Efficient Algorithms on Strings

We consider several computational problems that arise in information retrieval and molecular biology, namely string matching, determination of the RNA secondary structure and various versions of sequence alignment problems. For string matching, we provide new upper and lower bounds on the optimal number of comparisons that any algorithm must perform in order to solve the problem. Our results are based on new combinatorial properties of strings and a new charging mechanism for the amortized analysis of algorithms. For the RNA secondary structure and sequence analysis problems, we show how to obtain fast algorithms by taking advantage of several constraints that the problems must satisfy.