The Pareto Cover Problem

Authors Bento Natura , Meike Neuwohner , Stefan Weltge

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Author Details

Bento Natura
  • London School of Economics and Political Science, UK
Meike Neuwohner
  • Forschungsinstitut für Diskrete Mathematik, Universität Bonn, Germany
Stefan Weltge
  • Technische Universität München, Germany

Cite AsGet BibTex

Bento Natura, Meike Neuwohner, and Stefan Weltge. The Pareto Cover Problem. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 80:1-80:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We introduce the problem of finding a set B of k points in [0,1]ⁿ such that the expected cost of the cheapest point in B that dominates a random point from [0,1]ⁿ is minimized. We study the case where the coordinates of the random points are independently distributed and the cost function is linear. This problem arises naturally in various application areas where customers' requests are satisfied based on predefined products, each corresponding to a subset of features. We show that the problem is NP-hard already for k = 2 when each coordinate is drawn from {0,1}, and obtain an FPTAS for general fixed k under mild assumptions on the distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
  • Theory of computation → Dynamic programming
  • Theory of computation → Packing and covering problems
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Discrete optimization
  • Pareto
  • Covering
  • Optimization
  • Approximation Algorithm


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