Summary
Several problems are shown to be log space complete, when restricted to bandwidth f(n), for the subclass of NP defined by nondeterministic polynomial time bounded Turing machines with a simultaneous f(n) space restriction, denoted by NTISP(poly, f(n)). These problems are NOT-ALL-EQUAL 3SAT, MONOCHROMATIC TRIANGLE, CUBIC SUBGRAPH, DOMINATING SET, ONE-IN-THREE 3SAT and MONOTONE 3SAT. The problems DOMATIC NUMBER, PARTITION INTO FORESTS and DISJOINT CONNECTING PATHS restricted to bandwidth f(n) are shown to be log space hard for NTISP(poly, f(n)). Their membership in the class NTISP(poly, f(n)) is currently open. As one application of these results, we note that the first six of the problems mentioned are examples of NSPACE(log n) complete problems when restricted to bandwidth log n.
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All of the authors were partially supported by NSF grants MCS 79-08919 and MCS 81-09280
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Chung, M.J., Evangelist, W.M. & Sudborough, I.H. Complete problems for space bounded subclasses of NP. Acta Informatica 22, 379–395 (1985). https://doi.org/10.1007/BF00288774
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DOI: https://doi.org/10.1007/BF00288774