Relations Among Complexity Measures
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A PSPACE Complete Problem Related to a Pebble Game
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
On Eliminating Nondeterminism From Turing Machines Which Use Less Than Logarithmic Worktape Space
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Bounding the Bandwidth of NP-Complete Problems
WG '80 Proceedings of the International Workshop on Graphtheoretic Concepts in Computer Science
Deterministic CFL's are accepted simultaneously in polynomial time and log squared space
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
The relationship between the bandwidth of computational problems and their complexity
The relationship between the bandwidth of computational problems and their complexity
Efficient approximation algorithms for the routing open shop problem
Computers and Operations Research
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Bandwidth restrictions are considered on several NP-Complete problems, including the following problems: (1) 3-Satisfiability, (2) Independent Set and Vertex Cover, (3) Simple Max Cut (4) Partition into Triangles, (5) 3-Dimensional Matching, (6) Exact Cover by 3 Sets, (7) Dominating Set, (8) Graph Grundy Numbering (for graphs of finite degree), (9) 3-Colorability, (10) Directed and Undirected Hamiltonian Circuit, (11) Bandwidth Minimization, and (12) Feedback Vertex Set and Feedback Arc Set. It is shown that each of the problems (1)-(12) when restricted to graphs (formulas, triples, or sets) of bandwidth bounded by a function f is log space hard for the complexity class NTISP (poly,f(n)). (NTISP(poly,f(n)) denotes the family of problems solvable nondeterministically in polynomial time and simultaneous f(n) space, e.g., NTISP(poly,poly) &equil; NP and NTISP(poly, log n) &equil; NSPACE(log n).). In fact, (1)-(9) are log space complete for NTISP(poly,f(n)) when the bandwidth is bounded by the function f. This means, for example, that (1)-(9) provide several new examples of problems complete for NSPACE(log n), and hence solvable in polynomial time deterministically, when restricted to bandwidth log2n. In general, for a function f, if any of the problems (1)-(12), when restricted to bandwidth f(n), could be solved deterministically in polynomial time, then NTISP(poly, f(n)) @@@@ P. (This does not seem particularly likely even when f(n) &equil; log2n.) This indicates that several NP-Complete problems become easier with diminishing bandwidth. However, they remain intractable unless the bandwidth is restricted to c-log2n, for some c0.