Showing papers by "Ming-Yang Kao published in 2002"

A Decomposition Theorem for Maximum Weight Bipartite Matchings

Abstract: Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N, and W be the node count, the largest edge weight, and the total weight of G. Let k(x, y) be log x / log (x2/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an $O(\sqrt{n}W / k(n, W/N))$-time algorithm for computing a maximum weight matching of G. This algorithm bridges a long-standing gap between the best known time complexity of computing a maximum weight matching and that of computing a maximum cardinality matching. Given G and a maximum weight matching of G, we can further compute the weight of a maximum weight matching of G - {u} for all nodes u in O(W) time.

Optimal Buy-and-Hold Strategies for Financial Markets with Bounded Daily Returns

Abstract: In the context of investment analysis, we formulate an abstract online computing problem called a planning game and develop general tools for solving such a game. We then use the tools to investigate a practical buy-and-hold trading problem faced by long-term investors in stocks. We obtain the unique optimal static online algorithm for the problem and determine its exact competitive ratio. We also compare this algorithm with the popular dollar averaging strategy using actual market data.

Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

Abstract: We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with index j. The width of A(i,j) is w(i,j) = sum_{i =1 for all i.

Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

Abstract: We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A = ?a1, a2, . . . , an? of real numbers, a segment S is a consecutive subsequence ?ai, ai+1, . . . , aj?. The width of S is j - i + 1, while the density is (?i?k?jak)/j - i+ 1). The maximum-density segment problem takes A and two integers L and U as input and asks for a segment of A with the largest possible density among those of width at least L and at most U. If U = n (or equivalently, U = 2L - 1), we can solve the problem in O(n) time, improving upon the O(n log L)-time algorithm by Lin, Jiang and Chao for a general sequence A. Furthermore, if U and L are arbitrary, we solve the problem in O(n + n log(U - L + 1)) time. There has been no nontrivial result for this case previously. Both results also hold for a weighted variant of the maximum-density segment problem.

Provably Fast and Accurate Recovery of Evolutionary Trees through Harmonic Greedy Triplets

Abstract: We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm runs in $\smallbigO{ umtaxa^2}$ time using $\smallbigO{ umtaxa}$ work space, where $ umtaxa$ is the number of terminal taxa. These time and space complexities are optimal in the sense that the size of an input distance matrix is $ umtaxa^2$ and the size of an output tree is $ umtaxa$. Moreover, in the Jukes--Cantor model of evolution, the algorithm recovers the correct tree topology with high probability using sample sequences of length polynomial in (1) $ umtaxa$, (2) the logarithm of the error probability, and (3) the inverses of two small parameters.

Fast Universalization of Investment Strategies with Provably Good Relative Returns

Abstract: A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable. We present examples of common investment strategies that fit into our framework. The examples include both trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks. This work extends Cover's universal portfolio work. We also discuss the runtime efficiency of universalization algorithms. While a straightforward implementation of our algorithms runs in time exponential in the number of parameters, we show that the efficient universal portfolio computation technique of Kalai and Vempala involving the sampling of log-concave functions can be generalized to other classes of investment strategies.

Fast Universalization of Investment Strategies with Provably Good Relative Returns

Abstract: A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable. We present examples of common investment strategies that fit into our framework. The examples include both trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks. This work extends Cover's universal portfolio work. We also discuss the runtime efficiency of universalization algorithms. While a straightforward implementation of our algorithms runs in time exponential in the number of parameters, we show that the efficient universal portfolio computation technique of Kalai and Vempala involving the sampling of log-concave functions can be generalized to other classes of investment strategies.

The Risk Profile Problem for Stock Portfolio Optimization

Abstract: This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks that are considered by the investor are assumed to be known, while the joint distribution is unknown. The problem is to find the best investment strategy in order to minimize the probability of losing a certain percentage of the invested capital based on different attitudes of the investors towards future outcomes of the stock market.

Fast Optimal Genome Tiling with Applications to Microarray Design and Homology Search

Abstract: In this paper we consider several variations of the following basic tiling problem: given a sequence of real numbers with two size bound parameters, we want to find a set of tiles such that they satisfy the size bounds and the total weight of the tiles is maximized This solution to this problem is important to a number of computational biology applications, such as selecting genomic DNA fragments for amplicon microarrays, or performing homology searches with long sequence queries Our goal is to design efficient algorithms with linear or near-linear time and space in the normal range of parameter values for these problems For this purpose, we discuss the solution of a basic online interval maximum problem via a sliding window approach and show how to use this solution in a nontrivial manner for many of our tiling problems We also discuss NPhardness and approximation algorithms for generalization of our basic tiling problem to higher dimensions

A combinatorial toolbox for protein sequence design and landscape analysis in the grand canonical model.

Abstract: In modern biology, one of the most important research problems is to understand how protein sequences fold into their native 3D structures. To investigate this problem at a high level, one wishes to analyze the protein landscapes, i.e., the structures of the space of all protein sequences and their native 3D structures. Perhaps the most basic computational problem at this level is to take a target 3D structure as input and design a fittest protein sequence with respect to one or more fitness functions of the target 3D structure. We develop a toolbox of combinatorial techniques for protein landscape analysis in the Grand Canonical model of Sun, Brem, Chan, and Dill. The toolbox is based on linear programming, network flow, and a linear-size representation of all minimum cuts of a network. It not only substantially expands the network flow technique for protein sequence design in Kleinberg's seminal work but also is applicable to a considerably broader collection of computational problems than those considered by Kleinberg. We have used this toolbox to obtain a number of efficient algorithms and hardness results. We have further used the algorithms to analyze 3D structures drawn from the Protein Data Bank and have discovered some novel relationships between such native 3D structures and the Grand Canonical model.

Improved Phylogeny Comparisons: Non-Shared Edges Nearest Neighbor Interchanges, and Subtree Transfers

Abstract: The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest neighbor interchange (NNI) distance. In this paper, we give the first subquadratic-time algorithm for finding the non-shared edges, which are then used to speed up the existing approximating algorithm for the NNI distance from $O(n^2)$ time to $O(n \log n)$ time. Another popular distance metric for phylogenies is the subtree transfer (STT) distance. Previous work on computing the STT distance considered degree-3 trees only. We give an approximation algorithm for the STT distance for degree-$d$ trees with arbitrary $d$ and with generalized STT operations.

The Risk Profile Problem for Stock Portfolio Optimization: Computational Methods in Decision-Making, Economics, and Finance

Abstract: This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks that are considered by the investor are assumed to be known, while the joint distribution is unknown. The problem is to find the best investment strategy in order to minimize the probability of losing a certain percentage of the invested capital based on different attitudes of the investors towards future outcomes of the stock market.