Node Labels in Local Decision
Pierre Fraigniaud, Juho Hirvonen, Jukka Suomela

TL;DR
This paper investigates the minimal information leakage needed from node labels to solve local decision problems in network computing, classifying scalar oracles based on their asymptotic behavior and their power relative to unique identifiers.
Contribution
It provides a complete characterization of scalar oracles, distinguishing large and small ones, and their sufficiency in replacing unique identifiers for local decision problems.
Findings
Large oracles are as powerful as unique identifiers in local decision.
Small oracles do not fully replace unique identifiers for certain problems.
A dichotomy classification of scalar oracles based on their asymptotic properties.
Abstract
The role of unique node identifiers in network computing is well understood as far as symmetry breaking is concerned. However, the unique identifiers also leak information about the computing environment - in particular, they provide some nodes with information related to the size of the network. It was recently proved that in the context of local decision, there are some decision problems such that (1) they cannot be solved without unique identifiers, and (2) unique node identifiers leak a sufficient amount of information such that the problem becomes solvable (PODC 2013). In this work we give study what is the minimal amount of information that we need to leak from the environment to the nodes in order to solve local decision problems. Our key results are related to scalar oracles that, for any given , provide a multiset of labels; then the adversary assigns the…
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