A Local-Search Algorithm for Steiner Forest

Martin Groß; Anupam Gupta; Amit Kumar; Jannik Matuschke; Daniel R. Schmidt; Melanie Schmidt; José Verschae

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arXiv · 1707.02753

A Local-Search Algorithm for Steiner Forest

Martin Groß·Anupam Gupta·Amit Kumar·Jannik Matuschke·Daniel R. Schmidt·Melanie Schmidt·José Verschae

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Abstract

In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by, e.g., the elegant primal-dual algorithm of Agrawal, Klein, and Ravi from 1995. We give a local-search-based constant-factor approximation for the problem. Local search brings in new techniques to an area that has for long not seen any improvements and might be a step towards a combinatorial algorithm for the more general survivable network design problem. Moreover, local search was an essential tool to tackle the dynamic MST/Steiner Tree problem, whereas dynamic Steiner Forest is still wide open. It is easy to see that any constant factor local search algorithm requires steps that add/drop many edges together. We propose natural local moves which, at each step, either (a) add a shortest path in the current graph and then drop a bunch of inessential edges, or (b) add a set of edges to the current solution. This second type of moves is motivated by the potential function we use to measure progress, combining the cost of the solution with a penalty for each connected component. Our carefully-chosen local moves and potential function work in tandem to eliminate bad local minima that arise when using more traditional local moves.

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BibTeX RIS

Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, José Verschae. 2017-07-10. A Local-Search Algorithm for Steiner Forest. https://arxiv.org/abs/1707.02753

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