- Series
- Graph Theory Seminar
- Time
- Tuesday, December 3, 2024 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- 246 Classroom Guggenheim
- Speaker
- Chun-Hung Liu – Texas A&M University – https://people.tamu.edu/~chliu/
- Organizer
- Evelyne Smith-Roberge
(Note the unusual location!)
We study an extension of the k-Disjoint Paths Problem where, in addition to finding k disjoint paths joining k given pairs of vertices in a graph, we ask that those paths satisfy certain constraints expressable by abelian groups. We give an O(n^8) time algorithm to solve this problem under the assumption that the constraint can be expressed as avoiding a bounded number of group elements; moreover, our O(n^8) algorithm allows any bounded number of such constraints to be combined. Group-expressable constraints include, but not limited to: (1) paths of length r modulo m for any fixed r and m, (2) paths passing through any bounded number of prescribed sets of edges and/or vertices, and (3) paths that are long detours (paths of length at least r more than the distance between their ends for fixed r). The k=1 case with the modularity constraint solves problems of Arkin, Papadimitriou and Yannakakis from 1991. Our work also implies a polynomial time algorithm for testing the existence of a subgraph isomorphic to a subdivision of a fixed graph, where each path of the subdivision between branch vertices satisfies any combination of a bounded number of group-expressable constraints. In addition, our work implies similar results addressing edge-disjointness. It is joint work with Youngho Yoo.