Showing papers on "Dominating set published in 1981"
11 May 1981
TL;DR: Several NP-Complete problems become easier with diminishing bandwidth, however, they remain intractable unless the bandwidth is restricted to c-log2n, for some c>0.
Abstract: 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) = NP and NTISP(poly, log n) = 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))
34 citations
TL;DR: This paper presents a linear algorithm for partitioning an arbitrary tree into a minimum number of subtrees, each having a diameter at mostk, for a givenk.
Abstract: A matching and a dominating set in a graph G are related in that they determine diameter-bounded subtree partitions of G. For a maximum matching and a minimum dominating set, the associate partitions have the fewest numbers of trees. The problem of determining a minimum dominating set in an arbitrary graph G is known to be NP-complete. In this paper we present a linear algorithm for partitioning an arbitrary tree into a minimum number of subtrees, each having a diameter at mostk, for a givenk.
24 citations