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dc.contributor.authorCaraballo, Luis E.
dc.contributor.authorPérez Lantero, Pablo
dc.contributor.authorSeara Ojea, Carlos
dc.contributor.authorVentura, Inmaculada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2022-02-07T11:39:16Z
dc.date.available2022-02-07T11:39:16Z
dc.date.issued2021-10-28
dc.identifier.citationCaraballo, L. [et al.]. Maximum box problem on stochastic points. "Algorithmica", 28 Octubre 2021, vol. 83, p. 3741-3765.
dc.identifier.issn1432-0541
dc.identifier.urihttp://hdl.handle.net/2117/361833
dc.descriptionThis 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.abstractGiven 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.sponsorshipThis 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.extent25 p.
dc.language.isoeng
dc.publisherSpringer Nature
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshCombinatorial analysis
dc.subject.lcshComputer science--Mathematics
dc.subject.otherRandom weighted points
dc.subject.otherBoxes
dc.subject.otherRed and blue points
dc.subject.other#P-hardness
dc.titleMaximum box problem on stochastic points
dc.typeArticle
dc.subject.lemacCombinacions (Matemàtica)
dc.subject.lemacInformàtica--Matemàtica
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.identifier.doi10.1007/s00453-021-00882-z
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05E Algebraic combinatorics
dc.subject.amsClassificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
dc.relation.publisherversionhttps://link.springer.com/article/10.1007%2Fs00453-021-00882-z
dc.rights.accessOpen Access
local.identifier.drac32507352
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
local.citation.authorCaraballo, L.; Perez-Lantero, P.; Seara, C.; Ventura, I.
local.citation.publicationNameAlgorithmica
local.citation.volume83
local.citation.startingPage3741
local.citation.endingPage3765


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