Sequence Hypergraphs

Katerina Böhmová*, Jérémie Chalopin, Matús Mihalák, Guido Proietti, Peter Widmayer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

We introduce sequence hypergraphs by extending the concept of a directed edge (from simple directed graphs) to hypergraphs. Specifically, every hyperedge of a sequence hypergraph is defined as a sequence of vertices (imagine it as a directed path). Note that this differs substantially from the standard definition of directed hypergraphs. Sequence hypergraphs are motivated by problems in public transportation networks, as they conveniently represent transportation lines. We study the complexity of some classic algorithmic problems, arising (not only) in transportation, in the setting of sequence hypergraphs. In particular, we consider the problem of finding a shortest st-hyperpath: a minimum set of hyperedges that “connects” (allows to travel to) t from s; finding a minimum st-hypercut: a minimum set of hyperedges whose removal “disconnects” t from s; or finding a maximum st-hyperflow: a maximum number of hyperedge-disjoint st-hyperpaths.we show that many of these problems are apx-hard, even in acyclic sequence hypergraphs or with hyperedges of constant length. However, if all the hyperedges are of length at most 2, we show, these problems become polynomially solvable. We also study the special setting in which for every hyperedge there also is a hyperedge with the same sequence, but in the reverse order. Finally, we briefly discuss other algorithmic problems (e.g., finding a minimum spanning tree, or connected components).
Original languageEnglish
Title of host publicationProc. 42nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG)
PublisherSpringer
Pages282-294
Number of pages13
DOIs
Publication statusPublished - 2016

Publication series

SeriesLecture Notes in Computer Science
Volume9941

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