TY - GEN

T1 - Conflict-free coloring for rectangle ranges using O(n.382) colors

AU - Ajwani, Deepak

AU - Elbassioni, Khaled

AU - Govindarajan, Sathish

AU - Ray, Saurabh

PY - 2007

Y1 - 2007

N2 - Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?52 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

AB - Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?52 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

KW - Axis-parallel rectangles

KW - Conflict-free coloring

KW - Dominating sets

KW - Frequency assignment in wireless networks

KW - Monotone sequences

UR - http://www.scopus.com/inward/record.url?scp=35248897157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248897157&partnerID=8YFLogxK

U2 - 10.1145/1248377.1248406

DO - 10.1145/1248377.1248406

M3 - Conference contribution

AN - SCOPUS:35248897157

SN - 159593667X

SN - 9781595936677

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 181

EP - 187

BT - SPAA'07

T2 - SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures

Y2 - 9 June 2007 through 11 June 2007

ER -