Results on k-sets and j-facets via continuous motion

Artur Andrzejak; Boris Aronov; Sariel Har-Peled; Raimund Seidel; Emo Welzl

doi:10.1145/276884.276906

Results on k-sets and j-facets via continuous motion

Artur Andrzejak, Boris Aronov, Sariel Har-Peled, Raimund Seidel, Emo Welzl

Research output: Contribution to conference › Paper › peer-review

Abstract

The set P of n points in R^d in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

Original language	English (US)
Pages	192-199
Number of pages	8
DOIs	https://doi.org/10.1145/276884.276906
State	Published - 1998
Externally published	Yes
Event	Proceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA Duration: Jun 7 1998 → Jun 10 1998

Other

Other	Proceedings of the 1998 14th Annual Symposium on Computational Geometry
City	Minneapolis, MN, USA
Period	6/7/98 → 6/10/98

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

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10.1145/276884.276906

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title = "Results on k-sets and j-facets via continuous motion",

abstract = "The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.",

author = "Artur Andrzejak and Boris Aronov and Sariel Har-Peled and Raimund Seidel and Emo Welzl",

year = "1998",

doi = "10.1145/276884.276906",

language = "English (US)",

pages = "192--199",

note = "Proceedings of the 1998 14th Annual Symposium on Computational Geometry ; Conference date: 07-06-1998 Through 10-06-1998",

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T1 - Results on k-sets and j-facets via continuous motion

AU - Andrzejak, Artur

AU - Aronov, Boris

AU - Har-Peled, Sariel

AU - Seidel, Raimund

AU - Welzl, Emo

PY - 1998

Y1 - 1998

N2 - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

AB - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

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T2 - Proceedings of the 1998 14th Annual Symposium on Computational Geometry

Y2 - 7 June 1998 through 10 June 1998

ER -

Results on k-sets and j-facets via continuous motion

Abstract

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