skip to main content
10.1145/170791.170879acmconferencesArticle/Chapter ViewAbstractPublication PagescscConference Proceedingsconference-collections
Article
Free Access

An O(nlogn) algorithm for finding minimal path cover in circular-arc graphs

Authors Info & Claims
Published:01 March 1993Publication History

ABSTRACT

Whether there exists a polynomial algorithm for the minimal path cover problem in circular-arc graphs remains open. In this paper, we present a polynomial time algorithm for finding a minimal path cover for a set of n arcs in a circular-arc model. Our algorithm takes Ο(nlogn) time.

References

  1. 1.A.R. Arikati and C. P. Rmgan, A lineal' algorithm for peth covet problem on interval gret~, Inform. Process. Lat. 35 (1990) 149-153 Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2.M.A. Bonuccelli and D. P. Borer, Minimum node-disjoint path covering for circular-arc graphs, Inform. Process. Lea. 8 (1979) 159-161.Google ScholarGoogle Scholar
  3. 3.M. R. Oarey and D. S. Johnson, Computers and Intractability, A guide to the Theory of NP.Comple.teness, Freeman, San Francisco, 1979. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.M. C, Golmnhic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.Google ScholarGoogle Scholar
  5. 5.S.E. Goodman, S. T. Hedetniemi and P. J. Slater, Advances on Hamiltcmian comp~ problem, J. ACM 22 (1975) 352-360. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6.Y. D. Lians, C. Rhee, S. IL Dhall, and S. Lakshmiverahan, an O (nZlogn) algorithm for Hamiltanian path ixoblem in ~-~rc grephs, 29th AIIerton Conf~ 1991.Google ScholarGoogle Scholar
  7. 7.Y.D. Lian8, G. IC Msnacher; C. Rhee., T. A. Manku~ S. IC DlmIL and S. Lakslunivarahan, an O (n logn) ai~ for finding a Hamilumian paflm and circuit in circular-arc Oapl=, mammcri~ Augtmt, 1992.Google ScholarGoogle Scholar
  8. 8.G. IL Manacher, T. A. Mankus end A. J. Smith, An opthmnn O(nlogn) algorie~m for Rnding a c, manical Hamil~ circuit in a set of intervals, Inform. Process. L~. 35 (1990) 205-211 Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.S. Moran and Y. Wolfsmhl, Optimal covering of cacti by vertex-disjoint paths, Tech. Rept., Technion Instimm of TecJmology (1988).Google ScholarGoogle Scholar
  10. 10.W. Shih, T. C. C1mm, end W. L. H~ An O(n21ogn) algorithm for Hamfltonian cycle problem on circultr-arc graphs. Accepted for publicati~ in SIAM I. Cmnputing. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. An O(nlogn) algorithm for finding minimal path cover in circular-arc graphs

          Recommendations

          Comments

          Login options

          Check if you have access through your login credentials or your institution to get full access on this article.

          Sign in
          • Published in

            cover image ACM Conferences
            CSC '93: Proceedings of the 1993 ACM conference on Computer science
            March 1993
            543 pages
            ISBN:0897915585
            DOI:10.1145/170791

            Copyright © 1993 ACM

            Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

            Publisher

            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 1 March 1993

            Permissions

            Request permissions about this article.

            Request Permissions

            Check for updates

            Qualifiers

            • Article

          PDF Format

          View or Download as a PDF file.

          PDF

          eReader

          View online with eReader.

          eReader