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A UNIFIED ALGORITHM FOR ACCELERATING EDITDISTANCE COMPUTATION via . . .
, 2009
"... The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamicprogramming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N²) time. To th ..."
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The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamicprogramming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N²) time. To this date, this quadratic upperbound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings. As it turns out, practically all known o(N 2) editdistance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single editdistance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using straightline programs. These provide a generic platform
CarpeDiem: Optimizing the Viterbi Algorithm and Applications to Supervised Sequential Learning
"... The growth of information available to learning systems and the increasing complexity of learning tasks determine the need for devising algorithms that scale well with respect to all learning parameters. In the context of supervised sequential learning, the Viterbi algorithm plays a fundamental role ..."
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The growth of information available to learning systems and the increasing complexity of learning tasks determine the need for devising algorithms that scale well with respect to all learning parameters. In the context of supervised sequential learning, the Viterbi algorithm plays a fundamental role, by allowing the evaluation of the best (most probable) sequence of labels with a time complexity linear in the number of time events, and quadratic in the number of labels. In this paper we propose CarpeDiem, a novel algorithm allowing the evaluation of the best possible sequence of labels with a subquadratic time complexity. 1 We provide theoretical grounding together with solid empirical results supporting two chief facts. CarpeDiem always finds the optimal solution requiring, in most cases, only a small fraction of the time taken by the Viterbi algorithm; meantime, CarpeDiem is never asymptotically worse than the Viterbi algorithm, thus confirming it as a sound replacement.
Efficient Staggered Decoding for Sequence Labeling
 Proceedings of ACL
, 2010
"... The Viterbi algorithm is the conventional decoding algorithm most widely adopted for sequence labeling. Viterbi decoding is, however, prohibitively slow when the label set is large, because its time complexity is quadratic in the number of labels. This paper proposes an exact decoding algorithm that ..."
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The Viterbi algorithm is the conventional decoding algorithm most widely adopted for sequence labeling. Viterbi decoding is, however, prohibitively slow when the label set is large, because its time complexity is quadratic in the number of labels. This paper proposes an exact decoding algorithm that overcomes this problem. A novel property of our algorithm is that it efficiently reduces the labels to be decoded, while still allowing us to check the optimality of the solution. Experiments on three tasks (POS tagging, joint POS tagging and chunking, and supertagging) show that the new algorithm is several orders of magnitude faster than the basic Viterbi and a stateoftheart algorithm,
Computing the Discrete Fréchet Distance in Subquadratic Time ∗
, 2012
"... The Fréchet distance is a similarity measure between two curves ..."
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The Fréchet distance is a similarity measure between two curves
Accelerating Dynamic Programming
, 2009
"... Dynamic Programming (DP) is a fundamental problemsolving technique that has been widely used for solving a broad range of search and optimization problems. While DP can be invoked when more specialized methods fail, this generality often incurs a cost in efficiency. We explore a unifying toolkit fo ..."
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Dynamic Programming (DP) is a fundamental problemsolving technique that has been widely used for solving a broad range of search and optimization problems. While DP can be invoked when more specialized methods fail, this generality often incurs a cost in efficiency. We explore a unifying toolkit for speeding up DP, and algorithms that use DP as subroutines. Our methods and results can be summarized as follows. – Acceleration via Compression. Compression is traditionally used to efficiently store data. We use compression in order to identify repeats in the table that imply a redundant computation. Utilizing these repeats requires a new DP, and often different DPs for different compression schemes. We present the first provable speedup of the celebrated Viterbi algorithm (1967) that is used for the decoding and training of Hidden Markov Models (HMMs). Our speedup relies on the compression of the HMM’s observable sequence. – Totally Monotone Matrices. It is well known that a wide variety of DPs can be reduced to the problem of finding row minima in totally monotone matrices. We introduce this scheme in the context of planar graph problems. In particular, we show that planar graph problems
A Parallel Implementation of Viterbi’s Decoding Algorithm
"... Abstract. This report describes parallel Java implementations of several variants of Viterbi’s algorithm, discussed in my recent paper [1]. The aim of this project is to study the issues that arise when trying to implement the approach of [1] in parallel using Java. I compare and discuss the perform ..."
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Abstract. This report describes parallel Java implementations of several variants of Viterbi’s algorithm, discussed in my recent paper [1]. The aim of this project is to study the issues that arise when trying to implement the approach of [1] in parallel using Java. I compare and discuss the performance of several variants under various circumstances. 1
Open Access
"... Efficient algorithms for training the parameters of hidden Markov models using stochastic expectation maximization (EM) training and Viterbi training ..."
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Efficient algorithms for training the parameters of hidden Markov models using stochastic expectation maximization (EM) training and Viterbi training
Symposium on Theoretical Aspects of Computer Science year (city), pp. numbers www.stacsconf.org A UNIFIED ALGORITHM FOR ACCELERATING EDITDISTANCE COMPUTATION
"... Abstract. The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamicprogramming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N 2) t ..."
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Abstract. The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamicprogramming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N 2) time. To this date, this quadratic upperbound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings. As it turns out, practically all known o(N 2) editdistance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single editdistance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using straightline programs. These provide a generic platform
Unified CompressionBased Acceleration of EditDistance Computation
"... The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N²) time. To thi ..."
Abstract
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The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the editdistance between a pair of strings of total length O(N) in O(N²) time. To this date, this quadratic upperbound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings. As it turns out, practically all known o(N 2) editdistance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single editdistance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using straight line programs. These provide a generic platform for representing many popular compression schemes including the LZfamily, RunLength Encoding, BytePair Encoding, and dictionary methods. For two strings of total length N having straightline program representations of total size n, we present an
Improved CompressionBased Acceleration of EditDistance Computation
"... Abstract. We focus on accelerating the known solutions for the classical editdistance problem via compression techniques. Using straightline programs we show a single editdistance algorithm that works for strings which compress well under many popular compression schemes including the LZfamily, R ..."
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Abstract. We focus on accelerating the known solutions for the classical editdistance problem via compression techniques. Using straightline programs we show a single editdistance algorithm that works for strings which compress well under many popular compression schemes including the LZfamily, RunLength Encoding, BytePair Encoding, and dictionary methods. For two strings of total length N having straightline program representations of total size n, we present an algorithm running in O(nN lg(N/n)) time for computing the editdistance of these two strings under any rational scoring function, and an O(n 2/3 N 4/3) time algorithm for arbitrary scoring functions. Our new result, while providing a significant speedup for highly compressible strings, does not surpass the quadratic time bound even in the worstcase scenario. Supported by the Adams Fellowship of the Israel Academy of Sciences and Humanities. 1