# Bounding the bandwidth of NP-complete problems

Conference paper

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## Abstract

We study in this paper how the computational behaviour of NIP-complete graph problems is influenced by imposing a bound on the bandwidth. We show:

- (i)
A large number of problems are considerably simpler for graphs of small bandwidth. On the other hand, there are problems which remain NIP-complete even for graphs of bandwidth 3.

- (ii)
A large number of problems are equivalent under reductions which preserve bandwidth. All these problems are complete under bandwidth preserving reductions for a class RPP, which is defined by nondeterministic Turing machines operating with some space bound and simultaneous polynomial time. This indicates, because of earlier results, that "bandwidth" plays the same role for graph problems as "maximal number" does for number problems.

## Keywords

Schedule Problem Polynomial Time Turing Machine conjUnctive Normal Form Graph Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.Aho, A.V., Hopcroft, J.E. and J.D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading Mass., 1974Google Scholar
- 2.Ausiello, G., A. Marchetti-Spaccamela and M. Protasi, Toward a unified approach for the classification of NP-complete optimization problems, Proc.Frege-Conference 1979, Jena, DDR, 43–61Google Scholar
- 3.Cook, S.A., The complexity of theorem-proving procedures, Proc. of 1971 ACM Theory of Computing Conference, 151–158Google Scholar
- 4.Garey, M.R. and D.S. Johnson, "Strong" NP-Completeness Results: Motivation, Examples and Implications, J.Ass.Comp. Mach 25(1978),499–508Google Scholar
- 5.Garey, M.R. and D.S. Johnson, Computers and Intractability, A Guide to the Theory of NP-completeness, W.H.Freeman and Company, San Franzisco, 1979Google Scholar
- 6.Garey, M.R., Johnson, D.S. and L. Stockmeyer, Some simplified NP-complete graph problems, Theor. Comp. Sci. 1(1976), 237–267Google Scholar
- 7.Jones, N.D., Lien, Y.E. and W.T. Laaser, New problems complete for nondeterministic log space, Math. Syst. Th. 10 (1976), 1–17Google Scholar
- 8.Karp, R.M., Reducibility among combinatorial problems, in Complexity of Computer Computation, Ed. Miller, Thatcher, Plenum Press 1972, 85–103Google Scholar
- 9.Lenstra, J.K. and A.H.G. Rinnoy Kan, Complexity of Scheduling under Precedence Constraints, Operations Research 26 (1978), 22–35Google Scholar
- 10.Monien, B., On a subclass of pseudopolynomial problems, Proc. 8th Symp. on Math. Found. of Comp. Sci., Rydzyna-Zamek, PolandGoogle Scholar
- 11.Papadimitrion, Ch. H., The NP-completeness of the bandwidth minimization problem, Computing 16 (1976), 263–270Google Scholar
- 12.Paz, A. and S. Moran, Non-deterministic polynomial optimization problems and their approximation, Lecture Notes Comp.Sci. 52, 370–379, Springer-Verlag,Berlin-Heidelberg-New York, 1977Google Scholar
- 13.Saxe, J.B., Dynamic Programming algorithms for recognizing small-bandwidth graphs in polynomial time, Technicel Report, Comp.Sci.Dept., Carnegie Mellon University, PittsburghGoogle Scholar
- 14.Sudborough, I.H., Efficient algorithms for path system problems and applications to alternating and time-space complexity classes, Proc. of 1980 IEEE FOCS conferenceGoogle Scholar
- 15.Vornberger, O., Komplexität von Wegeproblemen in Graphen, Bericht Nr. 5/79, Theoret.Inf., Fachbereich Mathe/Inf.,GH.PaderbornGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1981