Exploramos o seguinte problema: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y sem símbolos repetidos. Estudamos a estrutura deste problema, particularmente do ponto de vista de grafos e de combinatória poliédrica. Desenvolvemos algoritmos de aproximação e heurísticas para este problema. O enfoque deste trabalho está na construção de um algoritmo baseado na técnica branch-and-cut, aproveitando-nos de um algoritmo de separação eficiente e de heurísticas e técnicas para encontrarmos uma solução ótima mais cedo. Também estudamos um problema mais fácil no qual este problema é baseado: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y. Exploramos este problema do ponto de vista de combinatória poliédrica e descrevemos vários algoritmos conhecidos para resolvê-lo. / We explore the following problem: given two sequences X and Y over a finite alphabet, find a longest common subsequence of X and Y without repeated symbols. We study the structure of this problem, particularly from the point of view of graphs and polyhedral combinatorics. We develop approximation algorithms and heuristics for this problem. The focus of this work is in the construction of an algorithm based on the branch-and-cut technique, taking advantage of an efficient separation algorithm and of heuristics and techniques to find an optimal solution earlier. We also study an easier problem on which this problem is based: given two sequences X and Y over a finite alphabet, find a longest common subsequence of X and Y. We explore this problem from the point of view of polyhedral combinatorics and describe several known algorithms to solve it.

Exploramos o seguinte problema: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y sem símbolos repetidos. Estudamos a estrutura deste problema, particularmente do ponto de vista de grafos e de combinatória poliédrica. Desenvolvemos algoritmos de aproximação e heurísticas para este problema. O enfoque deste trabalho está na construção de um algoritmo baseado na técnica branch-and-cut, aproveitando-nos de um algoritmo de separação eficiente e de heurísticas e técnicas para encontrarmos uma solução ótima mais cedo. Também estudamos um problema mais fácil no qual este problema é baseado: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y. Exploramos este problema do ponto de vista de combinatória poliédrica e descrevemos vários algoritmos conhecidos para resolvê-lo. / We explore the following problem: given two sequences X and Y over a finite alphabet, find a longest common subsequence of X and Y without repeated symbols. We study the structure of this problem, particularly from the point of view of graphs and polyhedral combinatorics. We develop approximation algorithms and heuristics for this problem. The focus of this work is in the construction of an algorithm based on the branch-and-cut technique, taking advantage of an efficient separation algorithm and of heuristics and techniques to find an optimal solution earlier. We also study an easier problem on which this problem is based: given two sequences X and Y over a finite alphabet, find a longest common subsequence of X and Y. We explore this problem from the point of view of polyhedral combinatorics and describe several known algorithms to solve it.

In security markets, the stock price movements are closely linked to the market information. For example, the subprime mortgage triggered a global financial crisis in 2007. Drops occurred in virtually every stock market in the world. After the Federal Reserve took several steps to address the crisis, the stock markets have been gradually stable. Reaction of the traders to the arrival information results in different patterns of the stock price movements. Thus pattern matching is an important subject in future movement prediction, rule discovery and computer aided diagnosis. In this research, we propose a pattern matching procedure to seize the similar stock price movements of two listed companies during one day. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time intervals where the two listed companies have the same integrated volatility levels and price rise/drop trends. Next we transform the raw price data in the found matching time periods to the Bollinger Band Percent data, then use the power spectrum to extract low frequency components. Adjusted Pearson chi-squared tests are performed to analyze the similarity of the price movement patterns in these periods. We perform the study by simulation investigation first, then apply the procedure to empirical analysis of high frequency transaction data of NYSE.

String-to-String Correction is the process of transforming some mutable string M into an exact copy of some other string (the target string T), using a shortest sequence of well-defined edit operations. The formal STRING-TO-STRING CORRECTION problem asks for the optimal solution using just two operations: symbol deletion, and swap of adjacent symbols. String correction problems using only swaps and deletions are computationally interesting; in his paper On the Complexity of the Extended String-to-String Correction Problem (1975), Robert Wagner proved that the String-to-String Correction problem under swap and deletion operations only is NP-complete for unbounded alphabets. In this thesis, we present the first careful examination of the binary-alphabet case, which we call Binary String-to-String Correction (BSSC). We present several special cases of BSSC for which an optimal solution can be found in polynomial time; in particular, the case where T and M have an equal number of occurrences of a given symbol has a polynomial-time solution. As well, we demonstrate and prove several properties of BSSC, some of which do not necessarily hold in the case of String-to-String Correction. For instance: that the order of operations is irrelevant; that symbols in the mutable string, if swapped, will only ever swap in one direction; that the length of the Longest Common Subsequence (LCS) of the two strings is monotone nondecreasing during the execution of an optimal solution; and that there exists no correlation between the effect of a swap or delete operation on LCS, and the optimality of that operation. About a dozen other results that are applicable to Binary String-to-String Correction will also be presented. / Graduate / 0984 / 0715 / tspreen@gmail.com

Consider a set B of blue points and a set R of red points in the plane such that R ∪ B is in general position. A graph drawn in the plane whose edges are straight-line segments is called a geometric graph. We investigate the problem of drawing non-crossing properly colored geometric graphs on the point set R ∪ B. We show that if ||B| − |R|| ≤ 1 and a subset of R forms the vertices of a convex polygon separating the points of B, lying inside the polygon, from the rest of the points of R, lying outside the polygon, then there exists a non-crossing properly colored geometric path on R∪B covering all points of R ∪ B. If R∪B lies on a circle, the size of the longest non-crossing geometric path is related to the size of the largest separated matching; a separated matching is a non-crossing properly colored geometric matching where all edges can be crossed by a line. A discrepancy of R ∪ B is the maximal difference between cardinalities of color classes of intervals on the circle. When the discrepancy of R ∪ B is at most 2, we show that there is a separated matching covering asymptotically 4 5 of points of R ∪ B. During this proof we use a connection between separated matchings and the longest common subsequences between two binary sequences where the symbols correspond to the colors of the points.

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The goal of this work is to design a generally useful versioning system for the administration of different types of electronics documents, to design in detail and to implement the client part of this system (based on the client-server model). The implementation is built on .NET platform. This text also describes general approaches to versioning in different systems and shows a survey over the principles of the existing versioning systems with respect to the interaction with user.