A heuristic for two bin partition problem

Abstract

There are many heuristics to address 2-bin integer partition problem. The range (R) of the values in the data set and the number of element (N) in the data set are 2-parameters which determine the appropriate heuristics. By and large, for large N, Karmarkar-Karp(KK) heuristics offers solutions. For low values of N, Complete Karmarkar-Karp heuristics (CKK), Horowitz and Sahni (HS), Schroeppel and Shamir (SS), Brute-Force search (BF) offers solutions. However, our computations indicate that for R > 1012 and for a specific range of N, depending on R, (R = 1014, N = 60 to 150) the best existing heuristics (CKK) takes long or very long CPU time. We are proposing a different heuristic to address this scenario. The proposed heuristic in the paper uses depth-first (like KK) set differencing till N become 48 and from N = 48 to 1 it performs exhaustive search (like HS). For the above mentioned scenario, we found that this combination of strategies gives better and faster solution compared to CKK.