Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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TL;DR: The computational complexity of a strategy improvement algorithm by Hoffman and Karp for simple stochastic games is studied, and a bound of O(2^n/n) on the convergence time of the Hoffman-Karp algorithm, and the first non-trivial upper bounds on the converge time of these strategy improvement algorithms are proved.
11 citations
TL;DR: The order structure allows us to prove some topological and quasi-metric properties of the new dual complexity spaces and it is shown that these complexity spaces are, under certain conditions, Hausdorff and satisfy a kind of completeness.
11 citations
TL;DR: It is shown that, for every k > 1, any algorithm that would yield an optimal k-processor schedule of a loop-free program, when such a schedule exists, will be of exponential-time complexity.
Abstract: The parallel scheduling of a partially ordered set of tasks has received great attention. The partially ordered tasks can be viewed as components of a straight-line program. In this note, we discuss some aspects of the nonpreemptive parallel scheduling of a program with more general control structures. We examine the existence of optimal k-processor schedules, and in line with recent interest in the complexity of computer computations and algorithms, we study the complexity of constructing optimal k-processor schedules. In particular we show that, for every k > 1, any algorithm that would yield an optimal k-processor schedule of a loop-free program, when such a schedule exists, will be of exponential-time complexity.
11 citations
07 Jul 2013
TL;DR: This paper analyzes the average joint complexity when both strings are generated by two Markov sources and provides fast converging asymptotic expansions and presents some experimental results showing usefulness of the joint complexity to text discrimination.
Abstract: We propose a classification test to discriminate Markov sources based on the joint string complexity. String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define the joint string complexity as the cardinality of the set of words which both strings have in common. In this paper we analyze the average joint complexity when both strings are generated by two Markov sources. We provide fast converging asymptotic expansions and present some experimental results showing usefulness of the joint complexity to text discrimination.
11 citations
TL;DR: The complexity of Bongartz's algorithm for determining a maximal common direct summand of a pair of modules M, N over k-algebra Λ is studied and it is shown that it applies to the isomorphism problem having at least an exponential complexity in a direct approach.
Abstract: We study the complexity of Bongartz's algorithm for determining a maximal common direct summand of a pair of modules M, N over k-algebra Λ; in particular, we estimate its pessimistic computational complexity Orm6n2n + m log n, where m = dimkM ≤ n = dimkN and r is a number of common indecomposable direct summands of M and N. We improve the algorithm to another one of complexity Orm4n2n+m log m and we show that it applies to the isomorphism problem having at least an exponential complexity in a direct approach. Moreover, we discuss a performance of both algorithms in practice and show that the “average” complexity is much lower, especially for the improved one which becomes a part of QPA package for GAP computer algebra system.
11 citations