On Directed Steiner Trees with Multiple Roots

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F16%3A00306347" target="_blank" >RIV/68407700:21240/16:00306347 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007/978-3-662-53536-3_22" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-662-53536-3_22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-662-53536-3_22" target="_blank" >10.1007/978-3-662-53536-3_22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Directed Steiner Trees with Multiple Roots

Popis výsledku v původním jazyce

We introduce a new Steiner-type problem for directed graphs named q-Root Steiner Tree. Here one is given a directed graph G = (V, A) and two subsets of its vertices, R of size q and T, and the task is to find a minimum size subgraph of G that contains a path from each vertex of R to each vertex of T. The special case of this problem with q = 1 is the well known Directed Steiner Tree problem, while the special case with T = R is the Strongly Connected Steiner Subgraph problem. We first show that the problem is W[1]-hard with respect to |T| for any q >= 2. Then we restrict ourselves to instances with R subseteq T (Pedestal version). Generalizing the methods of Feldman and Ruhl [SIAM J. Comput. 2006], we present an algorithm for this restriction with running time O(2^{2q+4|T|}* n^{2q+O(1)}), i.e., this restriction is FPT with respect to |T| for any constant q. We further show that we can, without significantly affecting the achievable running time, loosen the restriction to only requiring that in the solution there is a vertex v and a path from each vertex of R to v and from v to each vertex of T (Trunk version). Finally, we use the methods of Chitnis et al. [SODA 2014] to show that the Pedestal version can be solved in planar graphs in O(2^{O(q log q+|T|log q)}cdot n^{O(sqrt{q})}) time.

Název v anglickém jazyce

On Directed Steiner Trees with Multiple Roots

Popis výsledku anglicky

We introduce a new Steiner-type problem for directed graphs named q-Root Steiner Tree. Here one is given a directed graph G = (V, A) and two subsets of its vertices, R of size q and T, and the task is to find a minimum size subgraph of G that contains a path from each vertex of R to each vertex of T. The special case of this problem with q = 1 is the well known Directed Steiner Tree problem, while the special case with T = R is the Strongly Connected Steiner Subgraph problem. We first show that the problem is W[1]-hard with respect to |T| for any q >= 2. Then we restrict ourselves to instances with R subseteq T (Pedestal version). Generalizing the methods of Feldman and Ruhl [SIAM J. Comput. 2006], we present an algorithm for this restriction with running time O(2^{2q+4|T|}* n^{2q+O(1)}), i.e., this restriction is FPT with respect to |T| for any constant q. We further show that we can, without significantly affecting the achievable running time, loosen the restriction to only requiring that in the solution there is a vertex v and a path from each vertex of R to v and from v to each vertex of T (Trunk version). Finally, we use the methods of Chitnis et al. [SODA 2014] to show that the Pedestal version can be solved in planar graphs in O(2^{O(q log q+|T|log q)}cdot n^{O(sqrt{q})}) time.

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

—

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

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

Graph-Theoretic Concepts in Computer Science

ISBN

978-3-662-53535-6

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

12

Strana od-do

257-268

Název nakladatele

Springer Berlin Heidelberg

Místo vydání

Berlin

Místo konání akce

Istanbul

Datum konání akce

22. 6. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000390176900022