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 language | English |
|---|---|
| Pages (from-to) | 331-356 |
| Number of pages | 26 |
| Journal | Mathematical Systems Theory |
| Volume | 29 |
| Issue number | 4 |
| Publication status | Published - Jul 1 1996 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Mathematics(all)
- Computational Theory and Mathematics
Cite this
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 journal › Article
}
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.
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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 -