Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty

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

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.

Citation

Bampis, E., Dürr, C., Erlebach, T., de Lima, M. S., Megow, N., & Schlöter, J. (2021, December). Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty. Presented at 29th Annual European Symposium on Algorithms (ESA 2021), Lisbon, Portugal (Virtual Conference)

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 29th Annual European Symposium on Algorithms (ESA 2021)
• Acceptance Date: Jun 23, 2021
• Online Publication Date: Aug 31, 2021
• Publication Date: 2021
• Deposit Date: Dec 30, 2021
• Publicly Available Date: Jan 4, 2022
• Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
• Volume: 204
• Pages: 10:1-10:18
• Series Title: LIPIcs
• DOI: https://doi.org/10.4230/lipics.esa.2021.10
• Public URL: https://durham-repository.worktribe.com/output/1137240