Computing functions on asynchronous anonymous networks

Masafumi Yamashita, T. Kameda

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

In an "anonymous" network the processors have no identity numbers. We investigate the problem of computing a given function f on an asynchronous anonymous network in the sense that each processor computes f (I) for any input I = (I(υ1), . . . , I(υn)), where I(υi) is the input to processor υi, i = 1, 2, . . . , n. We address the following three questions: (1) What functions are computable on a given network? (2) Is there a "universal" algorithm which, given any network G and any function f computable on G as inputs, computes f on G? (3) How can one find lower bounds on the message complexity of computing various functions on anonymous networks? We give a necessary and sufficient condition for a function to be computable on an asynchronous anonymous network, and present a universal algorithm for computing f(I) on any network G, which accepts G and f computable on G, as well as {I(υi)}, as inputs. The universal algorithm requires O(mn) messages in the worst case, where n and m are the numbers of processors and links in the network, respectively. We also propose a method for deriving a lower bound on the number of messages necessary to solve the above problem on asynchronous anonymous networks.

Original languageEnglish
Pages (from-to)331-356
Number of pages26
JournalMathematical Systems Theory
Volume29
Issue number4
Publication statusPublished - Jul 1 1996

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics

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