TY - JOUR

T1 - Covering points by disjoint boxes with outliers

AU - Ahn, Hee Kap

AU - Bae, Sang Won

AU - Demaine, Erik D.

AU - Demaine, Martin L.

AU - Kim, Sang Sub

AU - Korman, Matias

AU - Reinbacher, Iris

AU - Son, Wanbin

N1 - Funding Information:
✩ This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0067195) and by the Brain Korea 21 Project in 2010. Work by S.W. Bae was supported by the Contents Convergence Software Research Center funded by the GRRC Program of Gyeonggi Province, South Korea. * Corresponding author. E-mail addresses: heekap@postech.ac.kr (H.-K. Ahn), swbae@kgu.ac.kr (S.W. Bae), edemaine@mit.edu (E.D. Demaine), mdemaine@mit.edu (M.L. Demaine), helmet1981@postech.ac.kr (S.-S. Kim), mkormanc@ulb.ac.be (M. Korman), irisrein@postech.ac.kr (I. Reinbacher), mnbiny@postech.ac.kr (W. Son).

PY - 2011/4

Y1 - 2011/4

N2 - For a set of n points in the plane, we consider the axis-aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+klogk) time for p=1, and O(nlogn+kplogpk) time for p=2,3. For rectangles we get O(n+k3) for p=1 and O(nlogn+k2+plogp-1k) time for p=2,3. In all cases, our algorithms use O(n) space.

AB - For a set of n points in the plane, we consider the axis-aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+klogk) time for p=1, and O(nlogn+kplogpk) time for p=2,3. For rectangles we get O(n+k3) for p=1 and O(nlogn+k2+plogp-1k) time for p=2,3. In all cases, our algorithms use O(n) space.

KW - Algorithms

KW - Covering

KW - NP hard

KW - Optimization

KW - Outliers

UR - http://www.scopus.com/inward/record.url?scp=78649318755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649318755&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2010.10.002

DO - 10.1016/j.comgeo.2010.10.002

M3 - Article

AN - SCOPUS:78649318755

VL - 44

SP - 178

EP - 190

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -