k best cuts for circulararc graphs
 K. H. Tsai,
 D. T. Lee
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Given a set ofn nonnegativeweighted circular arcs on a unit circle, and an integerk, thek Best Cust for CircularArcs problem, abbreviated as thekBCCA problem, is to find a placement ofk points, calledcuts, on the circle such that the total weight of the arcs that contain at least one cut is maximized.
We first solve a simpler version, thek Best Cuts for Intervals (kBCI) problem, inO(kn+n logn) time andO(kn) space using dynamic programming. The algorithm is then extended to solve a variation, called thekrestricted BCI problem, and the space complexity of thekBCI problem can be improved toO(n). Based on these results, we then show that thekBCCA problem can be solved inO(I(k,n)+nlogn) time, whereI(k, n) is the time complexity of thekBCI problem. As a byproduct, thek Maximum Cliques Cover problem (k>1) for the circulararc graphs can be solved inO(I(k,n)+nlogn) time.
 Title
 k best cuts for circulararc graphs
 Journal

Algorithmica
Volume 18, Issue 2 , pp 198216
 Cover Date
 199706
 DOI
 10.1007/BF02526033
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Circulararc graph
 Interval graph
 Facility location
 Competitive location
 Maximum clique cover
 Industry Sectors
 Authors

 K. H. Tsai ^{(1)}
 D. T. Lee ^{(2)}
 Author Affiliations

 1. Institute of Information Science, Academia Sinica, Nankang, Taipei, Taiwan
 2. Department of Electrical and Computer Engineering, Northwestern University, 60208, Evanston, IL, USA