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In fact, compression and computation are two sides of the same coin, as they exploit the same underlying structure both for storing and operating on data. The study in [[4]] establishes new upper bounds and a conditional lower bound on the indexed regular expression matching problem and [[5]] improves existing analyses on the approximation ratios for common grammar-based compressors. As the production of massive data has outpaced Moore's law in many scientific areas, the very notion of algorithms is transforming. [Extracted from the article]

In this paper, we consider several variants of the pattern matching with mismatches problem. In particular, given a text T = t1t2 . . . tn and a pattern P = p1p2 . . . pm, we investigate the following problems: (1) pattern matching with mismatches: for every i; 1 ≤ i ≤ n - m + 1 output, the distance between P and titi+1 . . . ti+m-1 and (2) pattern matching with k mismatches: output those positions i where the distance between P and tiiti+1 . . . ti+m-1 is less than a given threshold k. The distance metric used is the Hamming distance. We present some novel algorithms and techniques for solving these problems. We offer deterministic, randomized and approximation algorithms. We consider variants of these problems where there could be wild cards in either the text or the pattern or both. We also present an experimental evaluation of these algorithms. The source code is available at http://www.engr.uconn.edu/∼man09004/kmis.zip. [ABSTRACT FROM AUTHOR]

In this work, we study the d-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of r solutions of size at most k each, which has recently been introduced to the field of parameterized complexity. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process that models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are fixed-parameter tractable in k + r for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of 'base' solutions, computes a maximally diverse collection of solutions. We believe that this could be of independent interest. [ABSTRACT FROM AUTHOR]