Local Computation Algorithms for Graphs of Non-constant Degrees

Reut Levi, Ronitt Rubinfeld, Anak Yodpinyanee

Research output: Contribution to journalArticlepeer-review

Abstract

In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with subexponential dependence on d, while maintaining polylogarithmic dependence on n. We present:a randomized LCA for computing maximal independent sets whose time and space complexities are quasi-polynomial in d and polylogarithmic in n;for constant ε> 0 , a randomized LCA that provides a (1 - ε) -approximation to maximum matching with high probability, whose time and space complexities are polynomial in d and polylogarithmic in n.

Original languageEnglish
Pages (from-to)971-994
Number of pages24
JournalAlgorithmica
Volume77
Issue number4
DOIs
StatePublished - 1 Apr 2017

Keywords

  • Local computation algorithms
  • Maximal independent set
  • Maximum matching
  • Randomized algorithms

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