TY - JOUR

T1 - On guarding the vertices of rectilinear domains

AU - Katz, Matthew J.

AU - Roisman, Gabriel S.

N1 - Funding Information:
* Corresponding author. E-mail addresses: matya@cs.bgu.ac.il (M.J. Katz), roismang@cs.bgu.ac.il (G.S. Roisman). 1 Partially supported by grant no. 2000160 from the US–Israel Binational Science Foundation. 2 Partially supported by the Lynn and William Frankel Center for Computer Sciences.

PY - 2008/4/1

Y1 - 2008/4/1

N2 - We prove that guarding the vertices of a rectilinear polygon P, whether by guards lying at vertices of P, or by guards lying on the boundary of P, or by guards lying anywhere in P, is NP-hard. For the first two proofs (i.e., vertex guards and boundary guards), we construct a reduction from minimum piercing of 2-intervals. The third proof is somewhat simpler; it is obtained by adapting a known reduction from minimum line cover. We also consider the problem of guarding the vertices of a 1.5D rectilinear terrain. We establish an interesting connection between this problem and the problem of computing a minimum clique cover in chordal graphs. This connection yields a 2-approximation algorithm for the guarding problem.

AB - We prove that guarding the vertices of a rectilinear polygon P, whether by guards lying at vertices of P, or by guards lying on the boundary of P, or by guards lying anywhere in P, is NP-hard. For the first two proofs (i.e., vertex guards and boundary guards), we construct a reduction from minimum piercing of 2-intervals. The third proof is somewhat simpler; it is obtained by adapting a known reduction from minimum line cover. We also consider the problem of guarding the vertices of a 1.5D rectilinear terrain. We establish an interesting connection between this problem and the problem of computing a minimum clique cover in chordal graphs. This connection yields a 2-approximation algorithm for the guarding problem.

KW - Approximation algorithms

KW - Geometric optimization

KW - Guarding

KW - NP-hardness

UR - http://www.scopus.com/inward/record.url?scp=84867939400&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2007.02.002

DO - 10.1016/j.comgeo.2007.02.002

M3 - Article

AN - SCOPUS:84867939400

VL - 39

SP - 219

EP - 228

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -