A primal - dual approximation algorithm forthe
نویسنده
چکیده
Given an undirected graph with nonnegative edge-costs, a subset of nodes of size k called the terminals, and an integer q between 1 and k, the minimum q-Steiner forest problem is to nd a forest of minimum cost with at most q trees that spans all the terminals. When q = 1, we have the classical minimum-cost Steiner tree problem on networks. In this note, we adapt a primal-dual approximation algorithm for the latter problem due to Agrawal, Klein and Ravi to provide one for the former. The algorithm runs in time O(n log n + m) and outputs a solution of cost at most 2(1 ? 1 k?q+1) times the minimum. Here n and m denote respectively the number of nodes and edges in the input graph.
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