Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F17%3A00313780" target="_blank" >RIV/68407700:21240/17:00313780 - isvavai.cz</a>

Result on the web

<a href="http://epubs.siam.org/doi/10.1137/15M103618X" target="_blank" >http://epubs.siam.org/doi/10.1137/15M103618X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M103618X" target="_blank" >10.1137/15M103618X</a>

Result language

angličtina

Original language name

Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

Original language description

We study the parameterized complexity of the directed variant of the classical STEINER TREE problem on various classes of directed sparse graphs. While the parameterized complexity of STEINER TREE parameterized by the number of terminals is well understood, not much is known about the parameterization by the number of nonterminals in the solution tree. All that is known for this parameterization is that both the directed and the undirected versions are W[2]-hard on general graphs and hence unlikely to be fixed parameter tractable (FPT). The undirected STEINER TREE problem becomes FPT when restricted to sparse classes of graphs such as planar graphs, but the techniques used to show this result break down on directed planar graphs. In this article we precisely chart the tractability border for DIRECTED STEINER TREE (DST) on sparse graphs parameterized by the number of nonterminals in the solution tree. Specifically, we show that the problem is FPT on graphs excluding a topological minor but becomes W[2]-hard on graphs of degeneracy 2. On the other hand we show that if the subgraph induced by the terminals is acyclic, then the problem becomes FPT on graphs of bounded degeneracy. We further show that our algorithm achieves the best possible asymptotic running time dependence on the solution size and degeneracy of the input graph, under standard complexity theoretic assumptions. Using the ideas developed for DST, we also obtain improved algorithms for DOMINATING SET on sparse undirected graphs. These algorithms are asymptotically optimal.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GP14-13017P" target="_blank" >GP14-13017P: Parameterized Algorithms for Fundamental Network Problems Related to Connectivity</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Volume of the periodical

31

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

34

Pages from-to

1294-1327

UT code for WoS article

000404770300033

EID of the result in the Scopus database

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