Time vs. Information Tradeoffs for Leader Election in Anonymous Trees
Christian Glacet, Avery Miller, Andrzej Pelc

TL;DR
This paper investigates the tradeoffs between time and the amount of initial information needed for deterministic leader election in anonymous trees, providing bounds on advice size for various time constraints.
Contribution
It establishes tight bounds on advice size necessary for leader election in anonymous trees across different time regimes, revealing how information requirements decrease with increased time.
Findings
Leader election in time equal to diameter requires no advice.
For time just below diameter, advice size is tightly bounded by Θ(log D).
For shorter times, advice size scales with Θ(n) or Θ(log n) depending on parameters.
Abstract
The leader election task calls for all nodes of a network to agree on a single node. If the nodes of the network are anonymous, the task of leader election is formulated as follows: every node of the network must output a simple path, coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in anonymous trees. Our aim is to establish tradeoffs between the allocated time and the amount of information that has to be given to the nodes to enable leader election in time in all trees for which leader election in this time is at all possible. Following the framework of , this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire tree. The length of this string is called the…
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Taxonomy
TopicsInternet Traffic Analysis and Secure E-voting · Cryptography and Data Security · Complexity and Algorithms in Graphs
