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Approximating corridors and tours via restriction and relaxation techniques

Published: 02 July 2010 Publication History

Abstract

Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLCk problems. The MLCk problem is a generalization of the MLC-R problem where the rectangles are rectilinear c-gons, for ck and k is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear c-gons as in the MLCk problem. Our algorithms are based on the restriction and relaxation approximation techniques.

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      cover image ACM Transactions on Algorithms
      ACM Transactions on Algorithms  Volume 6, Issue 3
      June 2010
      304 pages
      ISSN:1549-6325
      EISSN:1549-6333
      DOI:10.1145/1798596
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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      Publication History

      Published: 02 July 2010
      Accepted: 01 August 2008
      Revised: 01 August 2008
      Received: 01 August 2007
      Published in TALG Volume 6, Issue 3

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      Author Tags

      1. Corridors
      2. approximation algorithms
      3. complexity
      4. computational geometry
      5. restriction and relaxation techniques

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