This paper introduces a special class of mathematical programming problem which maximizes the minimal value of a set of linear functions subject to a single linear constraint and upper bounding constraint on each vari...
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This paper introduces a special class of mathematical programming problem which maximizes the minimal value of a set of linear functions subject to a single linear constraint and upper bounding constraint on each variable. An O(n) algorithm for solving this problem is described by exploiting its special structure.
We investigate a special case of the bottleneck transportation problem where the number s of sources is bounded by a constant and not part of the input. For the subcase s = 2, a best-possible linear-time algorithm has...
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We investigate a special case of the bottleneck transportation problem where the number s of sources is bounded by a constant and not part of the input. For the subcase s = 2, a best-possible linear-time algorithm has been derived by Varadarajan [Oper. Res. Lett. 10 (1991) 525-529]. In this note we show that for any fixed number s greater than or equal to 1, the bottleneck transportation problem with s sources can be solved in linear-time. The algorithm is conceptually simple, and easy to implement. (C) 1999 Elsevier Science B.V, All rights reserved.
We consider a well-known strongly NP-hard K-Means problem. In this problem, one needs to partition a finite set of N points in Euclidean space into K non-empty clusters minimizing the sum over all clusters of the intr...
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ISBN:
(纸本)9783030406165
We consider a well-known strongly NP-hard K-Means problem. In this problem, one needs to partition a finite set of N points in Euclidean space into K non-empty clusters minimizing the sum over all clusters of the intracluster sums of the squared distances between the elements of each cluster and its centers. The cluster's center is defined as the centroid (geometrical center). We analyze the polynomial-solvable one-dimensional case of the problem and propose a novel parameterized approach to this case. Within the framework of this approach, we, firstly, introduce a new parameterized formulation of the problem for this case and, secondly, we show that our approach and proposed algorithm allows one to find an optimal input data partition and, contrary to existing approaches and algorithms, simultaneously find an optimal clusters number in O(N) time.
Since the introduction of the Perfect Phylogeny Haplotyping ( PPH) Problem in RECOMB 2002 ( Gusfield, 2002), the problem of finding a linear-time ( deterministic, worst-case) solution for it has remained open, despite...
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ISBN:
(纸本)3540258663
Since the introduction of the Perfect Phylogeny Haplotyping ( PPH) Problem in RECOMB 2002 ( Gusfield, 2002), the problem of finding a linear-time ( deterministic, worst-case) solution for it has remained open, despite broad interest in the PPH problem and a series of papers on various aspects of it. In this paper, we solve the open problem, giving a practical, deterministic linear-time algorithm based on a simple data structure and simple operations on it. The method is straightforward to program and has been fully implemented. Simulations show that it is much faster in practice than prior nonlinear methods. The value of a linear-time solution to the PPH problem is partly conceptual and partly for use in the inner loop of algorithms for more complex problems, where the PPH problem must be solved repeatedly.
In this paper we propose a new method for deriving a practical linear-time algorithm from the specification of a maximum-weightsum problem: From the elements of a data structure x, find a subset which satisfies a cert...
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In this paper we propose a new method for deriving a practical linear-time algorithm from the specification of a maximum-weightsum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for automatically generating linear-time algorithms are theoretically appealing, but the algorithms generated are hardly useful in practice due to a huge constant factor for space and time. The key points of our approach are to express the property p by a recursive boolean function over the structure x rather than a usual logical predicate and to apply program transformation techniques to reduce the constant factor. We present an optimization theorem, give a calculational strategy for applying the theorem, and demonstrate the effectiveness of our approach through several nontrivial examples which would be difficult to deal with when using the methods previously available.
In this paper we propose a new method for deriving a practical linear-time algorithm from the specification of a maximum-weightsum problem: From the elements of a data structure x, find a subset which satisfies a cert...
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ISBN:
(纸本)9781581132021
In this paper we propose a new method for deriving a practical linear-time algorithm from the specification of a maximum-weightsum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for automatically generating linear-time algorithms are theoretically appealing, but the algorithms generated are hardly useful in practice due to a huge constant factor for space and time. The key points of our approach are to express the property p by a recursive boolean function over the structure x rather than a usual logical predicate and to apply program transformation techniques to reduce the constant factor. We present an optimization theorem, give a calculational strategy for applying the theorem, and demonstrate the effectiveness of our approach through several nontrivial examples which would be difficult to deal with when using the methods previously available.
This paper demonstrates the generation of a linear-time query-answering algorithm based on the constructive proof of Higman's lemma by Murthy and Russell [Proceedings of the 5th IEEE Symposium on Logic in Computer...
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This paper demonstrates the generation of a linear-time query-answering algorithm based on the constructive proof of Higman's lemma by Murthy and Russell [Proceedings of the 5th IEEE Symposium on Logic in Computer Science, 1990, p. 257-267]. The target problem is linear-time evaluation of a fixed disjunctive monadic query on an indefinite database over linearly ordered domains, first posed by van der Meyden [Proceedings of the 11th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1992, p. 331-345]. Van der Meyden showed the existence of a linear-time algorithm, but an explicit construction has, until now, not been reported. (C) 2003 Elsevier Science (USA). All rights reserved.
This paper demonstrates the generation of a linear-time query-answering algorithm based on the constructive proof of Higman's lemma by Murthy and Russell [Proceedings of the 5th IEEE Symposium on Logic in Computer...
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This paper demonstrates the generation of a linear-time query-answering algorithm based on the constructive proof of Higman's lemma by Murthy and Russell [Proceedings of the 5th IEEE Symposium on Logic in Computer Science, 1990, p. 257-267]. The target problem is linear-time evaluation of a fixed disjunctive monadic query on an indefinite database over linearly ordered domains, first posed by van der Meyden [Proceedings of the 11th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1992, p. 331-345]. Van der Meyden showed the existence of a linear-time algorithm, but an explicit construction has, until now, not been reported. (C) 2003 Elsevier Science (USA). All rights reserved.
Despite significant advances in linear-time scanning algorithms, particularly those based wholly or in part on either Cook's linear-time simulation of two-way deterministic pushdown automata or Weiner's algori...
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A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n...
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A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n, the algorithm guarantees O(log n/g*) approximation ratio without suffix tree construction. (C) 2004 Elsevier B. V. All rights reserved.
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