dc.contributor.author Caraballo, Luis E. dc.contributor.author Pérez Lantero, Pablo dc.contributor.author Seara Ojea, Carlos dc.contributor.author Ventura, Inmaculada dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2022-02-07T11:39:16Z dc.date.available 2022-02-07T11:39:16Z dc.date.issued 2021-10-28 dc.identifier.citation Caraballo, L. [et al.]. Maximum box problem on stochastic points. "Algorithmica", 28 Octubre 2021, vol. 83, p. 3741-3765. dc.identifier.issn 1432-0541 dc.identifier.uri http://hdl.handle.net/2117/361833 dc.description This is a post-peer-review, pre-copyedit version of an article published in Algorithmica. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00453-021-00882-z. dc.description.abstract Given a finite set of weighted points in Rd (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is maximized. We consider that each point of the input has a probability of being present in the final random point set, and these events are mutually independent; then, the total weight of a maximum box is a random variable. We aim to compute both the probability that this variable is at least a given parameter, and its expectation. We show that even in d=1 these computations are #P-hard, and give pseudo-polynomial time algorithms in the case where the weights are integers in a bounded interval. For d=2, we consider that each point is colored red or blue, where red points have weight +1 and blue points weight -8. The random variable is the maximum number of red points that can be covered with a box not containing any blue point. We prove that the above two computations are also #P-hard, and give a polynomial-time algorithm for computing the probability that there is a box containing exactly two red points, no blue point, and a given point of the plane. dc.description.sponsorship This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922. dc.format.extent 25 p. dc.language.iso eng dc.publisher Springer Nature dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències dc.subject.lcsh Combinatorial analysis dc.subject.lcsh Computer science--Mathematics dc.subject.other Random weighted points dc.subject.other Boxes dc.subject.other Red and blue points dc.subject.other #P-hardness dc.title Maximum box problem on stochastic points dc.type Article dc.subject.lemac Combinacions (Matemàtica) dc.subject.lemac Informàtica--Matemàtica dc.contributor.group Universitat Politècnica de Catalunya. CGA - Computational Geometry and Applications dc.identifier.doi 10.1007/s00453-021-00882-z dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::05 Combinatorics::05E Algebraic combinatorics dc.subject.ams Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science dc.relation.publisherversion https://link.springer.com/article/10.1007%2Fs00453-021-00882-z dc.rights.access Open Access local.identifier.drac 32507352 dc.description.version Postprint (published version) dc.relation.projectid info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT local.citation.author Caraballo, L.; Perez-Lantero, P.; Seara, C.; Ventura, I. local.citation.publicationName Algorithmica local.citation.volume 83 local.citation.startingPage 3741 local.citation.endingPage 3765
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