On Conditional Covering Problem
 Balasubramanian Sivan,
 S. Harini,
 C. Pandu Rangan
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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.
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 Title
 On Conditional Covering Problem
 Journal

Mathematics in Computer Science
Volume 3, Issue 1 , pp 97107
 Cover Date
 20100301
 DOI
 10.1007/s1178600900011
 Print ISSN
 16618270
 Online ISSN
 16618289
 Publisher
 BirkhäuserVerlag
 Additional Links
 Topics
 Keywords

 Conditional covering problem
 Facility location
 Total domination problem
 Paths
 Interval graphs
 Primary 05C85
 Secondary 90C39
 Authors

 Balasubramanian Sivan ^{(1)}
 S. Harini ^{(2)}
 C. Pandu Rangan ^{(2)}
 Author Affiliations

 1. Computer Sciences Department, University of Wisconsin Madison, Madison, WI, 53706, USA
 2. Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, 600036, India