Skip to main content
SpringerLink
Log in

Non-oblivious local search for MAX 2-CCSP with application to MAX DICUT

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1335))

Included in the following conference series:

Abstract

In this paper we give a fully dynamic 5/2-approximate algorithm for the class of Maximum binary conjunctive constraint satisfaction problem, and thus for the Maximum directed cut problem. The proposed algorithm is based on the non-oblivious local search technique and on a neighborhood mapping that allows to change either one item, or all the items in the current solution. The total time required to maintain 5/2-approximate solutions, while an arbitrary sequence of q constraint insertions and deletions is performed, is O(m 2 + m · q). This give O(m) amortized time per update over a sequence of Ω(m) operations.

Work supported by: the CEE project ALCOM-IT ESPRIT LTR, project no. 20244, “Algorithms and Complexity in Information Technology”; the Italian Project “Algoritmi, Modelli di Calcolo e Structure Informative,” Ministero dell'Università e della Ricerca Scientifica e Tecnologica; Consiglio Nazionale delle Ricerche, Italy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Alimonti, Non-Oblivious Local Search for Graph and Hypergraph Coloring Problems, 21st International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science 1017, Springer Verlag, 167–180, 1995.

    Google Scholar 

  2. P. Alimonti, New Local Search Approximation Techniques for Maximum Generalized Satisfiability Problems. Information Processing Letters 57, 151–158, 1996.

    Google Scholar 

  3. P. Alimonti, and R. Ferroni, Algorithms for the Maximum Generalized Satisfiability Problem, Rapporto Tecnico, RAP 01.93, Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “la Sapienza”, 1993.

    Google Scholar 

  4. P. Alimonti, S. Leonardi, A. Marchetti Spaccamela, Average Case Analysis of Fully Dynamic Connectivity for Directed Graphs, RAIRO Journal on Theoretical Informatics and Applications 30, 4, 305–318, 1996.

    Google Scholar 

  5. G. Ausiello, and G.F. Italiano, On-Line Algorithms for Polynomially Solvable Satisfiability Problems, Journal of Logic Programming, 10, 69–90, 1991.

    Google Scholar 

  6. G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, U. Nanni, Incremental algorithms for minimal length paths, J. of Algorithms, 12, 615–638, 1991.

    Google Scholar 

  7. G. Ausiello, and M. Protasi, Local Search, Reducibility and Approximability of NP Optimization Problems, Information Processing Letters 54, 73–79, 1995.

    Google Scholar 

  8. R. Battiti, M. Protasi, Reactive local search for the maximum clique problem. Tech. Rep. TR-95-052, International Computer Science Institute, Berkeley, CA, 1995.

    Google Scholar 

  9. D.Eppstein, Z.Galil, G.F.Italiano, A.Nissenzweig, Sparsification — a technique for speeding up dynamic graph algorithms, Proc. 33rd Annual Symp. on Foundations of Computer Science, 1992.

    Google Scholar 

  10. U. Feige, M. Goemans, Approximating the value of the two prover proof system with applications to MAX 2SAT and MAX DICUT, Proceedings of the 3rd Israeli Symposium on Theory of Computing and Systems, 182–189, 1995.

    Google Scholar 

  11. S.T. Fischer, The solution Sets of Local Search Problems, PhD Thesis, Department of Computer Science, University of Amsterdam, Amsterdam, 1995.

    Google Scholar 

  12. G.N. Frederickson, Data Structure for On-Line Updating of Minimum Spanning Tree with Applications, SIAM J. Comput., 14, 781–798, 1985.

    Google Scholar 

  13. F. Glover, Tabu search, Part I, ORSA Journal of Computing, 1, 190–206, 1989.

    Google Scholar 

  14. M. Goemans, and D.P. Williamson,.878-Approximation Algorithms for MAX CUT and MAX 2SAT, Proc. of the 35th Annual IEEE Conference on Foundations of Computer Science, 1994.

    Google Scholar 

  15. P. Klein, H. Lu,i Efficient Approximation Algorithms for Semidefinite Programming Arising from MAX CUT and COLORING, Proc. 28th ACM Symposium on Theory of Computinga, 1996, 1996.

    Google Scholar 

  16. Z. Ivkovic, E.L.Lloyd, Fully Dynamic Maintenance of Vertex Cover, Proc. of the 19th International Workshop on Graph-Theoretic Concept in Computer Science, LNCS 790, 99–111, 1993.

    Google Scholar 

  17. D.S. Johnson, C.H. Papadimitriou, and M. Yannakakis, How Easy Is Local Search?, Journal of Computer and System Sciences, 37, 79–100, 1988.

    Google Scholar 

  18. S. Khanna, R. Motwani, M. Sudan, and U. Vazirani, On Syntactic versus Computational Views of Approximability, Proc. of the 35th Annual IEEE Conference on Foundations of Computer Science, 1994.

    Google Scholar 

  19. S. Kirkpatrick, C. Gelat, and M. Vecchi, Optimization by simulated annealing, Science, 220, 671–680, 1983.

    Google Scholar 

  20. J.A. La Poutré, Ivan Leeuwen, Maintenance of transitive closure and transitive reduction of graphs, Proc Work. on Graph Theoretic concepts in Comp. Sci., LNCS 314, Springer Verlag, Berlin, 106–120, 1988.

    Google Scholar 

  21. C. Papadimitriou, and M. Yannakakis, Optimization, Approximation, and Complexity Classes, Journal of Computer and System Sciences, 43, 425–440, 1991.

    Google Scholar 

  22. R.E. Tarjan, Amortized Computational Complexity, SIAM J.Alg.Disc. Math., 6, 306–318, 1985.

    Google Scholar 

  23. L.Trevisan, Positive linear programming, parallel approximation and PCP's, Proceedings 4th Annual European Symposium on Algorithms, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatioa e Sistemistica, Università di Roma“la Sapienza”, Italy

    Paola Alimonti

  2. Dipartimento di Matematica, Università di Roma“Tor Vergata”, Italy

    Paola Alimonti

Authors
  1. Paola Alimonti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rolf H. Möhring

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alimonti, P. (1997). Non-oblivious local search for MAX 2-CCSP with application to MAX DICUT. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024483

Download citation

  • DOI: https://doi.org/10.1007/BFb0024483

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63757-8

  • Online ISBN: 978-3-540-69643-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation