Set Cover with Delay -- Clairvoyance is not Required
Yossi Azar, Ashish Chiplunkar, Shay Kutten, Noam Touitou

TL;DR
This paper introduces the first non-clairvoyant algorithm for set cover with delay, achieving near-optimal competitiveness independent of request count, and establishes lower bounds showing clairvoyance offers limited advantage.
Contribution
It presents the first non-clairvoyant algorithm for set cover with delay with competitive ratio $O( ext{log } n ext{ log } m)$, matching the best clairvoyant results and providing new lower bounds.
Findings
Non-clairvoyant algorithm is $O( ext{log } n ext{ log } m)$-competitive.
Clairvoyance does not significantly improve competitiveness, with lower bounds of $ ext{Omega}( ext{sqrt(log n})$ and $ ext{Omega}( ext{sqrt(log m})$.
Algorithm's competitiveness is independent of the number of requests.
Abstract
In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) -- specifically, we present the first non-clairvoyant algorithm, which is -competitive, where is the number of elements and is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present lower bounds of and for SCD which apply for the clairvoyant case. In addition, the competitiveness of our algorithm does not depend on the number of requests. Such a guarantee on the size of the universe alone was not previously known even for the…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Distributed systems and fault tolerance
