVSQ, DAVID), Thierry, Mautor (UVSQ, DAVID)
TL;DR
This paper investigates the complexity of selecting minimum cycle bases across multiple graphs to maximize their intersection, providing a detailed analysis and exploring approximability and parameterized complexity.
Contribution
It offers a comprehensive complexity analysis of the maximum intersection problem for minimum cycle bases, including classifications based on graph parameters and new results on approximability.
Findings
Complexity classifications for various subcases
Results on approximability of the problem
Insights into parameterized complexity
Abstract
We address a specific case of the matroid intersection problem: given a set of graphs sharing the same set of vertices, select a minimum cycle basis for each graph to maximize the size of their intersection. We provide a comprehensive complexity analysis of this problem, which finds applications in chemoinformatics. We establish a complete partition of subcases based on intrinsic parameters: the number of graphs, the maximum degree of the graphs, and the size of the longest cycle in the minimum cycle bases. Additionally, we present results concerning the approximability and parameterized complexity of the problem.
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