Showing papers on "Average-case complexity published in 1981"
Journal Article•
106 citations
TL;DR: A number of simple tools are developed which facilitate the study of the structure of sets in NP and yield the existence of a minimal pair of sets A, S E NP which are not complete, which can be used to constru@ partial orders of degrees with respect to polynomial time reducibility.
79 citations
TL;DR: If the time bounds defining two nondeterministic complexity classes are too close for separation by the two known techniques, then they are almost too close to separation by any relativizable technique, implying $\operatorname{NSPACE}(\log n) = \operatORName{DSPACE})$.
Abstract: If the time bounds defining two nondeterministic complexity classes are too close for separation by the two known techniques, then they are almost too close for separation by any relativizable technique. Proof of an analogous result for space would be a major breakthrough, implying $\operatorname{NSPACE}(\log n) = \operatorname{DSPACE}(\log n)$.
21 citations
TL;DR: A survey is given of some results on the complexity of algorithms and computations published up to 1973.
Abstract: A survey is given of some results on the complexity of algorithms and computations published up to 1973.
18 citations
TL;DR: An algorithm for generation of trees of a connected, non-oriented, and simple graph is presented and the time complexity is drastically reduced compared to the brute-force technique.
Abstract: An algorithm for generation of trees of a connected, non-oriented, and simple graph is presented in this paper. The space complexity of the algorithm is independent of the number of trees and the time complexity is drastically reduced compared to the brute-force technique. The algorithm is easily programmable. Experimental results for several graphs are presented.
17 citations
TL;DR: A logical complexity measure — Horn complexity — for Boolean functions which measures the minimal length of quasi-Horn definitions of such functions by propositional formulae is proposed.
Abstract: We propose in this paper a logical complexity measure -- Horn complexity -- for Boolean functions which measures the minimal length of quasi-Horn definitions of such functions by propositional formulae. The interest for this complexity measure comes on the one hand from the observation that the satisfiability problem for Horn formulae is in P, on the other hand from a strong connection to Cook's problem. We show the proposed Horn complexity to be polynomially equivalent to network complexity and therefore to Turing complexity for Boolean functions.
15 citations
TL;DR: The proposed method for proving the lower bound of circuit complexity in the s.
Abstract: A set of disjunctions of some variables is constructed and a nonlinear lower bound is proved for the circuit complexity of this set in systems of functional elements (s. f. e.)* in a fixed monotone basis. The proposed method for proving the lower bound of circuit complexity in the s. f. e. differs from previously known methods (in a monotone basis).
3 citations
TL;DR: This paper studies critically six shortest-path algorithms which are considered to be highly efficient and elegant, and presents a comparison of their computational complexity, simplicity, accessibility, applicability, capacity and speed.
Abstract: Built into several heuristics available for the topological design of computer networks, and inherent in the multicommodity nature of flow, is the determination of the shortest paths between pairs of nodes. Owing to the repeated requirement for shortest-path analyses during the course of optimization, the computational complexity of the heuristics depends upon the computational complexity of the shortest-path problem. This paper studies critically six shortest-path algorithms which are considered to be highly efficient and elegant, and presents a comparison of their computational complexity, simplicity, accessibility, applicability, capacity and speed.
2 citations
1 citations
TL;DR: The author shows that the question of algebraic complexity reduces to determining the existence of what he calls (r) factorizations of A
Abstract: Defines and studies a class of on-line algebraic problems; a particular problem in this class is specified by providing an n×n matrix A. The author shows that the question of algebraic complexity reduces to determining the existence of what he calls (r, u) factorizations of A. Given an n×n matrix A, a factorization A =RU (R and U are n×m and m×n matrices, respectively; m unconstrained) is called an (r, u) factorization, provided that no row of R has more than r nonzero entries and no column of U has more than u nonzero entries. The existence of (r, u) factorization is explored from a general perspective.