A Hypergraph Solution to Generalized Assignment Problem and Application to Spatial Data Sets

Year 2017, Volume: 17 Issue: 1, 93 - 100, 24.04.2017

Mehmet Ali Balcı

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.

Keywords

Generalized Assignment Problem; Hypergraphs; Delaunay Triangulation, Spatial Data Sets

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