TY - GEN

T1 - Geometric spanners with small chromatic number

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Couture, Mathieu

AU - Maheshwari, Anil

AU - Smid, Michiel

AU - Zeh, Norbert

N1 - Funding Information:
✩ Research partially supported by HPCVL, NSERC, MRI, CFI, and MITACS.

PY - 2008/8/27

Y1 - 2008/8/27

N2 - Given an integer k ≥ 2, we consider the problem of computing the smallest real number t(k) such that for each set P of points in the plane, there exists a t(k)-spanner for P that has chromatic number at most k. We prove that t(2)∈=∈3, t(3)∈=∈2, , and give upper and lower bounds on t(k) for k∈>∈4. We also show that for any ε>∈0, there exists a (1∈+∈ε)t(k)-spanner for P that has O(|P|) edges and chromatic number at most k. Finally, we consider an on-line variant of the problem where the points of P are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that t(2)∈=∈3, , , and give upper and lower bounds on t(k) for k∈>∈4.

AB - Given an integer k ≥ 2, we consider the problem of computing the smallest real number t(k) such that for each set P of points in the plane, there exists a t(k)-spanner for P that has chromatic number at most k. We prove that t(2)∈=∈3, t(3)∈=∈2, , and give upper and lower bounds on t(k) for k∈>∈4. We also show that for any ε>∈0, there exists a (1∈+∈ε)t(k)-spanner for P that has O(|P|) edges and chromatic number at most k. Finally, we consider an on-line variant of the problem where the points of P are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that t(2)∈=∈3, , , and give upper and lower bounds on t(k) for k∈>∈4.

UR - http://www.scopus.com/inward/record.url?scp=49949113180&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-77918-6_7

DO - 10.1007/978-3-540-77918-6_7

M3 - Conference contribution

AN - SCOPUS:49949113180

SN - 3540779175

SN - 9783540779179

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 75

EP - 88

BT - Approximation and Online Algorithms - 5th International Workshop, WAOA 2007, Revised Papers

T2 - 5th International Workshop on Approximation and Online Algorithms, WAOA 2007

Y2 - 11 October 2007 through 12 October 2007

ER -