Randomized ε-RANKING Algorithm for Online Trichromatic Matching

Abstract

We study a randomized 1/e-competitive ε-RANKING algorithm for the onlinetrichromatic matching problem. This problem involves finding matching in tripartite graphs having three disjoint sets of vertices. Our model encompasses a tripartite graph configuration, where an offline vertex set is an intermediary connecting two opposing sets. The vertices from the latter sets unfold online, arriving individually over time. ε-RANKING employs a randomization strategy where offline vertices are assigned random ranks between [0, 1]. It extends the idea of finding the lowest-ranked neighbor of the newly arrived online vertex presented by Karp et al. [1] in their RANKING algorithm. This approach exploits the principles of RANKING and matching from the domain of online bipartite matching to the more complex context of online trichromatic matching.