Computing functions on asynchronous anonymous networks

Masafumi Yamashita, T. Kameda

Research output: Contribution to journalArticle

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

Fingerprint

Anonymous Networks
Computing
Lower bound
Message Complexity
Necessary Conditions
Necessary
Sufficient Conditions

All Science Journal Classification (ASJC) codes

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

Cite this

Yamashita, M., & Kameda, T. (1996). Computing functions on asynchronous anonymous networks. Mathematical Systems Theory, 29(4), 331-356.

Computing functions on asynchronous anonymous networks. / Yamashita, Masafumi; Kameda, T.

In: Mathematical Systems Theory, Vol. 29, No. 4, 01.07.1996, p. 331-356.

Research output: Contribution to journalArticle

Yamashita, M & Kameda, T 1996, 'Computing functions on asynchronous anonymous networks', Mathematical Systems Theory, vol. 29, no. 4, pp. 331-356.
Yamashita, Masafumi ; Kameda, T. / Computing functions on asynchronous anonymous networks. In: Mathematical Systems Theory. 1996 ; Vol. 29, No. 4. pp. 331-356.
@article{f0b721815743415cb07829ded17ece69,
title = "Computing functions on asynchronous anonymous networks",
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.",
author = "Masafumi Yamashita and T. Kameda",
year = "1996",
month = "7",
day = "1",
language = "English",
volume = "29",
pages = "331--356",
journal = "Theory of Computing Systems",
issn = "1432-4350",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - Computing functions on asynchronous anonymous networks

AU - Yamashita, Masafumi

AU - Kameda, T.

PY - 1996/7/1

Y1 - 1996/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33748851013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748851013&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33748851013

VL - 29

SP - 331

EP - 356

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 4

ER -