General Techniques for Analyzing Recursive Algorithms with Applications

The complexity of divide-and-conquer algorithms is often described by recurrences of various forms. In this paper, we develop general techniques and master theorems for solving several kinds of recurrences, and we give several applications of our results. In particular, almost all of the earlier work on solving the recurrences considered here is subsumed by our work. In the process of solving such recurrences, we establish interesting connections between some elegant mathematics and analysis of recurrences. Using our results and improved bipartite matching algorithms, we also improve existing bounds in the literature for several problems, viz, associative-commutative (AC) matching of linear terms, associative matching of linear terms, rooted subtree isomorphism, and rooted subgraph homeomorphism for trees.