Equal-Subset-Sum Faster Than the Meet-in-the-Middle.

In the Equal-Subset-Sum problem, we are given a set S of n integers and the problem is to decide if there exist two disjoint nonempty subsets A, B subset of S, whose elements sum up to the same value. The problem is NP-complete. The state-of-the-art algorithm runs in O*(3(n/2)) <= O*(1.7321(n)) time and is based on the meet-in-the-middle technique. In this paper, we improve upon this algorithm and give O*(1.7088(n)) worst case Monte Carlo algorithm. This answers a question suggested by Woeginger in his inspirational survey. Additionally, we analyse the polynomial space algorithm for Equal-Subset-Sum. A naive polynomial space algorithm for Equal-Subset-Sum runs in O*(3(n)) time. With read-only access to the exponentially many random bits, we show a randomized algorithm running in O*(2.6817(n)) time and polynomial space.