TY - GEN

T1 - What can be decided locally without identifiers

AU - Fraigniaud, Pierre

AU - Göös, Mika

AU - Korman, Amos

AU - Suomela, Jukka

PY - 2013

Y1 - 2013

N2 - Do unique node identifiers help in deciding whether a network G has a prescribed property P? We study this question in the context of distributed local decision, where the objective is to decide whether G has property P by having each node run a constant-time distributed decision algorithm. In a yes-instance all nodes should output yes, while in a no-instance at least one node should output no. Recently, Fraigniaud et al. (OPODIS 2012) gave several conditions under which identifiers are not needed, and they conjectured that identifiers are not needed in any decision problem. In the present work, we disprove the conjecture. More than that, we analyse two critical variations of the underlying model of distributed computing: (B): the size of the identifiers is bounded by a function of the size of the input network, (-B): the identifiers are unbounded, (C): the nodes run a computable algorithm, (-C): the nodes can compute any, possibly uncomputable function. While it is easy to see that under (B, C) identifiers are not needed, we show that under all other combinations there are properties that can be decided locally if and only if identifiers are present.

AB - Do unique node identifiers help in deciding whether a network G has a prescribed property P? We study this question in the context of distributed local decision, where the objective is to decide whether G has property P by having each node run a constant-time distributed decision algorithm. In a yes-instance all nodes should output yes, while in a no-instance at least one node should output no. Recently, Fraigniaud et al. (OPODIS 2012) gave several conditions under which identifiers are not needed, and they conjectured that identifiers are not needed in any decision problem. In the present work, we disprove the conjecture. More than that, we analyse two critical variations of the underlying model of distributed computing: (B): the size of the identifiers is bounded by a function of the size of the input network, (-B): the identifiers are unbounded, (C): the nodes run a computable algorithm, (-C): the nodes can compute any, possibly uncomputable function. While it is easy to see that under (B, C) identifiers are not needed, we show that under all other combinations there are properties that can be decided locally if and only if identifiers are present.

KW - Computabil-ity theory

KW - Distributed complexity

KW - Identifiers

KW - Local decision

UR - http://www.scopus.com/inward/record.url?scp=84883514526&partnerID=8YFLogxK

U2 - 10.1145/2484239.2484264

DO - 10.1145/2484239.2484264

M3 - Conference contribution

AN - SCOPUS:84883514526

SN - 9781450320658

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 157

EP - 165

BT - PODC 2013 - Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

T2 - 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013

Y2 - 22 July 2013 through 24 July 2013

ER -