D 2017

On Structural Parameterizations of the Edge Disjoint Paths Problem

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

Základní údaje

Originální název

On Structural Parameterizations of the Edge Disjoint Paths Problem

Autoři

GANIAN, Robert (203 Česká republika, garant, domácí), Sebastian ORDYNIAK (40 Rakousko) a M.S. RAMANUJAN (356 Indie)

Vydání

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

Nakladatel

LIPIcs

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10200 1.2 Computer and information sciences

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

Kód RIV

RIV/00216224:14330/17:00100549

Organizační jednotka

Fakulta informatiky

ISBN

978-3-95977-054-5

ISSN

DOI

Klíčová slova anglicky

Edge Disjont Paths; Parameterized Complexity; Treewidth

Štítky

Příznaky

Mezinárodní význam, Recenzováno
Změněno: 17. 5. 2018 17:24, RNDr. Pavel Šmerk, Ph.D.

Anotace

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.