Abstract
A ρ-independent set S in a graph is parameterized by a set ρ of non-negative integers that constrains how the independent set S can dominate the remaining vertices (fV υ ∋ S: ¦N(υ) ∩ S¦ ∃ ρ.) For all values of ρ, we classify as either NP-complete or polynomial-time solvable the problems of deciding if a given graph has a ρ-independent set. We complement this with approximation algorithms and inapproximability results, for all the corresponding optimization problems.
These approximation results extend also to several related independence problems. In particular, we obtain a √m approximation of the Set Packing problem, where m is the number of base elements, as well as a √n approximation of the maximum independent set in power graphs G t, for t even.
Research support in part by Czech research grants GAUK 194 and GAčR 0194/1996.
Preview
Unable to display preview. Download preview PDF.
References
R. B. Boppana and M.M. Halldórsson, Approximating maximum independent sets by excluding subgraphs, BIT, 32 (1992), 180–196.
M. R. Garey and D. S. Johnson, Computers and Intractability (Freeman, New York, 1979).
M.M. Halldórsson, Approximating the minimum maximal independence number, Information Processing Letters 46 (1993), 169–172.
J. Håstad, Clique is hard to approximate within 187-01, In Proc. 37th IEEE Symp. on Found, of Comput. Sci., (1996), 627–636.
S. Khanna, M. Sudan and D. P. Williamson, A complete classification of the approximability of maximization problems derived from boolean constraint satisfaction, in Proc. 29th ACM Symp. on Theory of Computing, (1997), 11–20.
J. Kratochvíl, Perfect codes in general graphs, monograph, Academia Praha (1991).
J. Kratochvíl, P. Manuel and M. Miller, Generalized domination in chordal graphs, Nordic Journal of Computing 2 (1995), 41–50
T.J. Schaefer, The complexity of satisfiability problems, In Proc. 10th ACM Symp. on Theory of Computing (1978), 216–226.
J.A. Telle, Characterization of domination-type parameters in graphs, Proceedings of 24th Southeastern International Conference on Combinatorics, Graph Theory and Computing-Congressus Numerantium Vol.94 (1993), 9–16.
J.A. Telle, Complexity of domination-type problems in graphs, Nordic Journal of Computing 1 (1994), 157–171.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Halldórsson, M.M., Kratochvíl, J., Telle, J.A. (1998). Independent sets with domination constraints. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055051
Download citation
DOI: https://doi.org/10.1007/BFb0055051
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64781-2
Online ISBN: 978-3-540-68681-1
eBook Packages: Springer Book Archive