Balanced allocation on graphs: a random walk approach

Ali Pourmiri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
13 Downloads (Pure)


We propose algorithms for allocating n sequential balls into n bins that are interconnected as a d-regular n-vertex graph G, where d ≥ 3 can be any integer. In general, the algorithms proceeds in n succeeding rounds. Let ℓ > 0 be an integer, which is given as an input to the algorithms. In each round, ball 1 ≤ tn picks a node of G uniformly at random and performs a nonbacktracking random walk of length ℓ from the chosen node and simultaneously collects the load information of a subset of the visited nodes. It then allocates itself to one of them with the minimum load (ties are broken uniformly at random). For graphs with sufficiently large girths, we obtain upper and lower bounds for the maximum number of balls at any bin after allocating all n balls in terms of ℓ, with high probability.

Original languageEnglish
Pages (from-to)980-1009
Number of pages30
JournalRandom Structures and Algorithms
Issue number4
Publication statusPublished - Dec 2019


  • balanced allocation
  • balls-into-bins models
  • nonbacktracking random walks


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