An Improved Algorithm For Online Min-Sum Set Cover
Marcin Bienkowski, Marcin Mucha

TL;DR
This paper introduces new online algorithms for the Min-Sum Set Cover problem that adapt to evolving preferences, achieving competitive ratios independent of the total number of elements.
Contribution
It presents the first algorithms with competitive ratios independent of the total element count, improving upon previous ratios that depended on n.
Findings
Randomized algorithm with O(r^2) ratio
Deterministic algorithm with O(r^4) ratio
First ratio independent of n
Abstract
We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of elements. An input is a stream of preferred sets . Upon seeing and without knowledge of any future sets, an algorithm has to rerank elements (change the list ordering), so that at least one element of is found near the list front. The incurred cost is a sum of the list update costs (the number of swaps of neighboring list elements) and access costs (position of the first element of on the list). This scenario occurs naturally in applications such as ordering items in an online shop using aggregated preferences of shop customers. The theoretical underpinning of this problem is known as Min-Sum Set Cover. Unlike previous work (Fotakis et al., ICALP 2020, NIPS 2020) that mostly studied the performance of an online algorithm ALG…
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Taxonomy
TopicsOptimization and Search Problems · Advanced Bandit Algorithms Research · Auction Theory and Applications
MethodsOPT · Balanced Selection
