A Scalable Work Function Algorithm for the k-Server Problem

Authors Sharath Raghvendra, Rachita Sowle

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Sharath Raghvendra
  • Department of Computer Science, Virginia Tech, Blacksburg, VA, USA
Rachita Sowle
  • Department of Computer Science, Virginia Tech, Blacksburg, VA, USA

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Sharath Raghvendra and Rachita Sowle. A Scalable Work Function Algorithm for the k-Server Problem. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We provide a novel implementation of the classical Work Function Algorithm (WFA) for the k-server problem. In our implementation, processing a request takes O(n²+k²) time per request; where n is the total number of requests and k is the total number of servers. All prior implementations take Ω(kn² +k³) time per request. Previous approaches process a request by solving a min-cost flow problem. Instead, we show that processing a request can be reduced to an execution of the Dijkstra’s shortest-path algorithm on a carefully computed weighted graph leading to the speed-up.

Subject Classification

ACM Subject Classification
  • Theory of computation → K-server algorithms
  • k-server
  • Work Function Algorithm
  • Minimum-cost Flow


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