Genelleştirilmiş Atama Probleminin Hypergraf Çözümü ve Uzaysal Veri Kümelerine Uygulaması

Abstract

In the simple task assignment problem, at most one task should be assigned to each agent; this constraint is relaxed in the multiple task assignment problems. The goal of the well-known Generalized Assignment Problem is to assign tasks to agents such that the capacity of the agent does not exceed its limits as it minimizes the total cost. In this study we present a novel approach to solve the general assignment problem by using the hypergraphs. Hypergraphs can be considered as the generalization of the graphs in such way that an edge can connect any number of vertices, and can be seen as the set systems. In the hypergraph multi-assignment problem, we are looking for a cost minimizing solution to tasks assignment to the agents which are the individual hyperedges. For this purpose, we first determine the tasks as hyperedges and then obtain the vertex cover of the simple graph representation of a hypergraph. Amongst the all possible covers, we choose the cost minimizing one as the solution.