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: This article uses list coloring to model coloring with a fractional number of colors between χ − 1 and χ and turns out that the complexity follows an alternating three-dimensional pattern; understanding this pattern is very important for benchmarking purposes.
Abstract: It is known that the problem of deciding k-colorability of a graph exhibits an easy-hard-easy pattern,—that is, the average-case complexity for backtrack-type algorithms, as a function of k, has a peak. This complexity peak is either at k = χ − 1 or k = χ, where χ is the chromatic number of the graph. However, the behavior around the complexity peak is poorly understood. In this article, we use list coloring to model coloring with a fractional number of colors between χ − 1 and χ. We present a comprehensive computational study on the complexity of backtrack-type graph coloring algorithms in this critical range. According to our findings, an easy-hard-easy pattern can be observed on a finer scale between χ − 1 and χ as well. The highest complexity found this way can be higher than for any integer value of k. It turns out that the complexity follows an alternating three-dimensional pattern; understanding this pattern is very important for benchmarking purposes. Our results also answer the previously open question whether coloring with χ − 1 or with χ colors is harder: this depends on the location of the maximal fractional complexity.
5 citations
13 Nov 1996
TL;DR: A complexity model for discrete surfaces obtained by regular subdivisions of cells is shown, under the assumption that surfaces have uniform orientations in the space, and can be locally compared to planes, to show that their average number of points is a quadratic function of the subdivision factors.
Abstract: The main result of this paper is to exhibit a complexity model for discrete surfaces obtained by regular subdivisions of cells. We use it for estimating the number of points that will be generated by the Dividing-Cubes algorithm to represent the surface of 3D medical objects. Under the assumption that surfaces have uniform orientations in the space, and can be locally compared to planes, we show that their average number of points is a quadratic function of the subdivision factors. We give analytical expressions for the coefficients of the quadratic form.
5 citations
TL;DR: This paper presents an exception for which the time complexity of SBA is at least O(B/sup 3/), and points out the discrepancy in the complexity analysis.
Abstract: In a recent paper by B.S. Yoo and C.R. Das (2002), the so-called stack-based allocation (SBA) algorithm is claimed to be, at worst, O(B/sup 2/) expensive. In this paper, we present an exception for which the time complexity of SBA is at least O(B/sup 3/). Furthermore, we point out the discrepancy in the complexity analysis.
5 citations
01 Nov 2006
TL;DR: The complexity of MIMO sphere decoder is evaluated in terms of resource complexity and processing cycle with various tree- searching algorithm for SD and Schnorr Euchner algorithm has the smallest resource complexity among tree-searching algorithms for SD.
Abstract: Since finding the nearest point in a lattice for multi -input multi-output (MIMO) channels is NP-hard, simplified algorithms such as a sphere decoder (SD) have been proposed with various tree-searching strategy. This paper evaluate the complexity of MIMO sphere decoder in terms of resource complexity and processing cycle with various tree- searching algorithm for SD. Resource complexity is analyzed in closed form with various parameter such as the number of antennas and modulations, etc. and processing cycles is evaluated by computer simulation, as a result the resource complexity of Fincke and Phost algorithm is the lowest resource complexity among tree-searching algorithms for SD, but to obtain same processing cycles per one MIMO vector, Schnorr Euchner algorithm has the smallest resource complexity among tree-searching algorithms for SD.
5 citations
20 Mar 2016
TL;DR: The proposed algorithm generalizes the Orthonormal Projection Approximation Subspace Tracking approach for tracking a class of third-order tensors which have one dimension growing with time and has linear complexity, good convergence rate and good estimation accuracy.
Abstract: We present a fast adaptive PARAFAC decomposition algorithm with low computational complexity. The proposed algorithm generalizes the Orthonormal Projection Approximation Subspace Tracking (OPAST) approach for tracking a class of third-order tensors which have one dimension growing with time. It has linear complexity, good convergence rate and good estimation accuracy. To deal with large-scale problems, a parallel implementation can be applied to reduce both computational complexity and storage. We illustrate the effectiveness of our algorithm in comparison with the state-of-the-art algorithms through simulation experiments.
5 citations