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Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty

Authors Evripidis Bampis , Christoph Dürr , Thomas Erlebach , Murilo Santos de Lima , Nicole Megow , Jens Schlöter

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Author Details

Evripidis Bampis
  • Sorbonne Université, CNRS, LIP6, Paris, France
Christoph Dürr
  • Sorbonne Université, CNRS, LIP6, Paris, France
Thomas Erlebach
  • School of Informatics, University of Leicester, UK
Murilo Santos de Lima
  • School of Informatics, University of Leicester, UK
Nicole Megow
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany
Jens Schlöter
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany

Funding

  • Bampis, Evripidis: Supported by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).
  • Dürr, Christoph: Supported by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).
  • Erlebach, Thomas: Supported by EPSRC grant EP/S033483/1.
  • de Lima, Murilo Santos: Funded by EPSRC grant EP/S033483/1.
  • Megow, Nicole: Supported by the German Science Foundation (DFG) under contract ME 3825/1.
  • Schlöter, Jens: Funded by the German Science Foundation (DFG) under contract ME 3825/1.

Acknowledgements

The authors would like to thank the anonymous referees for their careful reading and helpful suggestions.

Cite As Get BibTex

Evripidis Bampis, Christoph Dürr, Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter. Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.10

Abstract

Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge. Querying a node has a cost and reveals the precise weight of the node, drawn from the given probability distribution. Using competitive analysis, we compare the expected query cost of an algorithm with the expected cost of an optimal query set for the given instance. For the general case, we give a polynomial-time f(α)-competitive algorithm, where f(α) ∈ [1.618+ε,2] depends on the approximation ratio α for an underlying vertex cover problem. We also show that no algorithm using a similar approach can be better than 1.5-competitive. Furthermore, we give polynomial-time 4/3-competitive algorithms for bipartite graphs with arbitrary query costs and for hypergraphs with a single hyperedge and uniform query costs, with matching lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Discrete mathematics
Keywords
  • Explorable uncertainty
  • queries
  • stochastic optimization
  • graph orientation
  • selection problems

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