Optimally stable matchings for resource allocations

Abstract

The stable marriage problem (SMP) and its variants have received much attention in the literature due to their wide range of applications. One of their applications is resource allocation in network environments. In this paper, we consider two resource allocation problems. The first one is to maximize the performance of a system in the fog computing environment while maintaining a low cost. In the problem, the resource allocation task will be rewritten as the MAX-SMTI variant (i.e., finding the maximum cardinality stable matching of the stable marriage with ties and incomplete lists). It is then formulated under an integer linear program to solve. The best allocation can then be chosen to be the lowest cost one among stable matchings. In the same manner, another variant called MAX-HRT (i.e., finding the maximum cardinality stable matching of the hospital-residents with ties) is applied for the second application regarding the virtual machine allocation. By using MAX-SMTI and MAX-HRT models which are solved via integer linear programs, we aim to not only find stable matchings for the resource allocation problems but also maximum length matchings. Consequently, a maximum number of user requests should be served at a time. The models are implemented in C++ using the SCIP solver. Numerical experiments are conducted for large datasets and results are given to show the efficiency of the models.