Worst case optimal union-intersection expression evaluation

Abstract

We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets in the comparison model. Given the expression and the sizes of the sets, we are interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume the sets in the given expression are independent. We show a lower bound on this problem and present an algorithm that matches the lower bound asymptotically.