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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07 Nov 1983
TL;DR: In this article, the authors define a generalized Kolmogorov complexity of finite strings, which measures how much and how fast a string can be compressed and show that this string complexity measure is an efficient tool for the study of computational complexity.
Abstract: In this paper we define a generalized, two-parameter, Kolmogorov complexity of finite strings which measures how much and how fast a string can be compressed and we show that this string complexity measure is an efficient tool for the study of computational complexity. The advantage of this approach is that it not only classifies strings as random or not random, but measures the amount of randomness detectable in a given time. This permits the study how computations change the amount of randomness of finite strings and thus establish a direct link between computational complexity and generalized Kolmogorov complexity of strings. This approach gives a new viewpoint for computational complexity theory, yields natural formulations of new problems and yields new results about the structure of feasible computations.
139 citations
31 May 1999
TL;DR: A scheduling algorithm that is capable of providing service guarantees for input-buffered crossbar switches and uniformly good for all non-uniform traffic is proposed, and thus imply 100% throughput.
Abstract: Based on a decomposition result by Birkhoff (1946) and von Neumann (1953) for a doubly substochastic matrix, in this paper we propose a scheduling algorithm that is capable of providing service guarantees for input-buffered crossbar switches. Our service guarantees are uniformly good for all non-uniform traffic, and thus imply 100% throughput. The off-line computational complexity to identify the scheduling algorithm is O(N/sup 4.5/) for an N/spl times/N switch. Once the algorithm is identified, its on-line computational complexity is O(logN) and its on-line memory complexity is O(N/sup 3/logN). Neither framing nor internal speedup is required for our approach.
138 citations
TL;DR: The extent to which a set of related graph-theoretic properties can be used to accont for the superlinear complexity of computational problems is explored and certain limited lower bounds can be proved by means of such properties.
134 citations
TL;DR: It is proved that HENS is N P -hard, thus refuting the possibility for the existence of a computationally efficient (polynomial) exact solution algorithm for this problem and facilitating the computational complexity analysis of more complex HENS problems and providing new insights to structural properties of the problem.
133 citations
Book•
01 Dec 2005
TL;DR: These topics are considered from an algorithmic point of view stressing the implications for algorithm design.
Abstract: Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design
127 citations