This paper studies a fundamental dynamic clustering problem. The input is an online sequence of pairwise communication requests between n nodes (e.g., tasks or virtual machines). Our goal is to minimize the communication cost by partitioning the communicating nodes into ℓ clusters (e.g., physical servers) of size k (e.g., number of virtual machine slots). We assume that if the communicating nodes are located in the same cluster, the communication request costs 0; if the nodes are located in different clusters, the request is served remotely using intercluster communication, at cost 1. Additionally, we can migrate: a node from one cluster to another at cost α ≥ 1. We initiate the study of a stochastic problem variant where the communication pattern follows a fixed distribution, set by an adversary. Thus, the online algorithm needs to find a good tradeoff between benefitting from quickly moving to a seemingly good configuration (of low inter-cluster communication costs), and the risk of prematurely ending up in a configuration which later turns out to be bad, entailing high migration costs. Our main technical contribution is a deterministic online algorithm which is O(log n)-competitive with high probability (w.h.p.), for a specific but fundamental class of problems: namely on ring graphs.
CITATION STYLE
Avin, C., Cohen, L., & Schmid, S. (2017). Competitive clustering of stochastic communication patterns on a ring. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10299 LNCS, pp. 231–247). Springer Verlag. https://doi.org/10.1007/978-3-319-59647-1_18
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