Mostra el registre d'ítem simple
Maximum box problem on stochastic points
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.rights | Attribution 4.0 International |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ |
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 |
Fitxers d'aquest items
Aquest ítem apareix a les col·leccions següents
-
Articles de revista [3.261]
-
Articles de revista [31]