Finding shadows among disks

N. Jovanovic; J.H.M. Korst; Z. Aleksovski; W.P.A.J. Michiels; J.J. Lukkien; E.H.L. Aarts

Finding shadows among disks

N. Jovanovic, J.H.M. Korst, Z. Aleksovski, W.P.A.J. Michiels, J.J. Lukkien, E.H.L. Aarts

Research output: Other contribution

Abstract

Given a set of n non-overlapping unit disks in the plane, a line l is called blocked if it intersects at least one of the disks and a point p is called a shadow point if all lines containing p are blocked. In addition, a maximal closed set of shadow points is called a shadow region. We derive properties of shadow regions, and present an O(n^4) algorithm that outputs all shadow regions. We prove that the number of shadow regions is O(n^4) for some instances, which implies that the worst-case time complexity of the presented algorithm is optimal.

Original language	English
Number of pages	6
Publication status	Published - 2012
Externally published	Yes

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title = "Finding shadows among disks",

abstract = "Given a set of n non-overlapping unit disks in the plane, a line l is called blocked if it intersects at least one of the disks and a point p is called a shadow point if all lines containing p are blocked. In addition, a maximal closed set of shadow points is called a shadow region. We derive properties of shadow regions, and present an O(n^4) algorithm that outputs all shadow regions. We prove that the number of shadow regions is O(n^4) for some instances, which implies that the worst-case time complexity of the presented algorithm is optimal.",

author = "N. Jovanovic and J.H.M. Korst and Z. Aleksovski and W.P.A.J. Michiels and J.J. Lukkien and E.H.L. Aarts",

year = "2012",

language = "English",

type = "Other",

}

TY - GEN

T1 - Finding shadows among disks

AU - Jovanovic, N.

AU - Korst, J.H.M.

AU - Aleksovski, Z.

AU - Michiels, W.P.A.J.

AU - Lukkien, J.J.

AU - Aarts, E.H.L.

PY - 2012

Y1 - 2012

N2 - Given a set of n non-overlapping unit disks in the plane, a line l is called blocked if it intersects at least one of the disks and a point p is called a shadow point if all lines containing p are blocked. In addition, a maximal closed set of shadow points is called a shadow region. We derive properties of shadow regions, and present an O(n^4) algorithm that outputs all shadow regions. We prove that the number of shadow regions is O(n^4) for some instances, which implies that the worst-case time complexity of the presented algorithm is optimal.

AB - Given a set of n non-overlapping unit disks in the plane, a line l is called blocked if it intersects at least one of the disks and a point p is called a shadow point if all lines containing p are blocked. In addition, a maximal closed set of shadow points is called a shadow region. We derive properties of shadow regions, and present an O(n^4) algorithm that outputs all shadow regions. We prove that the number of shadow regions is O(n^4) for some instances, which implies that the worst-case time complexity of the presented algorithm is optimal.

M3 - Other contribution

ER -

Finding shadows among disks

Abstract

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