TY - GEN
T1 - Covering arbitrary point patterns
AU - Mazumdar, Arya
AU - Wang, Ligong
PY - 2012
Y1 - 2012
N2 - This paper considers the problem of covering an arbitrary point pattern - a set of λT points in the interval [0, T] - with a subset of [0, T] that is drawn from a predefined codebook. The subset is required to contain either all or a certain proportion of the points in the pattern, depending on the problem setting. Also, all subsets in this codebook must have Lebesgue measure not exceeding dT where d ≤ 1 is a given constant. The problem of interest here is to find the trade-off between d and the size of the codebook. We find this trade-off asymptotically as T goes to infinity. When the subset is required to cover all the points, the answer turns out to be the same as in the case where the points were randomly generated by a Poisson process of intensity λ, the latter being obtained in an earlier work.
AB - This paper considers the problem of covering an arbitrary point pattern - a set of λT points in the interval [0, T] - with a subset of [0, T] that is drawn from a predefined codebook. The subset is required to contain either all or a certain proportion of the points in the pattern, depending on the problem setting. Also, all subsets in this codebook must have Lebesgue measure not exceeding dT where d ≤ 1 is a given constant. The problem of interest here is to find the trade-off between d and the size of the codebook. We find this trade-off asymptotically as T goes to infinity. When the subset is required to cover all the points, the answer turns out to be the same as in the case where the points were randomly generated by a Poisson process of intensity λ, the latter being obtained in an earlier work.
UR - http://www.scopus.com/inward/record.url?scp=84875735743&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875735743&partnerID=8YFLogxK
U2 - 10.1109/Allerton.2012.6483478
DO - 10.1109/Allerton.2012.6483478
M3 - Conference contribution
AN - SCOPUS:84875735743
SN - 9781467345385
T3 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
SP - 2075
EP - 2080
BT - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
T2 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Y2 - 1 October 2012 through 5 October 2012
ER -