Article

Mathematics in Computer Science

, Volume 3, Issue 1, pp 97-107

First online:

On Conditional Covering Problem

  • Balasubramanian SivanAffiliated withComputer Sciences Department, University of Wisconsin Madison Email author 
  • , S. HariniAffiliated withDepartment of Computer Science and Engineering, Indian Institute of Technology Madras
  • , C. Pandu RanganAffiliated withDepartment of Computer Science and Engineering, Indian Institute of Technology Madras

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Abstract

The conditional covering problem (CCP) aims to locate facilities on a graph, where the vertex set represents both the demand points and the potential facility locations. The problem has a constraint that each vertex can cover only those vertices that lie within its covering radius and no vertex can cover itself. The objective of the problem is to find a set that minimizes the sum of the facility costs required to cover all the demand points. An algorithm for CCP on paths was presented by Horne and Smith (Networks 46(4):177–185, 2005). We show that their algorithm is wrong and further present a correct O(n 3) algorithm for the same. We also propose an O(n 2) algorithm for the CCP on paths when all vertices are assigned unit costs and further extend this algorithm to interval graphs without an increase in time complexity.

Keywords

Conditional covering problem Facility location Total domination problem Paths Interval graphs

Mathematics Subject Classification (2000)

Primary 05C85 Secondary 90C39