On Using Gray Codes to Improve the Efficiency of the Parallel Exhaustive Search Algorithm for the Knapsack Problem

Abstract

In previous papers, we stated that splitting the lexicographic sequence into equal parts does not yield uniform workload distribution for a parallel computational system. One of the options we have considered is breaking the packing vectors space into classes based on the vectors’ Hamming weight, and then split each of the classes into equal parts. In this paper, we investigate another load balancing technique based on using the Gray codes instead of the lexicographic sequence. As only one element of the packing changes on every step, we can calculate the packing weight dynamically. Thus, the time needed to weigh a packing becomes both shorter and more uniform. We study the properties of the Gray codes and analyze their impact on the algorithm run time and efficiency of parallel computation.