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17
Software Process Validation: Quantitatively Measuring the Correspondence of a Process to a Model
 ACM Transactions on Software Engineering and Methodology
, 1996
"... this article. ..."
A Subquadratic Sequence Alignment Algorithm for Unrestricted Cost Matrices
, 2002
"... The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring ..."
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Cited by 56 (4 self)
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The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring matrix of unrestricted weights. Our algorithm applies to both local and global alignment computations. The speedup is achieved by dividing the dynamic programming matrix into variable sized blocks, as induced by LempelZiv parsing of both strings, and utilizing the inherent periodic nature of both strings. This leads to an O(n 2 = log n) algorithm for an input of constant alphabet size. For most texts, the time complexity is actually O(hn 2 = log n) where h 1 is the entropy of the text. Institut GaspardMonge, Universite de MarnelaVallee, Cite Descartes, ChampssurMarne, 77454 MarnelaVallee Cedex 2, France, email: mac@univmlv.fr. y Department of Computer Science, Haifa University, Haifa 31905, Israel, phone: (9724) 8240103, FAX: (9724) 8249331; Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY 112013840; email: landau@poly.edu; partially supported by NSF grant CCR0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation (grants 173/98 and 282/01), by the FIRST Foundation of the Israel Academy of Science and Humanities, and by IBM Faculty Partnership Award. z Department of Computer Science, Haifa University, Haifa 31905, Israel; On Education Leave from the IBM T.J.W. Research Center; email: michal@cs.haifa.il; partially supported by by the Israel Science Foundation (grants 173/98 and 282/01), and by the FIRST Foundation of the Israel Academy of Science ...
Perspectives of Monge Properties in Optimization
, 1995
"... An m × n matrix C is called Monge matrix if c ij + c rs c is + c rj for all 1 i ! r m, 1 j ! s n. In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) funda ..."
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Cited by 53 (3 self)
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An m × n matrix C is called Monge matrix if c ij + c rs c is + c rj for all 1 i ! r m, 1 j ! s n. In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) fundamental combinatorial properties of Monge structures, (ii) applications of Monge properties to optimization problems and (iii) recognition of Monge properties.
Parallel Dynamic Programming
, 1992
"... We study the parallel computation of dynamic programming. We consider four important dynamic programming problems which have wide application, and that have been studied extensively in sequential computation: (1) the 1D problem, (2) the gap problem, (3) the parenthesis problem, and (4) the RNA probl ..."
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Cited by 18 (1 self)
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We study the parallel computation of dynamic programming. We consider four important dynamic programming problems which have wide application, and that have been studied extensively in sequential computation: (1) the 1D problem, (2) the gap problem, (3) the parenthesis problem, and (4) the RNA problem. The parenthesis problem has fast parallel algorithms; almost no work has been done for parallelizing the other three. We present a unifying framework for the parallel computation of dynamic programming. We use two wellknown methods, the closure method and the matrix product method, as general paradigms for developing parallel algorithms. Combined with various techniques, they lead to a number of new results. Our main results are optimal sublineartime algorithms for the 1D, parenthesis, and RNA problems.
Process Discovery and Validation through EventData Analysis
, 1996
"... Software process is how an organization goes about developing or maintaining a software system. It is the methodology employed when people use machines, tools, and artifacts to create a product. Recent work has applied formal modeling to software process, with the hope of reaping the benefits of una ..."
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Cited by 18 (6 self)
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Software process is how an organization goes about developing or maintaining a software system. It is the methodology employed when people use machines, tools, and artifacts to create a product. Recent work has applied formal modeling to software process, with the hope of reaping the benefits of unambiguous and analyzable formalisms. Yet industry has been slow to adopt formal model technologies. Two reasons are that it is costly to develop a formal model and, once developed, there are no methods to ensure that the model indeed reflects reality. This thesis develops techniques for process event data analysis that help solve these two problems, which are termed process discovery and process validation. For process discovery, event data captured from an ongoing process is used to generate a formal model of process behavior. To do this, results from the field of grammar inference are applied, and a new method is also developed. The methods are shown to be efficient and practical to use in...
Linear and O(n log n) Time MinimumCost Matching Algorithms for Quasiconvex Tours (Extended Abstract)
"... Samuel R. Buss # Peter N. Yianilos + Abstract Let G be a complete, weighted, undirected, bipartite graph with n red nodes, n # blue nodes, and symmetric cost function c(x, y) . A maximum matching for G consists of min{n, n # edges from distinct red nodes to distinct blue nodes. Our objective is ..."
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Cited by 17 (3 self)
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Samuel R. Buss # Peter N. Yianilos + Abstract Let G be a complete, weighted, undirected, bipartite graph with n red nodes, n # blue nodes, and symmetric cost function c(x, y) . A maximum matching for G consists of min{n, n # edges from distinct red nodes to distinct blue nodes. Our objective is to find a minimumcost maximum matching, i.e. one for which the sum of the edge costs has minimal value. This is the weighted bipartite matching problem; or as it is sometimes called, the assignment problem.
Multiple sequence alignment with arbitrary gap costs: Computing an optimal solution using polyhedral combinatorics
, 2002
"... ..."
Approximate Regular Expression Pattern Matching with Concave Gap Penalties
 ALGORITHMICA
, 1992
"... Given a sequence A of length M and a regular expression R of length P , an approximate regular expression pattern matching algorithm computes the score of the optimal alignment between A and one of the sequences B exactly matched by R. An alignment between sequences A = a 1 a 2 : : : aM and B = b ..."
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Cited by 9 (0 self)
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Given a sequence A of length M and a regular expression R of length P , an approximate regular expression pattern matching algorithm computes the score of the optimal alignment between A and one of the sequences B exactly matched by R. An alignment between sequences A = a 1 a 2 : : : aM and B = b 1 b 2 : : : b N is a list of ordered pairs, !(i 1 ; j 1 ); (i 2 ; j 2 ); : : : (i t ; j t )? such that i k ! i k+1 and j k ! j k+1 . In this case, the alignment aligns symbols a i k and b jk , and leaves blocks of unaligned symbols, or gaps, between them. A scoring scheme S associates costs for each aligned symbol pair and each gap. The alignment's score is the sum of the associated costs, and an optimal alignment is one of minimal score. There are a variety of schemes for scoring alignments. In a concave gappenalty scoring scheme S = fffi; wg, a function ffi (a; b) gives the score of each aligned pair of symbols a and b, and a concave function w(k) gives the score of a gap of lengt...
ReUse Dynamic Programming for Sequence Alignment: An Algorithmic Toolkit
 STRING ALGORITHMICS, UNITED KINGDOM
, 2005
"... ..."
Approximation of Staircases By Staircases
, 1992
"... The simplest nontrivial monotone functions are "staircases." The problem arises: what is the best approximation of some monotone function f(x) by a staircase with M jumps? In particular: what if f(x) is itself a staircase with N , N ? M , steps? This paper considers algorithms for solving, and theo ..."
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Cited by 5 (3 self)
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The simplest nontrivial monotone functions are "staircases." The problem arises: what is the best approximation of some monotone function f(x) by a staircase with M jumps? In particular: what if f(x) is itself a staircase with N , N ? M , steps? This paper considers algorithms for solving, and theorems relating to, this problem. All of the algorithms we propose are spaceoptimal up to a constant factor and and also runtimeoptimal except for at most a logarithmic factor. One application of our results is to "data compression" of probability distributions. We find yet another remarkable property of Monge's inequality, called the "concave cost as a function of zigzag number theorem." This property leads to new ways to get speedups in certain 1dimensional dynamic programming problems satisfying this inequality. Keywords  Histograms, data compression, cumulative distribution functions, approximation, monotone functions, dynamic programming, Monge's quadrangle inequality, concave cost...