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Effectiveness of Local Search for Geometric Optimization

Authors Vincent Cohen-Addad, Claire Mathieu

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Vincent Cohen-Addad
Claire Mathieu

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Vincent Cohen-Addad and Claire Mathieu. Effectiveness of Local Search for Geometric Optimization. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 329-344, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.SOCG.2015.329

Abstract

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude 1/epsilon^c is an approximation scheme for the following problems in the Euclidean plane: TSP with random inputs, Steiner tree with random inputs, uniform facility location (with worst case inputs), and bicriteria k-median (also with worst case inputs). The randomness assumption is necessary for TSP.

Subject Classification

Keywords
  • Local Search
  • PTAS
  • Facility Location
  • k-Median
  • TSP
  • Steiner Tree

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