Core Concepts
The authors design efficient content-oblivious algorithms that elect a leader in oriented and non-oriented rings, without relying on any message content.
Abstract
The paper presents two main results:
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For oriented rings:
- The authors design a quiescently terminating content-oblivious algorithm that elects a leader in oriented rings of n nodes with unique IDs.
- The algorithm has a message complexity of O(n·IDmax), where IDmax is the maximum ID assigned to a node.
- The key ideas are:
- Running two parallel instances of a basic algorithm, one over the clockwise (CW) channel and one over the counterclockwise (CCW) channel.
- Ensuring the CCW instance lags behind the CW one, so that the leader can be uniquely identified by the event where a node's CW and CCW pulse counts match its ID.
- Using this event to initiate a termination pulse that propagates through the network, allowing all nodes to quiescently terminate.
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For non-oriented rings:
- The authors design a quiescently stabilizing content-oblivious algorithm that elects a leader and orients the ring in non-oriented rings of n nodes with unique IDs.
- The algorithm has a message complexity of O(n·IDmax).
- The key idea is to have each node simulate two parallel executions of the basic algorithm, one using each of its two ports. The direction with more pulses is declared as the clockwise orientation.
- The algorithm does not terminate but reaches quiescence, where all nodes have correctly identified the leader and the ring orientation.
The authors also prove a lower bound, showing that any deterministic terminating content-oblivious leader election algorithm in rings must send at least Ω(n log(IDmax/n)) messages.