EFFICIENT ALGORITHMS FOR SEQUENCE ANALYSIS WITH CONCAVE AND CONVEX GAP COSTS David A. Eppstein We describe algorithms for two problems in sequence analysis: sequence alignment with gaps (multiple consecutive insertions and deletions treated as a unit) and RNA secondary structure with single loops only. We make the assumption that the gap cost or loop cost is a convex or concave function of the length of the gap or loop, and show how this assumption may be used to develop e#cient algorithms for these problems. We show how the restriction to convex or concave functions may be relaxed, and give algorithms for solving the problems when the cost functions are neither convex nor concave, but can be split into a small number of convex or concave functions. Finally we point out some sparsity in the structure of our sequence analysis problems, and describe how we may take advantage of that sparsity to further speed up our algorithms. CONTENTS 1. Introduction ............................1 ...

: 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...

Finding matches, both exact and approximate, between a sequence of symbols A and a pattern P has long been an active area of research in algorithm design. Some of the more well-known byproducts from that research are the diff program and grep family of programs. These problems form a sub-domain of a larger areas of problems called discrete pattern matching which has been developed recently to characterise the wide range of pattern matching problems. This dissertation presents new algorithms for discrete pattern matching over sequences and develops a new sub-domain of problems called discrete pattern matching over interval sets. The problems and algorithms presented here are characterised by pattern matching over interval sets. The problems and al