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.

On the average sequence complexity

Abstract: This paper discusses the measure of complexity of a sequence called the complexity index. The complexity index captures the "richness of the language" used in a sequence. The measure is simple but quite intuitive. Sequences with low complexity index contain a large number of repeated substrings and they eventually become periodic (e.g., tandem repeats in a DNA sequence). The complexity index is used to characterize the sequence statistically and has a long history of applications in several fields, such as data compression, computational biology, data mining, computational linguistics, among others.

Fine-grained complexity of integer programming: The case of bounded branch-width and rank.

Abstract: We use the Exponential Time and Strong Exponential Time hypotheses (ETH & SETH) to provide conditional lower bounds on the solvability of the integer programming (IP) problem. We provide evidence that the running times of known pseudo-polynomial time algorithms solving IP, when the number of constraints is a constant [Papadimitriou, J. ACM 1981] and when the branch-width of the corresponding column-matroid is a constant [Cunningham and Geelen, IPCO 2007], are probably optimal. ∗Department of Informatics, University of Bergen, Norway. {fomin|fahad.panolan}@ii.uib.no †Technische Universität Wien, Vienna, Austria. ramanujan@ac.tuwien.ac.at ‡The Institute of Mathematical Sciences, Chennai, India. saket@imsc.res.in ar X iv :1 60 7. 05 34 2v 1 [ cs .D S] 1 8 Ju l 2 01 6

Randomizing Reductions of Search Problems

Abstract: This paper closes a gap in the foundations of the theory of average case complexity. First, we clarify the notion of a (feasible) solution for a search problem and prove its robustness. Second, we give a general and usable notion of many-one randomizing reductions of search problems and prove that it has desirable properties. All reductions of search problems to search problems in the literature on average case complexity can be viewed as such many-one randomizing reductions. This includes those reductions in the literature that use iterations and therefore do not look manyone.

An efficient algorithm for the k-error linear complexity of periodic sequences

Abstract: An efficient algorithm for computing the k-error linear complexity of a sequence with period pn over GF(q) is presented, where p and q are primes, with q a primitive root modulo p2. The new algorithm is a generalization of an algorithm presented by Xiao, Wei, Lam and Imamura.

Asymptotic optimal detection for MIMO communication systems employing tree search with incremental channel partition preprocessing

Abstract: The high complexity of optimal detection for spatial multplexing multiple-input multiple-output systems motivates the need for more practical alternatives. Among many suboptimal schemes reported in the literature, very few can be proven to provide close to optimal performance with low fixed complexity. The recently introduced Selection based Minimum Mean Square Error Ordered Successive Interference Cancellation (Sel-MMSE-OSIC) algorithm is one such scheme that employs list-based detection. Simulations results showed that its performance is nearly indistinguishable from optimal at almost all signal-to-noise ratio (SNR) levels. In this paper, we propose an improved asymptotically optimal fixed-complexity algorithm that provides substantial complexity reductions over Sel-MMSE-OSIC with similar error rate performance. This scheme is based on simplified channel partition and efficient tree-based list detection. To achieve further reductions in complexity for large constellation sizes, a variable complexity version of this scheme is proposed. The resulting algorithm is a variable complexity scheme that operates on a very small subset of candidates and employs an improved channel partition preprocessing that not only reduces complexity but also guarantees high SNR optimality over space uncorrelated channels. Simulations results confirm that the proposed scheme provides significant complexity reductions over conventional variable complexity detection schemes. Copyright © 2012 John Wiley & Sons, Ltd.