Proving relative lower bounds for incremental algorithms

Abstract

A general method that permits simple proofs of relative lower bounds for incremental update algorithms is presented. This method is applied to classify functions by relative lower bounds. We demonstrate our technique by bounding a number of incremental algorithms drawn from various domains. The method described expands upon work by Paull, Berman, and Cheng [PCB] and generalizes a result of Even and Gazit [EG]. Our results have interesting implications with respect to the optimality of an incremental algorithm previously developed by Ryder in [R, RP2]. Perhaps most importantly, the proof method and function classification suggest which types of problems are likely to yield good incremental algorithms (i.e., of lower complexity) and which cannot be improved by an incremental approach.