Designing Space-Efficient Top-k Enumeration Algorithms

Abstract

One way to measure the efficiency of enumeration algorithms is to evaluate it with respect to the input size and the number of solutions. Since the number of solutions can be typically exponentially larger than the size of the input, the running time of an enumeration algorithm is huge even if we manage to design an extremely efficient enumeration algorithm. However, in realworld problems, it is not always necessary to enumerate all the solutions and it may be required to enumerate sufficiently many "good" solutions. In such a situation, top-k enumeration algorithms are of great importance in many areas. On the theoretical side, Lawler (Lawler, Management Science 1972) developed a general framework for designing efficient top-k enumeration algorithms. The outline of Lawler's framework is a kind of best-first search. By using this framework, we can design a top-k enumeration algorithm that works in space linear with respect to k, where k is the number of solutions we wish to enumerate. However, since k may be exponentially larger than the input size n, the algorithm needs a huge amount of memory if k is large. In this paper, we modify Lawler's framework and obtain a space-efficient framework that runs in space depending only on a polynomial in n.