Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

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

Projekt

<a href="/cs/project/GP14-13017P" target="_blank" >GP14-13017P: Parametrizované algoritmy pro základní síťové problémy spojené se souvislostí</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Svazek periodika

31

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

1294-1327

Kód UT WoS článku

000404770300033

EID výsledku v databázi Scopus

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