An Improved Algorithm For Online Reranking

09/11/2022
by   Marcin Bienkowski, et al.
0

We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of n elements. An input is a stream of preferred sets R_1, R_2, …, R_t, …. Upon seeing R_t and without knowledge of any future sets, an algorithm has to rerank elements (change the list ordering), so that at least one element of R_t 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 R_t 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 against the static optimal solution (a single optimal list ordering), in this paper, we study an arguably harder variant where the benchmark is the provably stronger optimal dynamic solution OPT (that may also modify the list ordering). In terms of an online shop, this means that the aggregated preferences of its user base evolve with time. We construct a computationally efficient randomized algorithm whose competitive ratio (ALG-to-OPT cost ratio) is O(r^2) and prove the existence of a deterministic O(r^4)-competitive algorithm. Here, r is the maximum cardinality of sets R_t. This is the first algorithm whose ratio does not depend on n: the previously best algorithm for this problem was O(r^3/2·√(n))-competitive and Ω(r) is a lower bound on the performance of any deterministic online algorithm.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/30/2023

An Improved Deterministic Algorithm for the Online Min-Sum Set Cover Problem

We study the online variant of the Min-Sum Set Cover (MSSC) problem, a g...
research
03/04/2020

The Online Min-Sum Set Cover Problem

We consider the online Min-Sum Set Cover (MSSC), a natural and intriguin...
research
03/28/2022

Efficient Algorithm for Deterministic Search of Hot Elements

When facing a very large stream of data, it is often desirable to extrac...
research
10/25/2020

A Novel Move-To-Front-or-Logarithmic Position (MFLP) Online List Update Algorithm

In this paper we propose a novel online deterministic list update algori...
research
11/05/2020

Efficient Online Learning of Optimal Rankings: Dimensionality Reduction via Gradient Descent

We consider a natural model of online preference aggregation, where sets...
research
05/02/2023

A Subquadratic Bound for Online Bisection

In the online bisection problem one has to maintain a partition of n ele...
research
04/18/2021

Online List Access with Precedence Constraints

This paper considers a natural generalization of the online list access ...

Please sign up or login with your details

Forgot password? Click here to reset