Abstract
We consider the following class of problems: given a graph, find the maximum number of nodes inducing a subgraph that satisfies a desired property π, such as planar, acyclic, bipartite, etc. We show that this problem is hard to approximate for any property π on directed or undirected graphs that is nontrivial and hereditary on induced subgraphs.
Preview
Unable to display preview. Download preview PDF.
References
N. Alon, O. Goldreich, J. Håstad, and R. Peralta. Simple constructions of almost k-wise independent random variables. In Proc. of the 31st IEEE Symp. on Foundations of Computer Science, pp. 544–553, 1990.
S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. In Proc. of the 33rd IEEE Symp. on Foundations of Computer Science, pages 14–23, 1992.
S. Arora, and S. Safra. Probabilistic checking of proofs. In Proc. of the 33rd IEEE Symp. on Foundations of Computer Science, pp. 2–13, 1992.
B. S. Baker. Approximation algorithms for NP-complete problems on planar graphs. In Proc. of the 24th IEEE Symp. on Foundations of Computer Science, pp. 265–273, 1983.
M. Bellare, S. Goldwasser, C. Lund and A. Russell. Efficient Probabilistically Checkable Proofs: Applications to Approximation. In Proc. of the 25th ACM Symp. on the Theory of Computing, 1993.
C. Berge. Graphs and Hypergraphs. North-Holland, Amsterdam, 1973.
P. Berman and G. Schnitger. On the complexity of approximating the independent set problem. In Information and Computation, 96, pp. 77–94, 1992.
U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy. Approximating clique is almost NP-complete. In Proc. of the 32nd IEEE Symp. on Foundations of Computer Science, pp. 2–12, 1991.
U. Feige and L. Lóvasz. Two-prover one-round proof systems: Their power and their problems. In Proc. of the 24th ACM Symp. on the Theory of Computing, pp. 733–744, 1992.
M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science, pp. 237–267, 1976.
M. R. Garey and D. S. Johnson. Computers and Intractability: A guide to the theory of NP-completeness. W. H. Freeman and co., San Fransisco, 1979.
M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
F. Harary. Graph Theory. Addison-Wesley, Reading, Mass., 1970.
V. Kann. On the approximability of NP-complete optimization problems. Ph.D. Thesis, Royal Institute of Technology, Stockholm, 1992.
M. S. Krishnamoorthy and N. Deo. Node-deletion NP-complete problems. In SIAM J. on Computing, pp. 619–625, 1979.
F. T. Leighton, and S. Rao. An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In Proc. of the 28th IEEE Symp. on Foundations of Computer Science, pp. 256–269, 1988.
D. Lapidot and A. Shamir. Fully parallelized multi prover protocols for NEXP-time. In Proc. of the 32nd IEEE Symp. on Foundations of Computer Science, pp. 13–18, 1991.
R. J. Lipton, and R. E. Tarjan. Applications of a planar separator theorem. In SIAM J. on Computing, pp. 615–627, 1980.
J. M. Lewis, and M. Yannakakis. The node-deletion problem for hereditary properties is NP-complete. In J. of Computer and System Sciences, pp. 219–230, 1980.
C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. In Proc. of the 25th ACM Symp. on the Theory of Computing, 1993.
T. Nishizeki, and N. Chiba. Planar Graphs: Theory and Algorithms. Vol. 32 of Annals of Discrete Mathematics, Elsevier Pub. co., Amsterdam, 1988.
C. H. Papadimitriou, and M. Yannakakis. Optimization, approximation and complexity classes. In J. of Computer and System Sciences, pp. 425–440, 1991.
H. U. Simon. On approximate solutions for combinatorial optimization problems. SIAM J. Disc. Meth., 3, pp. 294–310, 1990.
M. Yannakakis. The effect of a connectivity requirement on the complexity of maximum subgraph problems. In J. of the ACM, pp. 618–630, 1979.
M. Yannakakis. Edge-deletion problems. In SIAM J. on Computing, pp. 297–309, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lund, C., Yannakakis, M. (1993). The approximation of maximum subgraph problems. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_60
Download citation
DOI: https://doi.org/10.1007/3-540-56939-1_60
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56939-8
Online ISBN: 978-3-540-47826-3
eBook Packages: Springer Book Archive