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The Directed Steiner Network Problem is Tractable for a Constant Number of Terminals
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Journal Article
The Directed Steiner Network Problem is Tractable for a Constant Number of Terminals
2006
Overview
We consider the Directed Steiner Network problem, also called the Point-to-Point Connection problem. Given a directed graph $G$ and $p$ pairs $\\{ (s_1,t_1), \\dotsc, (s_p,t_p) \\}$ of nodes in the graph, one has to find the smallest subgraph $H$ of $G$ that contains paths from $s_i$ to $t_i$ for all $i$. The problem is NP-hard for general $p$, since the Directed Steiner Tree problem is a special case. Until now, the complexity was unknown for constant $p \\geq 3$. We prove that the problem is polynomially solvable if $p$ is any constant number, even if nodes and edges in $G$ are weighted and the goal is to minimize the total weight of the subgraph $H$. In addition, we give an efficient algorithm for the Strongly Connected Steiner Subgraph problem for any constant $p$, where given a directed graph and $p$ nodes in the graph, one has to compute the smallest strongly connected subgraph containing the $p$ nodes.
Publisher
Society for Industrial and Applied Mathematics
Subject
