| Summary: | 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 diffprogram and grep family of programs. These problems form a sub-domain of a larger area of problems called discrete pattern matching which has been developed recently to characterize 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 characterized by three common features: (1) a "computable scoring function" which defines the quality of matches; (2) a graph based, dynamic programming framework which captures the structure of the algorithmic solutions; and (3) an interdisciplinary aspect to the research, particularly between computer science and molecular biology, not found in other topics in computer science. The first half of the dissertation considers discrete pattern matching over sequences. It develops the alignment-graph/dynamic-programming framework for the algorithms in the sub-domain and then presents several new algorithms for regular expression and extended regular expression pattern matching. The second half of the dissertation develops the sub-domain of discrete pattern matching over interval sets, also called super-pattern matching. In this sub-domain, the input consists of sets of typed intervals, defined over a finite range, and a pattern expression of the interval types. A match between the interval sets and the pattern consists of a sequence of consecutive intervals, taken from the interval sets, such that their corresponding sequence of types matches the pattern. The name super-pattern matching comes from those problems where the interval sets corresponds to the sets of substrings reported by various pattern matching problems over a common input sequence. The pattern for the super-pattern matching problem, then, represents a "pattern of patterns," or super-pattern, and the sequences of intervals matching the super-pattern correspond to the substring of the original sequence which match that larger "pattern."
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