Let x denote a given nonempty string of length n = Absolute value of x greater-than-or-equal-to 1. A string u is a cover of x if and only if every position of x lies within an occurrence of u within x. Thus x is alway...
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Let x denote a given nonempty string of length n = Absolute value of x greater-than-or-equal-to 1. A string u is a cover of x if and only if every position of x lies within an occurrence of u within x. Thus x is always a cover of itself. In this paper we characterize all the covers of x in terms of an easily computed normal form for x. The characterization theorem then gives rise to a simple recursive algorithm which computes all the covers of x in time THETA(n).
The link or route blocking probabilities of a loss network are typically used to assess its performance. Unfortunately, closed form expressions for these, whilst being easy to write down, are quite intractable to eval...
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The link or route blocking probabilities of a loss network are typically used to assess its performance. Unfortunately, closed form expressions for these, whilst being easy to write down, are quite intractable to evaluate computationally. Consequently, a number of approximations to the blocking probabilities have been proposed. One of the most intensively studied of these is the Erlang fixed-point approximation. We study the dynamical behaviour of performing sequential iteration on the Erlang fixed-point equations and prove that, for an arbitrary fixed-routing topology with constant bandwidth on all routes, sequential iteration converges to the Erlang fixed point. (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper, we improve a width-3 joint sparse form proposed by Okeya, Katoh, and Nogami. After the improvement, the representation can attain an asymtotically optimal complexity found in our previous work. Although...
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In this paper, we improve a width-3 joint sparse form proposed by Okeya, Katoh, and Nogami. After the improvement, the representation can attain an asymtotically optimal complexity found in our previous work. Although claimed as optimal by the authors, the average computation time of multi-scalar multiplication obtained by the representation is 563/1574n + o(n) approximate to 0.3577n + o(n). That number is larger than the optimal complexity 281/786n + o(n) approximate to 0.3575n + o(n) found in our previous work. To optimize the width-3 joint sparse form, we add more cases to the representation. After the addition, we can show that the complexity is updated to 281/786n + o(n) approximate to 0.3575n + o(n), which implies that the modified representation is asymptotically optimal. Compared to our optimal algorithm in the previous work, the modified width-3 joint sparse form uses less dynamic memory, but it consumes more static memory.
Let G be a complete (undirected) graph with 31 vertices. Given a binary weight function on the edges of G, the BINARY MAXIMUM 2-PATH PARTITIONING PROBLEM is to compute a set of l vertex-disjoint simple 2-edge paths wi...
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Let G be a complete (undirected) graph with 31 vertices. Given a binary weight function on the edges of G, the BINARY MAXIMUM 2-PATH PARTITIONING PROBLEM is to compute a set of l vertex-disjoint simple 2-edge paths with maximum total edge weight. The problem is NP-hard (Garey and Johnson 1979) [1]. In this paper we propose a simple local search algorithm with polynomial running time for the problem and analyze its performance for several search depths. For depth 2, we show that the algorithm is a 0.3333-approximation, and that the bound is tight. For depth 3, we show that the algorithm is a 0.4-approximation. For depth 9, we show that the algorithm is a 0.55-approximation, improving on the best-known 0.5265 bound for the problem. We also consider the special case where G is subcubic, that is, the maximum degree in its subgraph induced by the unit-weight edges is 3. In this case we show that the algorithm is a 0.375-approximation for depth 2 and a 0.5-approximation for depth 3. In addition, we show that depth 7 is sufficient for the 0.55 bound guarantee. Finally we give, by means of bad instances, upper bounds on the performance guarantees of the algorithm. For depth 2 we show a 0.4 upper bound in the subcubic case. For depth 3 we show a 0.6 upper bound, as well as a 0.7 upper bound in the subcubic case. For the general (non-negative) weight problem we show a 0.5556 upper bound for depth 3 (for depth 2, the tight 0.3333 ratio holds for this problem as well). (C) 2013 Elsevier B.V. All rights reserved.
The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local sea...
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The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local search. Starting with an upper bound on the number of bins obtained by a greedy heuristic, the presented algorithm iteratively decreases the number of bins, each time searching for a feasible packing of the boxes. The process terminates when a given time limit has been reached or the upper bound matches a pre-computed lower bound. The algorithm can also be applied to two-dimensional bin-packing problems by having a constant depth for all boxes and bins. Computational experiments are reported for two- and three-dimensional instances with up to 200 boxes, showing that the algorithm on average finds-better solutions than do heuristics from the literature.
The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Dir...
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The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Directed Acyclic Graph) approach, an O (kn(2)) time sequential algorithm is designed in this paper to solve the maximum weight k-independent set problem on weighted trapezoid graphs. The weights considered here are all non-negative and associated with each of the n vertices of the graph.
In online platforms, the reviews posted by existing consumers are playing an increasingly important role in the purchasing decisions of potential consumers. Motivated by this observation, we study the problems faced b...
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In online platforms, the reviews posted by existing consumers are playing an increasingly important role in the purchasing decisions of potential consumers. Motivated by this observation, we study the problems faced by a platform selling a single product with no capacity constraint, where the demand is explicitly influenced by the reviews presented to the consumers. More precisely, we model a consumer’s browsing of reviews for a single product as following a cascade click model, with each consumer seeing some initial number of reviews and forming a utility estimate for the product based on the reviews the consumer has read. In the first part of the paper, we consider how to rank the reviews to induce short- and long-term revenue-maximizing purchasing behaviors. In the second part, we study how to set the price of the product. We derive structural insights and bounds on both problems. We also consider the case that the parameters of the model are unknown, where we propose algorithms that learn the parameters and optimize the ranking of the reviews or the price online. We show that our algorithms have regretsO(T23).
Block sorting in the Burrows-Wheeler transformation is to sort all of the n circular shifts of a string of length n lexicographically. We introduce a notion called the width of a sequence of n strings of length n and ...
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Block sorting in the Burrows-Wheeler transformation is to sort all of the n circular shifts of a string of length n lexicographically. We introduce a notion called the width of a sequence of n strings of length n and show that the values of widths are very different between the two types of sequences of strings;(1) a sequence of n randomly generated strings of length n, and (2) the sequence of n circular shifts of a randomly generated string of length n. (C) 2011 Elsevier B.V. All rights reserved.
This study presents an approach to effectively suppress the annoying false contour inherently introduced in a JPEG compressed image. The false contour is mainly caused by the discrepancy between the original DCT coeff...
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This study presents an approach to effectively suppress the annoying false contour inherently introduced in a JPEG compressed image. The false contour is mainly caused by the discrepancy between the original DCT coefficient prior quantization in the encoder and the inverse quantization coefficient in the decoder. In this study, the error diffusion with the optimized error kernels is involved to compensate the quantization errors to the pixels in the neighboring blocks. As documented in the experimental results, the proposed method has been proven to significantly reduce the false contour in a JPEG image. (C) 2014 Elsevier B.V. All rights reserved.
We present an approximation algorithm for graph coloring which achieves a performance guarantee of O(n(log log n)2/(log n)3), a factor of log log n improvement.
We present an approximation algorithm for graph coloring which achieves a performance guarantee of O(n(log log n)2/(log n)3), a factor of log log n improvement.
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