Hiding in the crowd: asympstotic bounds on blocking sets

N. Jovanovic; J.H.M. Korst; Z. Aleksovski; R. Jovanovic

Hiding in the crowd: asympstotic bounds on blocking sets

N. Jovanovic, J.H.M. Korst, Z. Aleksovski, R. Jovanovic

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

Abstract

We consider the problem of blocking all rays emanating from a unit disk U by a minimum number N_d of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of N_d, as d tends to infinity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that $\frac{\pi^2}{16} \leq \frac{N_d}{d^2} \leq \frac{\pi^2}{2}$, as d goes to infinity.

Original language	English
Title of host publication	Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)
Editors	J. Vahrenhold
Place of Publication	Dortmund
Publisher	Technische Universität Dortmund
Pages	197-200
Publication status	Published - 2010
Event	26th European Workshop on Computational Geometry (EuroCG 2010) - Dortmund Duration: 22 Mar 2010 → 24 Mar 2010 Conference number: 26 http://eurocg.org/

Workshop

Workshop	26th European Workshop on Computational Geometry (EuroCG 2010)
Abbreviated title	EuroCG 2010
City	Dortmund
Period	22/03/10 → 24/03/10
Internet address	http://eurocg.org/

Cite this

@inproceedings{58e7355a354f4a7aa625639bd95d56ff,

title = "Hiding in the crowd: asympstotic bounds on blocking sets",

abstract = "We consider the problem of blocking all rays emanating from a unit disk U by a minimum number N_d of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of N_d, as d tends to infinity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that $\frac{\pi^2}{16} \leq \frac{N_d}{d^2} \leq \frac{\pi^2}{2}$, as d goes to infinity.",

author = "N. Jovanovic and J.H.M. Korst and Z. Aleksovski and R. Jovanovic",

year = "2010",

language = "English",

pages = "197--200",

editor = "J. Vahrenhold",

booktitle = "Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)",

publisher = "Technische Universit{\"a}t Dortmund",

note = "26th European Workshop on Computational Geometry (EuroCG 2010), EuroCG 2010 ; Conference date: 22-03-2010 Through 24-03-2010",

url = "http://eurocg.org/",

}

Jovanovic, N, Korst, JHM, Aleksovski, Z & Jovanovic, R 2010, Hiding in the crowd: asympstotic bounds on blocking sets. in J Vahrenhold (ed.), Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010). Technische Universität Dortmund, Dortmund, pp. 197-200, 26th European Workshop on Computational Geometry (EuroCG 2010), Dortmund, 22/03/10.

Hiding in the crowd: asympstotic bounds on blocking sets. / Jovanovic, N.; Korst, J.H.M.; Aleksovski, Z. et al.
Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010). ed. / J. Vahrenhold. Dortmund: Technische Universität Dortmund, 2010. p. 197-200.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

TY - GEN

T1 - Hiding in the crowd: asympstotic bounds on blocking sets

AU - Jovanovic, N.

AU - Korst, J.H.M.

AU - Aleksovski, Z.

AU - Jovanovic, R.

N1 - Conference code: 26

PY - 2010

Y1 - 2010

N2 - We consider the problem of blocking all rays emanating from a unit disk U by a minimum number N_d of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of N_d, as d tends to infinity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that $\frac{\pi^2}{16} \leq \frac{N_d}{d^2} \leq \frac{\pi^2}{2}$, as d goes to infinity.

AB - We consider the problem of blocking all rays emanating from a unit disk U by a minimum number N_d of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of N_d, as d tends to infinity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that $\frac{\pi^2}{16} \leq \frac{N_d}{d^2} \leq \frac{\pi^2}{2}$, as d goes to infinity.

M3 - Conference contribution

SP - 197

EP - 200

BT - Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)

A2 - Vahrenhold, J.

PB - Technische Universität Dortmund

CY - Dortmund

T2 - 26th European Workshop on Computational Geometry (EuroCG 2010)

Y2 - 22 March 2010 through 24 March 2010

ER -

Hiding in the crowd: asympstotic bounds on blocking sets

Abstract

Workshop

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