Statistical Analysis of Binary Vector Enumeration Methods in Combinatorial Optimization

In this paper, we review and analyze the efficiency of several binary vector enumeration algorithms we have been using in our work on the Knapsack Problem. As we keep in mind the possibility of massively parallel computation, we are interested in algorithms that are able to start the search from any vector (identified by ordinal number). In this case, it is possible to implement static load balancing efficiently. Apart from the actual implementation performance, we study the load balancing diagrams for each of the algorithms. We assume that every bit of the binary vector is associated with some fixed amount of work a computer must do and examine the resulting complexity of subtasks obtained by splitting the vector sequences into subsequences.