Dynamic balanced graph partitioning

Chen Avin, Marcin Bienkowski, Andreas Loukas, Maciej Pacut, Stefan Schmid

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

This paper initiates the study of the classic balan ced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between n nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into L clusters, each of size k, such that frequently communicating nodes are located in the same cluster. The partitioning can be updated dynamically by migrating nodes between clusters. The goal is to devise online algorithms which jointly minimize the amount of intercluster communication and migration cost. The problem feat ures interesting connections to other well-known online problems. For example, scenarios with L = 2 generalize online paging, and scenarios with k = 2 constitute a novel online variant of maximum matching. We present several lower bounds and algorithms for settings both with and without cluster-size augmentation. In particular, we prove that any deterministic online algorithm has a competitive ratio of at least k, even with significant augmentation. Our main algorithmic contributions are an O(k log k)-competitive deter¬ ministic algorithm for the general setting with constant augmentation and a constant competitive algorithm for the maximum matching variant.

Original languageEnglish
Pages (from-to)1791-1812
Number of pages22
JournalSIAM Journal on Discrete Mathematics
Volume34
Issue number3
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Cloud computing
  • Clustering
  • Competitive analysis
  • Graph partitioning

ASJC Scopus subject areas

  • Mathematics (all)

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