Weighted Set Multi-Cover on Bounded Universe and Applications in Package Recommendation
Nima Shahbazi, Aryan Esmailpour, Stavros Sintos

TL;DR
This paper introduces exact and approximation algorithms for the weighted set multi-cover problem with a bounded universe, improving efficiency and solution quality for large data-driven applications like recommendation and data selection.
Contribution
It presents novel algorithms, including a dynamic programming exact solution and faster approximation algorithms, tailored for the bounded universe case of the weighted set multi-cover problem.
Findings
Exact dynamic programming algorithm solves small universe cases efficiently.
A 2-approximation algorithm based on LP rounding outperforms greedy methods.
Faster (2+ε)-approximation algorithm suitable for large datasets.
Abstract
The weighted set multi-cover problem is a fundamental generalization of set cover that arises in data-driven applications where one must select a small, low-cost subset from a large collection of candidates under coverage constraints. In data management settings, such problems arise naturally either as expressive database queries or as post-processing steps over query results, for example, when selecting representative or diverse subsets from large relations returned by database queries for decision support, recommendation, fairness-aware data selection, or crowd-sourcing. While the general weighted set multi-cover problem is NP-complete, many practical workloads involve a \emph{bounded universe} of items that must be covered, leading to the Weighted Set Multi-Cover with Bounded Universe (WSMC-BU) problem, where the universe size is constant. In this paper, we develop exact and…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Packing Problems · Facility Location and Emergency Management
