Online minimum matching in real-time spatial data

Abstract

Recently, with the development of mobile Internet and smartphones, the <u>o</u>nline <u>m</u>inimum <u>b</u>ipartite <u>m</u>atching in real time spatial data (OMBM) problem becomes popular. Specifically, given a set of service providers with specific locations and a set of users who dynamically appear one by one, the OMBM problem is to find a maximum-cardinality matching with minimum total distance following that once a user appears, s/he must be immediately matched to an unmatched service provider, which cannot be revoked, before subsequent users arrive. To address this problem, existing studies mainly focus on analyzing the worst-case competitive ratios of the proposed online algorithms, but study on the performance of the algorithms in practice is absent. In this paper, we present a comprehensive experimental comparison of the representative algorithms of the OMBM problem. Particularly, we observe a surprising result that the simple and efficient greedy algorithm, which has been considered as the worst due to its exponential worst-case competitive ratio, is significantly more effective than other algorithms. We investigate the results and further show that the competitive ratio of the worst case of the greedy algorithm is actually just a constant, 3.195, in the average-case analysis. We try to clarify a 25-year misunderstanding towards the greedy algorithm and justify that the greedy algorithm is not bad at all. Finally, we provide a uniform implementation for all the algorithms of the OMBM problem and clarify their strengths and weaknesses, which can guide practitioners to select appropriate algorithms for various scenarios.