TY - GEN
T1 - On the impact of identifiers on local decision
AU - Fraigniaud, Pierre
AU - Halldórsson, Magnús M.
AU - Korman, Amos
PY - 2012
Y1 - 2012
N2 - The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that are inherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local computation, i.e., when nodes can gather information only from nodes at bounded distances, some insight regarding the role of identities has been established. For instance, it was shown that, for large classes of construction problems, the role of the identities can be rather small. However, for the identities to play no role, some other kinds of mechanisms for breaking symmetry must be employed, such as edge-labeling or sense of direction. When it comes to local distributed decision problems, the specification of the decision task does not seem to involve symmetry breaking. Therefore, it is expected that, assuming nodes can gather sufficient information about their neighborhood, one could get rid of the identities, without employing extra mechanisms for breaking symmetry. We tackle this question in the framework of the LOCAL model. Let LD be the class of all problems that can be decided in a constant number of rounds in the LOCAL model. Similarly, let LD* be the class of all problems that can be decided at constant cost in the anonymous variant of the LOCAL model, in which nodes have no identities, but each node can get access to the (anonymous) ball of radius t around it, for any t, at a cost of t. It is clear that LD* ⊆ LD. We conjecture that LD*=LD. In this paper, we give several evidences supporting this conjecture. In particular, we show that it holds for hereditary problems, as well as when the nodes know an arbitrary upper bound on the total number of nodes. Moreover, we prove that the conjecture holds in the context of non-deterministic local decision, where nodes are given certificates (independent of the identities, if they exist), and the decision consists in verifying these certificates. In short, we prove that NLD*=NLD.
AB - The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that are inherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local computation, i.e., when nodes can gather information only from nodes at bounded distances, some insight regarding the role of identities has been established. For instance, it was shown that, for large classes of construction problems, the role of the identities can be rather small. However, for the identities to play no role, some other kinds of mechanisms for breaking symmetry must be employed, such as edge-labeling or sense of direction. When it comes to local distributed decision problems, the specification of the decision task does not seem to involve symmetry breaking. Therefore, it is expected that, assuming nodes can gather sufficient information about their neighborhood, one could get rid of the identities, without employing extra mechanisms for breaking symmetry. We tackle this question in the framework of the LOCAL model. Let LD be the class of all problems that can be decided in a constant number of rounds in the LOCAL model. Similarly, let LD* be the class of all problems that can be decided at constant cost in the anonymous variant of the LOCAL model, in which nodes have no identities, but each node can get access to the (anonymous) ball of radius t around it, for any t, at a cost of t. It is clear that LD* ⊆ LD. We conjecture that LD*=LD. In this paper, we give several evidences supporting this conjecture. In particular, we show that it holds for hereditary problems, as well as when the nodes know an arbitrary upper bound on the total number of nodes. Moreover, we prove that the conjecture holds in the context of non-deterministic local decision, where nodes are given certificates (independent of the identities, if they exist), and the decision consists in verifying these certificates. In short, we prove that NLD*=NLD.
KW - Distributed complexity
KW - decision problems
KW - identities
KW - locality
KW - non-determinism
KW - symmetry breaking
UR - http://www.scopus.com/inward/record.url?scp=84871645676&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-35476-2_16
DO - 10.1007/978-3-642-35476-2_16
M3 - Conference contribution
AN - SCOPUS:84871645676
SN - 9783642354755
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 224
EP - 238
BT - Principles of Distributed Systems - 16th International Conference, OPODIS 2012, Proceedings
T2 - 16th International Conference on Principles of Distributed Systems, OPODIS 2012
Y2 - 18 December 2012 through 20 December 2012
ER -