A spanning tree T is said to be a tree t-spanner of a graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in network and distributed e...
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A spanning tree T is said to be a tree t-spanner of a graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in network and distributed environments. This problem is NP-hard for general graph even for some special classes of graphs. This problem is polynomial solvable for interval graph when t greater than or equal to 3. When t = 2 the exact complexity of the problem still remains open, but, for t = 2 a polynomial time 2-approximation algorithm is available. An O(n + in) time sequential algorithm is available to solve tree 3-spanner problem. where In and n, respectively, represent the number of edges and the number of vertices of the interval graph. Here, a parallel algorithm is designed to solve a tree 3-spanner problem in O(log n) time using O(n/log n) processors on an EREW PRAM. As a byproduct, a parallel algorithm is also designed to find the increasing sequence of numbers of a set of N numbers in O(log N) time using O(N/log N) processors.
An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O(n(2)/log n) processors on an EREW PRAM, provided the graph has at most O(n...
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An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O(n(2)/log n) processors on an EREW PRAM, provided the graph has at most O(n) maximal independent sets. The best known parallel algorithm takes O(log(2) n) time and O(n(3)/log n) processors on a CREW PRAM.
Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in...
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Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in strings. The present paper focuses on repetitions in two dimensions that manifest themselves in form of two "tandem" occurrences of a same primitive rectangular pattern W where the two replicas touch each other with either one side or corner. Being primitive here means that W cannot be expressed in turn by repeated tiling of another array. The main result of the paper is an O(n(3) log n) algorithm for detecting all "side-sharing" repetitions in an n x n array. This is optimal, based on bounds on the number of such repetitions established in previous work. With easy adaptations, these constructions lead to an equally optimal, O(n(4)) algorithm for repetitions of the second type. (c) 2005 Elsevier B.V. All rights reserved.
Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in...
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Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in strings. The present paper focuses on repetitions in two dimensions that manifest themselves in form of two "tandem" occurrences of a same primitive rectangular pattern W where the two replicas touch each other with either one side or corner. Being primitive here means that W cannot be expressed in turn by repeated tiling of another array. The main result of the paper is an O(n(3) log n) algorithm for detecting all "side-sharing" repetitions in an n x n array. This is optimal, based on bounds on the number of such repetitions established in previous work. With easy adaptations, these constructions lead to an equally optimal, O(n(4)) algorithm for repetitions of the second type. (c) 2005 Elsevier B.V. All rights reserved.
In this paper, we define a family of patterns with don't cares occurring in a text. We call them primitive patterns. The set of primitive patterns forms a basis for all the maximal patterns occurring in the text. ...
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In this paper, we define a family of patterns with don't cares occurring in a text. We call them primitive patterns. The set of primitive patterns forms a basis for all the maximal patterns occurring in the text. The number of primitive patterns is smaller than other known basis. We present an incremental algorithm that computes the primitive patterns occurring at least q times in a text of length n, given the N primitive patterns occurring at least q - 1 times, in time O(|Sigma| Nn(2) log n), where Sigma is the alphabet. In the particular case where q = 2, the complexity in time is only O(|Sigma| n(2) log n). We also give an algorithm that decides if a given pattern is primitive in a given text. These algorithms are generalized, taking many sequences in input. Finally, we give a solution for reducing the number of patterns of interest by using scoring techniques, as we show that the number of primitive patterns is exponential. (C) 2004 Elsevier B. V. All rights reserved.
The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different pos...
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The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different possible rotated patterns. Subsequently, given an m x m array (pattern) and an n x n array (text) over some finite alphabet Sigma, we present a new method yielding an O(n(2)m(3)) time algorithm for this problem. (C) 2003 Published by Elsevier B.V.
The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length in and every length in substring of the text T. Currently, the fastest algorithms for this problem ...
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The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length in and every length in substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O (nk). The Abrahamson algorithm finds the number of mismatches at every location in time O (nrootm log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(nrootk log k). We also show an algorithm that solves the above problem in time O ((n + (nk(3))/m) log k). (C) 2003 Elsevier Inc. All rights reserved.
The tree pattern matching problem over labeled trees is addressed in this paper Several tree pattern matching algorithms are known which are based on the decomposition of the pattern into strings, with each string rep...
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ISBN:
(纸本)0769521606
The tree pattern matching problem over labeled trees is addressed in this paper Several tree pattern matching algorithms are known which are based on the decomposition of the pattern into strings, with each string representing a root-to-leaf path. Among these, Alfs T. Berztiss gave a simple tree pattern matching algorithm which remained unknown to the research community. In this paper the tree pattern matching algorithm of Berztiss is reviewed, its correctness is established, and its complexity is shown to be O(mn) time and space in the worst case and O(n) on the average, where n is the text size and m is the pattern size.
The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length in and every length in substring of the text T. Currently, the fastest algorithms for this problem ...
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ISBN:
(纸本)0898714532
The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length in and every length in substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O (nk). The Abrahamson algorithm finds the number of mismatches at every location in time O (nrootm log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(nrootk log k). We also show an algorithm that solves the above problem in time O ((n + (nk(3))/m) log k). (C) 2003 Elsevier Inc. All rights reserved.
We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and pattern, such as intervals, are si...
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We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and pattern, such as intervals, are singled out. A "match" is a text location where a specified relation between the text and pattern areas is satisfied. In particular we define the structural matching problem of overlap (parity) matching. We seek the text locations where all overlaps of the given pattern and text intervals have even length. We show that this problem can be solved in time O(n log m), where the text length is n and the pattern length is m. As an application of overlap matching, we show how to reduce the string matching with swaps problem to the overlap matching problem. The string matching with swaps problem is the problem of string matching in the presence of local swaps. The best deterministic upper bound known for this problem was O(nm(1/3) log m log sigma) for a general alphabet Sigma, where sigma = min(m, \Sigma\). Our reduction provides a solution to the pattern matching with swaps problem in time 0 (n log m log a). (C) 2002 Elsevier Science (USA). All rights reserved.
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