TY - GEN

T1 - Spanners of complete k-Partite geometric graphs

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Couture, Mathieu

AU - Maheshwari, Anil

AU - Morin, Pat

AU - Smid, Michiel

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

PY - 2008/5/12

Y1 - 2008/5/12

N2 - We address the following problem: Given a complete k-partite geometric graph K whose vertex set is a set of n points in ℝ d , compute a spanner of K that has a "small" stretch factor and "few" edges. We present two algorithms for this problem. The first algorithm computes a (5∈+∈ε)-spanner of K with O(n) edges in O(n logn) time. The second algorithm computes a (3∈+∈ε)-spanner of K with O(n logn) edges in O(n logn) time. Finally, we show that there exist complete k-partite geometric graphs K such that every subgraph of K with a subquadratic number of edges has stretch factor at least 3.

AB - We address the following problem: Given a complete k-partite geometric graph K whose vertex set is a set of n points in ℝ d , compute a spanner of K that has a "small" stretch factor and "few" edges. We present two algorithms for this problem. The first algorithm computes a (5∈+∈ε)-spanner of K with O(n) edges in O(n logn) time. The second algorithm computes a (3∈+∈ε)-spanner of K with O(n logn) edges in O(n logn) time. Finally, we show that there exist complete k-partite geometric graphs K such that every subgraph of K with a subquadratic number of edges has stretch factor at least 3.

UR - http://www.scopus.com/inward/record.url?scp=43049084794&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-78773-0_15

DO - 10.1007/978-3-540-78773-0_15

M3 - Conference contribution

AN - SCOPUS:43049084794

SN - 3540787720

SN - 9783540787723

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

SP - 170

EP - 181

BT - LATIN 2008

T2 - 8th Latin American TheoreticalINformatics Symposium, LATIN 2008

Y2 - 7 April 2008 through 11 April 2008

ER -