Beep-And-Sleep: Message and Energy Efficient Set Cover
Thorsten G\"otte, Christina Kolb, Christian Scheideler, Julian, Werthmann

TL;DR
This paper introduces message and energy-efficient distributed algorithms for the Set Cover problem, achieving near-optimal time and message complexity in the $KT_0$ model and a beeping model variant with trade-offs.
Contribution
It presents the first near-optimal distributed algorithms for Set Cover in both the $KT_0$ and beeping models, improving efficiency and energy consumption.
Findings
Achieves $ ilde{O}( ext{log}^2( ext{Delta}))$-time and $O( ext{sqrt}( ext{Delta})(n+m))$-message algorithm in $KT_0$ model.
Provides a Beeping model algorithm with carrier-sensing that balances runtime and approximation ratio.
Demonstrates near-optimality of the proposed algorithms in their respective models.
Abstract
We observe message-efficient distributed algorithms for the Set Cover problem. Given a ground set of elements and subsets of , we aim to find the minimal number of these subsets that contain all elements. In the default distributed setup of this problem, each set has a bidirected communication link with each element it contains. Our first result is a -time and -message algorithm with expected approximation ration of in the model. The value denotes the maximal cardinality of each subset. Our algorithm is \emph{almost} optimal with regard to time and message complexity. Further, we present Set Cover algorithm in the Beeping model that only relies on carrier-sensing and can trade runtime for approximation ratio similar to the celebrated algorithm by Kuhn and Wattenhofer [PODC '03].
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Cryptography and Data Security · Distributed systems and fault tolerance
