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Piercing axis-parallel boxes

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dc.contributor.authorChudnovsky, Maria
dc.contributor.authorSpirkl, Sophie
dc.contributor.authorZerbib, Shira
dc.date.accessioned2022-08-12T01:16:49Z
dc.date.available2022-08-12T01:16:49Z
dc.date.issued2018
dc.description.abstractLet F be a finite family of axis-parallel boxes in Rd such that F contains no k + 1 pairwise disjoint boxes. We prove that if F contains a subfamily M of k pairwise disjoint boxes with the property that for every F E F and M E M with F ∩ M ≠ 6= Ø, either F contains a corner of M or M contains 2d-1 corners of F, then F can be pierced by O(k) points. One consequence of this result is that if d = 2 and the ratio between any of the side lengths of any box is bounded by a constant, then F can be pierced by O(k) points. We further show that if for each two intersecting boxes in F a corner of one is contained in the other, then F can be pierced by at most O(k log log(k)) points, and in the special case where F contains only cubes this bound improves to O(k).en
dc.description.sponsorshipSupported by NSF grant DMS-1550991 and US Army Research Office Grant W911NF-16-1-0404en
dc.identifier.urihttps://doi.org/10.37236/7034
dc.identifier.urihttp://hdl.handle.net/10012/18533
dc.language.isoenen
dc.publisherThe Electronic Journal of Combinatoricsen
dc.subjectaxis-parallel boxesen
dc.subjecthitting seten
dc.subjectpiercingen
dc.subjectpacking and coveringen
dc.subjectmatching and coveringen
dc.titlePiercing axis-parallel boxesen
dc.typeArticleen
dcterms.bibliographicCitationChudnovsky, M., Spirkl, S., & Zerbib, S. (2018). Piercing Axis-Parallel Boxes. The Electronic Journal of Combinatorics, P1.70-P1.70. https://doi.org/10.37236/7034en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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