BibTeX
@MISC{Tsai97kbest,
author = {K. H. Tsai and D. T. Lee},
title = {k Best Cuts for Circular-Arc Graphs},
year = {1997}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Given a set of n nonnegative weighted circular-arcs on a unit circle, and an integer k, the k Best Cuts for Circular-Arcs problem, abbreviated as k-BCCA problem, is to find a placement of k points, called cuts, 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 using dynamic programming, the k Best Cuts for Intervals (k-BCI) problem in O(kn + n log n) time and O(kn) space. The algorithm is then extended to solve a variation, called the k-restricted BCI problem, and the space complexity of the k-BCI problem can be improved to O(n). Based on these results, we then show that the k-BCCA problem can be solved in O(I(k; n) + n log n) time, where I(k; n) is the time complexity of the k-BCI problem. As a by-product, the k Maximum Cliques Cover problem, (k ? 1) for the circular-arc graphs can be solved in O(I(k; n) + n log n) time. Supported in part by the National Science Foundation under the Grants CCR-890181...
