On Directed Steiner Trees with Multiple Roots

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On Directed Steiner Trees with Multiple Roots
Original language description
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.
Czech name
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Czech description
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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
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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