Line extensions-variants of existing products with new appearances, functions, or forms-constitute a significant fraction of products launched each year. While line extensions typically share components with existing ...
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Line extensions-variants of existing products with new appearances, functions, or forms-constitute a significant fraction of products launched each year. While line extensions typically share components with existing products, they can also cannibalize the demand of existing products. The choice of an appropriate set of line extensions is an important recurring issue for a firm and they must incorporate constraints that arise naturally from operational, financial, and marketing considerations, resulting in an analytically challenging optimization problem. We consider several variants of this problem, develop efficient heuristics that deliver near-optimal solutions, and derive a variety of interesting insights on the inherent tradeoffs in the selection of line extensions.
The algorithmic complexity of periodicity detection of Boolean functions given in a polynomial form is investigated. A function is said to be periodic with period if it takes the same values on input strings which dif...
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The algorithmic complexity of periodicity detection of Boolean functions given in a polynomial form is investigated. A function is said to be periodic with period if it takes the same values on input strings which differ only by inverting the components corresponding to nonzero entries in the bit string . Two polynomial-time algorithms for checking whether a given bit string is a period of a given Boolean function are presented. The relationship between the periods of a function and the length of its polynomial is investigated. The problem of finding the periods is explicitly reduced in polynomialtime to the problem of solving a system of Boolean equations.
In this paper, we introduce and solve a particular generalization of the quadratically constrained quadratic programming (QCQP) problem which is frequently encountered in different fields of signal processing and comm...
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ISBN:
(纸本)9781479928934
In this paper, we introduce and solve a particular generalization of the quadratically constrained quadratic programming (QCQP) problem which is frequently encountered in different fields of signal processing and communications. Specifically, we consider such generalization of the QCQP problem that comprises compositions of one-dimensional convex and quadratic functions in the constraint and the objective functions. We show that this class of problems can be precisely or approximately recast as the difference-of-convex functions (DC) programming problem. Although the DC programming problem can be solved through the branch-and-bound methods, these methods do not have any worst-case polynomial-time complexity guarantees. Therefore, we develop a new approach with worst-case polynomial-time complexity that can solve the corresponding DC problem of a generalized QCQP problem. It is analytically guaranteed that the point obtained by this method satisfies the Karsuh-Kuhn-Tucker (KKT) optimality conditions. Furthermore, the global optimality can be proved analytically under certain conditions. The new proposed method can be interpreted in terms of the Newton's method as applied to a non-constrained optimization problem.
Read trimming is a fundamental first step of the analysis of next generation sequencing (NGS) data. Traditionally, read trimming is performed heuristically, and algorithmic work in this area has been neglected. Here, ...
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ISBN:
(纸本)9783319079530;9783319079523
Read trimming is a fundamental first step of the analysis of next generation sequencing (NGS) data. Traditionally, read trimming is performed heuristically, and algorithmic work in this area has been neglected. Here, we address this topic and formulate three constrained optimization problems for block-based trimming, i.e., truncating the same low-quality positions at both ends for all reads and removing low-quality truncated reads. We find that the three problems are NP-hard. However, the non-random distribution of quality scores in NGS data sets makes it tempting to speculate that quality constraints for read positions are typically satisfied by fulfilling quality constraints for reads. Based on this speculation, we propose three relaxed problems and develop efficient polynomial-time algorithms for them. We find that (i) the omitted constraints are indeed almost always satisfied and (ii) the algorithms for the relaxed problems typically yield a higher number of untrimmed bases than traditional heuristics.
In the stable marriage problem, any instance admits the so-called man-optimal stable matching, in which every man is assigned the best possible partner. However, there are instances for which all men receive low-ranke...
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In the stable marriage problem, any instance admits the so-called man-optimal stable matching, in which every man is assigned the best possible partner. However, there are instances for which all men receive low-ranked partners even in the man-optimal stable matching. In this paper we consider the problem of improving the man-optimal stable matching by changing only one mans preference list. We show that the optimization variant and the decision variant of this problem can be solved in time O(n(3)) and O(n(2)), respectively, where n is the number of men (women) in an input. We further extend the problem so that we are allowed to change k mens preference lists. We show that the problem is W[1]-hard with respect to the parameter k and give O(n(2k+1))-time and O(n(k+1))-time exact algorithms for the optimization and decision variants, respectively. Finally, we show that the problems become easy when k = n;we give O(n(2.5) log n)-time and O(n(2))-timealgorithms for the optimization and decision variants, respectively
This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing ...
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This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h. Our technique is based on a refinement of an algorithm of A. Barvinok in the unweighted case (i.e., ha parts per thousand 1). In contrast to Barvinok's method, our method is local, obtains an approximation on the level of generating functions, handles the general weighted case, and provides the coefficients in closed form as step polynomials of the dilation. To demonstrate the practicality of our approach, we report on computational experiments which show that even our simple implementation can compete with state-of-the-art software.
This paper addresses the problem of finding the route with maximum end-to-end spectral efficiency, under the constraint of equal bandwidth sharing, in multihop wireless networks that use time division multiple access ...
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This paper addresses the problem of finding the route with maximum end-to-end spectral efficiency, under the constraint of equal bandwidth sharing, in multihop wireless networks that use time division multiple access (TDMA) or frequency division multiple access (FDMA). The conceptual difficulty of this problem arises from the fact that the associated routing metric is neither isotonic nor monotone, and, thus, it cannot be solved directly using shortest path algorithms. The author has recently presented the first polynomial-time algorithm that solves the problem to exact optimality for TDMA networks. The contribution of this paper is twofold. For TDMA networks, we present a new algorithm that achieves a significant improvement in the computational complexity as compared to the algorithms previously known. For FDMA networks, we introduce the first polynomial-time algorithm that provides provably optimal routes. The proposed algorithms rely on the divide-and-conquer principle and a modified Bellman-Ford algorithm for widest path computation. Our computational results further illustrate the efficiency of the proposed approach. (C) 2011 Elsevier B.V. All rights reserved.
Haplotyping, also known as haplotype phase prediction, is the problem of predicting likely haplotypes based on genotype data. One fast computational haplotyping method is based on an evolutionary model where a perfect...
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Haplotyping, also known as haplotype phase prediction, is the problem of predicting likely haplotypes based on genotype data. One fast computational haplotyping method is based on an evolutionary model where a perfect phylogenetic tree is sought that explains the observed data. An extension of this approach tries to incorporate prior knowledge in the form of a set of candidate haplotypes from which the right haplotypes must be chosen. The objective is to increase the accuracy of haplotyping methods, but it was conjectured that the resulting formal problem constrained perfect phylogeny haplotyping might be NP-complete. In the paper at hand we present a polynomial-time algorithm for it. Our algorithmic ideas also yield new fixed-parameter algorithms for related haplotyping problems based on the maximum parsimony assumption. (C) 2012 Elsevier Inc. All rights reserved.
Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the softwired sense if, for each cluster in the inpu...
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Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the softwired sense if, for each cluster in the input set, at least one tree embedded in the network contains that cluster. Motivated by parsimony we might wish to construct such a network using as few reticulations as possible, or minimizing the level of the network, i.e., the maximum number of reticulations used in any "tangled" region of the network. Although these are NP-hard problems, here we prove that, for every fixed k >= 0, it is polynomial-time solvable to construct a phylogenetic network with level equal to k representing a cluster set, or to determine that no such network exists. However, this algorithm does not lend itself to a practical implementation. We also prove that the comparatively efficient CASS algorithm correctly solves this problem (and also minimizes the reticulation number) when input clusters are obtained from two not necessarily binary gene trees on the same set of taxa but does not always minimize level for general cluster sets. Finally, we describe a new algorithm which generates in polynomial-time all binary phylogenetic networks with exactly r reticulations representing a set of input clusters (for every fixed r >= 0).
Text mining from large scaled data is of great importance in computer science. In this paper, we consider fundamental problems on text mining from compressed strings, i.e., computing a longest repeating substring, lon...
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Text mining from large scaled data is of great importance in computer science. In this paper, we consider fundamental problems on text mining from compressed strings, i.e., computing a longest repeating substring, longest non-overlapping repeating substring, most frequent substring, and most frequent non-overlapping substring from a given compressed string. Also, we tackle the following novel problem: given a compressed text and compressed pattern, compute the representative of the equivalence class of the pattern w.r.t. the text. We present algorithms that solve the above problems in timepolynomial in the size of input compressed strings. The compression scheme we consider is straight line program (SLP) which has exponential compression, and therefore our algorithms are more efficient than any existing algorithms that require decompression of given SLPs.
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