The set LCS problem

An efficient algorithm is presented that solves a generalization of the Longest Common Subsequence problem, in which one of the two input strings contains sets of symbols which may be permuted. This problem arises from a music application

Variants of Constrained Longest Common Subsequence

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co from A to N, the DC-LCS problem consists in finding the longest subsequence s of s1 and s2 such that s is a supersequence of all the strings in Cs and such that the number of occurrences in s of each symbol a in A is upper bounded by Co(a). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem: the Constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution. Secondly, we prove a parameterized hardness result for the Constrained LCS problem when the parameter is the number of the constraint strings and the size of the alphabet A. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant

Stable and Efficient Networks with Farsighted Players: the Largest Consistent Set

In this paper we study strategic formation of bilateral networks with farsighted players in the classic framework of Jackson and Wolinsky (1996). We use the largest consistent set (LCS)(Chwe (1994)) as the solution concept for stability. We show that there exists a value function such that for every component balanced and anonymous allocation rule, the corresponding LCS does not contain any strongly efficient network. Using Pareto efficiency, a weaker concept of efficiency, we get a more positive result. However, then also, at least one environment of networks (with a component balanced and anonymous allocation rule) exists for which the largest consistent set does not contain any Pareto efficient network. These confirm that the well-known problem of the incompatibility between the set of stable networks and the set of efficient networks persists even in the environment with farsighted players. Next we study some possibilities of resolving this incompatibility.networks, farsighted, largest consistent set

Learning Mazes with Aliasing States: An LCS Algorithm with Associative Perception

Learning classifier systems (LCSs) belong to a class of algorithms based on the principle of self-organization and have frequently been applied to the task of solving mazes, an important type of reinforcement learning (RL) problem. Maze problems represent a simplified virtual model of real environments that can be used for developing core algorithms of many real-world applications related to the problem of navigation. However, the best achievements of LCSs in maze problems are still mostly bounded to non-aliasing environments, while LCS complexity seems to obstruct a proper analysis of the reasons of failure. We construct a new LCS agent that has a simpler and more transparent performance mechanism, but that can still solve mazes better than existing algorithms. We use the structure of a predictive LCS model, strip out the evolutionary mechanism, simplify the reinforcement learning procedure and equip the agent with the ability of associative perception, adopted from psychology. To improve our understanding of the nature and structure of maze environments, we analyze mazes used in research for the last two decades, introduce a set of maze complexity characteristics, and develop a set of new maze environments. We then run our new LCS with associative perception through the old and new aliasing mazes, which represent partially observable Markov decision problems (POMDP) and demonstrate that it performs at least as well as, and in some cases better than, other published systems

Fluctuations of the Longest Common Subsequence for Sequences of Independent Blocks

The problem of the fluctuation of the Longest Common Subsequence (LCS) of two i.i.d. sequences of length $n>0$ has been open for decades. There exist contradicting conjectures on the topic. Chvatal and Sankoff conjectured in 1975 that asymptotically the order should be $n^{2/3}$, while Waterman conjectured in 1994 that asymptotically the order should be $n$. A contiguous substring consisting only of one type of symbol is called a block. In the present work, we determine the order of the fluctuation of the LCS for a special model of sequences consisting of i.i.d. blocks whose lengths are uniformly distributed on the set $\{l-1,l,l+1\}$, with $l$ a given positive integer. We showed that the fluctuation in this model is asymptotically of order $n$, which confirm Waterman's conjecture. For achieving this goal, we developed a new method which allows us to reformulate the problem of the order of the variance as a (relatively) low dimensional optimization problem.Comment: PDFLatex, 40 page

The Longest Common Subsequence via Generalized Suffix Trees

Given two strings S1 and S 2, finding the longest common subsequence (LCS) is a classical problem in computer science. Many algorithms have been proposed to find the longest common subsequence between two strings. The most common and widely used method is the dynamic programming approach, which runs in quadratic time and takes quadratic space. Other algorithms have been introduced later to solve the LCS problem in less time and space. In this work, we present a new algorithm to find the longest common subsequence using the generalized suffix tree and directed acyclic graph.;The Generalized suffix tree (GST) is the combined suffix tree for a set of strings {lcub}S1, S 2, ..., Sn{rcub}. Both the suffix tree and the generalized suffix tree can be calculated in linear time and linear space. One application for generalized suffix tree is to find the longest common substring between two strings. But finding the longest common subsequence is not straight forward using the generalized suffix tree. Here we describe how we can use the GST to find the common substrings between two strings and introduce a new approach to calculate the longest common subsequence (LCS) from the common substrings. This method takes a different view at the LCS problem, shading more light at novel applications of the LCS. We also show how this method can motivate the development of new compression techniques for genome resequencing data

Toward Open-Set Text-Independent Speaker Identification in Tactical Communications

Abstract-We present the design and implementation of an open-set textindependent speaker identification system using genetic Learning Classifier Systems (LCS). We examine the use of this system in a real-number problem domain, where there is strong interest in its application to tactical communications. We investigate different encoding methods for representing real-number knowledge and study the efficacy of each method for speaker identification. We also identify several difficulties in solving the speaker identification problems with LCS and introduce new approaches to resolve the difficulties. Experimental results show that our system successfully learns 200 voice features at accuracies of 90% to 100% and 15,000 features to more than 80% for the closed-set problem, which is considered a strong result in the speaker identification community. The open-set capability is also comparable to existing numeric-based methods