The complexity of path problems in graphs and path systems of bounded bandwidth

  • I. H. Sudborough
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)


The graph accessibility problem (GAP), the solvable path system problem (SPS), and the and/or graph accessibility problem (AGAP) restricted to graphs or path systems of bandwidth S(n), for some function S on the natural numbers, are considered. These problems are denoted by GAP(S(n)), SPS(S(n)), and AGAP(S(n)), respectively. The monotone and acyclic versions of AGAP(S(n)) are also considered, denoted by \(AGA\vec P\) (S(n)) and AAGAP(S(n)), respectively. It is shown that AGAP(S(n)) and SPS(S(n)) are equivalent via log space reductions for finite-degree graphs and path systems. (This equivalence is also valid for montone graphs and path systems.) It is also shown that AAGAP(S(n)) is in NTISP(poly,S(n)), i.e. the class of problems solvable by nondeterministic algorithms in polynomial time and simultaneous S(n) Space. Previous results that show GAP(S(n)) ε DSPACE (log S(n) × log n) and AGAP(S(n)) ε DSPACE(S(n) × log n) are surveyed. (It is known, also, that \(AGA\vec P\) (S(n)) is in DTISP(poly,S(n)) and, in fact, is log space complete for this class.)


Turing Machine Black Marker White Marker Path System Pebble Game 
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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  1. (1).
    Aleliunas, R., R.M. Karp, R.J. Lipton, L.Lovasz, C. Rackoff, Random walks, universal sequences, and the complexity of maze problems, Proceedings 1979 IEEE Foundations of Computer Science Conference.Google Scholar
  2. (2).
    Chandra, A.K., D. Kozen, L.J. Stockmeyer, Alternation, Technical Report RC 7489 (# 32286), IBM T.J. Watson Research Center, Yorktown Heights, New York.Google Scholar
  3. (3).
    Cook, S.A., Path systems and language recognition, 1970 ACM Symp. Theory of Computing, 70–72.Google Scholar
  4. (4).
    —, An observation on time-storage trade-off, J. Computer System Sci. (1974), 308–316.Google Scholar
  5. (5).
    —, Deterministic CFLs are accepted simultaneously in polynomial time and log squared space, 1979 ACM Symp. Theory of Computing, 338–345.Google Scholar
  6. (6).
    —, Towards a complexity theory of synchronous parallel computation, Technical Report # 141/80, University of Toronto, Canada.Google Scholar
  7. (7).
    Cook, S.A. and R. Sethi, Storage requirements for deterministic polynomial time recognizable languages, J. Computer System Sci, 13 (1976), 25–37.Google Scholar
  8. (8).
    Garey, M.R., R.L. Graham, D.S. Johnson, and D.E. Knuth, Complexity results for bandwidth minimization, SIAM J. Appl. Math. (May 1978), 477–495.Google Scholar
  9. (9).
    Gilbert, J.R., T. Lengauer, R.E. Tarjan, The pebbling problem is complete in polynomial space, 1979 ACM Symp. Theory of Computing, 237–248.Google Scholar
  10. (10).
    Immerman, N. Length of predicate calculus formulas as a new complexity measure, Proc. 1979 IEEE FOCS, 337–347.Google Scholar
  11. (11).
    Lewis, H., and C.H. Papadimitriou, Symmetric space bounded Computation, Proceedings of 1980 ICALP Conference, Lecture Notes in Computer Sience Vd. 85, Springer-Verlag, pp. 374–384.Google Scholar
  12. (12).
    Lingas, A., A P-Space complete problem related to a pebble game, 1978 ICALP Proceedings, Vol. 62, Lecture Notes in Computer Science, Springer-Verlag, 300–321.Google Scholar
  13. (13).
    Monien, B. and I.H. Sudborough, Eliminating nondeterminism from Turing machines which use less than logarithm worktape space, 1979 ICALP Proceedings, Vol. 72, Lecture Notes in Computer Science, Springer-Verlag, 431–445.Google Scholar
  14. (14).
    Monien, B., and I.H. Sudborough, Bounding the bandwidth of NP-complete problems, Proceedings of Workshop on Graph Theoretic Concepts in Computer Science, Bad Honnef/Bonn, June 15–18, 1980.Google Scholar
  15. (15).
    Papadimitriou, C.H., The NP-completeness of the bandwidth minimization problem, Computing (1976), 263–270.Google Scholar
  16. (16).
    Savitch, W.J., Relationship between nondeterministic and deterministic tape complexities, J. Computer System Sci. (1970), 177–192.Google Scholar
  17. (17).
    Saxe, J.B., Dynamic-Programming algorithms for recognizing small-bandwidth graphs in polynomial time, Technical Report, Computer Science Dept. Carnegie Mellon University, Pittsburgh, Pennsylvania.Google Scholar
  18. (18).
    Sudborough, I.H., Efficient algorithms for path system problems and applications to alternating and time-space complexity classes, Proceedings of 1980 IEEE Foundations of Computer Science Conference (to appear).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • I. H. Sudborough
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität-Gesamthochschule PaderbornPaderbornWest Germany

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