this article.

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 sub-quadratic time, for metrics which use a scoring matrix of unrestricted weights. Our algorithm applies to both local and global alignment computations. The speed-up is achieved by dividing the dynamic programming matrix into variable sized blocks, as induced by Lempel-Ziv 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 Gaspard-Monge, Universite de Marne-la-Vallee, Cite Descartes, Champs-surMarne, 77454 Marne-la-Vallee Cedex 2, France, email: mac@univ-mlv.fr. y Department of Computer Science, Haifa University, Haifa 31905, Israel, phone: (972-4) 824-0103, FAX: (972-4) 824-9331; Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY 11201-3840; email: landau@poly.edu; partially supported by NSF grant CCR-0104307, 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 ...

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.

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 on-going 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...

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 well-known 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 sublinear-time algorithms for the 1D, parenthesis, and RNA problems.

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 minimum-cost 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.

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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 space-optimal up to a constant factor and and also runtime-optimal 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 1-dimensional dynamic programming problems satisfying this inequality. Keywords --- Histograms, data compression, cumulative distribution functions, approximation, monotone functions, dynamic programming, Monge's quadrangle inequality, concave cost...

The semantic interpretation of video sequences by computer is often formulated as probabilistically relating lowerlevel features to higher-level states, constrained by a transition graph. Using Hidden Markov Models inference is efficient but time-in-state data cannot be included, whereas using Hidden Semi-Markov Models we can model duration but have inefficient inference. We present a new efficient O(T ) algorithm for inference in certain HSMMs and show experimental results on video sequence interpretation in television footage to demonstrate that explicitly modelling timein -state improves interpretation performance.

: We consider new algorithms for the solution of many dynamic programming recurrences for sequence comparison and for RNA secondary structure prediction. The techniques upon which the algorithms are based e#ectively exploit the physical constraints of the problem to derive more e#cient methods for sequence analysis. 1. INTRODUCTION In this paper we consider algorithms for two problems in sequence analysis. The first problem is sequence alignment, and the second is the prediction of RNA structure. Although the two problems seem quite di#erent from each other, their solutions share a common structure, which can be expressed as a system of dynamic programming recurrence equations. These equations also can be applied to other problems, including text formatting and data storage optimization. We use a number of well motivated assumptions about the problems in order to provide e#cient algorithms. The primary assumption is that of concavity or convexity. The recurrence relations for bo...