Optimal Parametrization of the Gale-Shapley Preallocation Method for Combinatorial Auction-based Channel Assignment

Algorithms based on combinatorial auctions show significant potential regarding their application for channel assignment problems in multi-connectivity ultra-reliable wireless networks. However the computational effort required by such algorithms grows fast with the number of users and resources. Therefore, preallocation-based combinatorial auction represents a promising approach for these setups. The aim of the pre-allocation is to constrain the number of bids submitted by participants in the combinatorial auction process, thus reducing computational demands and enabling numerical feasibility of the auction problem. Reduction of bid number is achieved via limiting the number of items (channels) considered by auction participants (tenants) in their bids. Thus the aim of preallocation is to non-exclusively assign channels to tenants. This assignment serves as a basis for the later bid generation in the auction procedure. In this paper we analyze the optimal parametrization of the many-to-many Gale-Shapley preallocation method and formulate recommendations for optimal performance. Numerical assessments illustrate that the appropriate preallocation has significant impact on the performance and computational demand.