Finding a minimum weight K-link path in graphs with Monge property and applications

Alok Aggarwal, Baruch Schieber, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

25 Citations (Scopus)

Abstract

Let G be a weighted, complete, directed acyclic graph (DAG), whose edge weights obey the Monge condition. We give an efficient algorithm for finding the minimum weight K-link path between a given pair of vertices for any given K. The time complexity of our algorithm is O(n√K log n) for the concave case and O(nα(n) log3 n) for the convex case. Our algorithm uses some properties of DAGs with Monge property together with a refined parametric search technique. We apply our algorithm (for the concave case) to get efficient solutions for the following problems, improving on previous results: (1) Finding the largest K-gon contained in a given polygon. (2) Finding the smallest K-gon that is the intersection of K halfplanes out of given set of halfplanes defining an n-gon. (3) Computing maximum K-cliques of an interval graph. (4) Computing length limited Huffman codes. (5) Computing optimal discrete quantization.

Original languageEnglish
Title of host publicationProceedings of the 9th Annual Symposium on Computational Geometry
PublisherPubl by ACM
Pages189-197
Number of pages9
ISBN (Print)0897915828, 9780897915823
DOIs
Publication statusPublished - 1993
EventProceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA
Duration: 1993 May 191993 May 21

Publication series

NameProceedings of the 9th Annual Symposium on Computational Geometry

Other

OtherProceedings of the 9th Annual Symposium on Computational Geometry
CitySan Diego, CA, USA
Period93/5/1993/5/21

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Aggarwal, A., Schieber, B., & Tokuyama, T. (1993). Finding a minimum weight K-link path in graphs with Monge property and applications. In Proceedings of the 9th Annual Symposium on Computational Geometry (pp. 189-197). (Proceedings of the 9th Annual Symposium on Computational Geometry). Publ by ACM. https://doi.org/10.1145/160985.161135