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On-line models and algorithms for max independent set

Published online by Cambridge University Press:  12 October 2006

Bruno Escoffier  and
Vangelis Th. Paschos
Bruno Escoffier
Affiliation:
LAMSADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France; e-mail: {escoffier,paschos}@lamsade.dauphine.fr
Vangelis Th. Paschos
Affiliation:
LAMSADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France; e-mail: {escoffier,paschos}@lamsade.dauphine.fr
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Abstract

In on-line computation, the instance of the problem dealt is notentirely known from the beginning of the solution process, but itis revealed step-by-step. In this paper we deal with on-lineindependent set. On-line models studied until now for this problemsuppose that the input graph is initially empty and revealedeither vertex-by-vertex, or cluster-by-cluster. Here we present anew on-line model quite different to the ones already studied. Itassumes that a superset of the final graph is initially present(in our case the complete graph on the order n of the finalgraph) and edges are progressively removed until the achievementof the final graph. Next, we revisit the model introduced in[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)326–334] and study relaxations assuming that somepaying backtracking is allowed.

Keywords

Approximation algorithmscompetitive ratiomaximum independent seton-line algorithms.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 2: ROADEF 03 , April 2006 , pp. 129 - 142
Copyright
© EDP Sciences, 2006

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References

Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L. and Talamo, M., Algorithms for the on-line traveling salesman problem. Algorithmica 29 (2001) 560–581. CrossRef
C. Berge, Graphs and hypergraphs. North Holland, Amsterdam (1973).
M. Demange, X. Paradon and V.Th. Paschos, On-line maximum-order induced hereditary subgraph problems, in SOFSEM 2000—Theory and Practice of Informatics, edited by V. Hlaváč, K.G. Jeffery and J. Wiedermann. Springer-Verlag, Lect. Notes Comput. Sci. 1963 (2000) 326–334.
Demange, M., Paschos, V.Th., Improved approximations for maximum independent set via approximation chains. Appl. Math. Lett. 10 (1997) 105–110. CrossRef
M. Demange, V.Th. Paschos, Improved approximations for weighted and unweighted graph problems. Theor. Comput. Syst. To appear.
B. Escoffier, Problème on-line du stable de cardinalité maximale. Mémoire de DEA (2002).
M.M. Halldórsson, Approximations via partitioning. JAIST Research Report IS-RR-95-0003F, Japan Advanced Institute of Science and Technology, Japan (1995).
Halldórsson, M.M., Approximations of weighted independent set and hereditary subset problems. J. Graph Algorithms Appli. 4 (2000) 1–16. CrossRef
Halldórsson, M.M., Iwama, K., Miyazaki, S. and Taketomi, S., Online independent sets. Theoret. Comput. Sci. 289 (2002) 953–962. CrossRef
D.S. Hochbaum, editor, Approximation algorithms for NP-hard problems. PWS, Boston (1997).
Paschos, V.Th., A survey about how optimal solutions to some covering and packing problems can be approximated. ACM Comput. Surveys 29 (1997) 171–209. CrossRef