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: Weak average-case analysis as mentioned in this paper is an attempt to achieve theoretical complexity results that are closer to practical experience than those resulting from traditional approaches, and has been used in other areas such as nonasymptotic random matrix theory and compressive sensing.
17 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
Journal Article•
TL;DR: This work presents the first example of a natural distribution on instances of an NP-complete problem, with high probability a random formula from this distribution is unsatisfiable, but has a short proof that can be found easily, and does not have a short (general) resolution proof.
Abstract: We present the first example of a natural distribution on instances of an NP-complete problem, with the following properties. With high probability a random formula from this distribution (a) is unsatisfiable, (b) has a short proof that can be found easily, and (c) does not have a short (general) resolution proof. This happens already for a very low clause/variable density ratio of = logn (n is the number of variables). This is the first example of such a natural distribution for which general resolution proofs are not the best way for proving unsatisfiability of random instances. Our result gives hope that efficient proof methods might be found for random 3-CNFs with small clause density (significantly less than pn).
17 citations
09 Jul 2007
TL;DR: It follows from the existential result that any function that is complete for the class of functions with polylogarithmic nondeterministic k-party communication complexity does not have polylogARithmic deterministic complexity.
Abstract: We solve some fundamental problems in the number-onforehead (NOF) k-party communication model. We show that there exists a function which has at most logarithmic communication complexity for randomized protocols with a one-sided error probability of 1/3 but which has linear communication complexity for deterministic protocols. The result is true for k = nO(1) players, where n is the number of bits on each players' forehead. This separates the analogues of RP and P in the NOF communication model. We also show that there exists a function which has constant randomized complexity for public coin protocols but at least logarithmic complexity for private coin protocols. No larger gap between private and public coin protocols is possible. Our lower bounds are existential and we do not know of any explicit function which allows such separations. However, for the 3-player case we exhibit an explicit function which has Ω(log log n) randomized complexity for private coins but only constant complexity for public coins.
It follows from our existential result that any function that is complete for the class of functions with polylogarithmic nondeterministic k-party communication complexity does not have polylogarithmic deterministic complexity. We show that the set intersection function, which is complete in the number-in-hand model, is not complete in the NOF model under cylindrical reductions.
17 citations
TL;DR: Simulation results confirm fast convergence rate and small misalignment of the proposed new variable step-size pseudo affine projection (VSS-PAP) algorithm, which not only has a much lower complexity than the VSS-AP algorithm but also provides performance comparable with the conventional algorithm.
Abstract: Recently, a variable step-size affine projection (VSS-AP) algorithm has been introduced. The algorithm provides faster convergence rate and lower misadjustment but has heavy computational complexity. Proposed is a new variable step-size pseudo affine projection (VSS-PAP) algorithm, which not only has a much lower complexity than the VSS-AP algorithm but also provides performance comparable with the conventional algorithm. Simulation results confirm fast convergence rate and small misalignment of the proposed algorithm with less computational complexity.
17 citations