D 2017

On Structural Parameterizations of the Edge Disjoint Paths Problem

GANIAN, Robert, Sebastian ORDYNIAK and M.S. RAMANUJAN

Basic information

Original name

On Structural Parameterizations of the Edge Disjoint Paths Problem

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution), Sebastian ORDYNIAK (40 Austria) and M.S. RAMANUJAN (356 India)

Edition

92. vyd. Nemecko, 28th International Symposium on Algorithms and Computation, ISAAC 2017, December 9-12, 2017, Phuket, Thailand, p. 1-13, 13 pp. 2017

Publisher

LIPIcs

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

RIV identification code

RIV/00216224:14330/17:00100549

Organization unit

Faculty of Informatics

ISBN

978-3-95977-054-5

ISSN

DOI

Keywords in English

Edge Disjont Paths; Parameterized Complexity; Treewidth

Tags

Tags

International impact, Reviewed
Změněno: 17/5/2018 17:24, RNDr. Pavel Šmerk, Ph.D.

Abstract

V originále

In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an fpt-algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.