Spanners of Complete k-Partite Geometric Graphs [article]

Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Pat Morin, Michiel Smid
2007 arXiv   pre-print
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 n) time. The second algorithm computes a (3+ϵ)-spanner of K with O(n n) edges in O(n n) time. The latter result is optimal: We show that for any 2 ≤ k ≤ n - Θ(√(n n)), spanners with
more » ... n n) edges and stretch factor less than 3 do not exist for all complete k-partite geometric graphs.
arXiv:0712.0554v1 fatcat:safhlubecjaarcfymjylbendj4