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 -