Spanners of Complete $k$-Partite Geometric Graphs
| dc.creator | Bose, Prosenjit | |
| dc.creator | Carmi, Paz | |
| dc.creator | Couture, Mathieu | |
| dc.creator | Maheshwari, Anil | |
| dc.creator | Morin, Pat | |
| dc.creator | Smid, Michiel | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:47:16Z | |
| dc.date.available | 2026-07-07T08:47:16Z | |
| dc.description | We address the following problem: Given a complete $k$-partite geometric graph $K$ whose vertex set is a set of $n$ points in $\mathbb{R}^d$, 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 $O(n \log n)$ time. The second algorithm computes a $(3+ε)$-spanner of $K$ with $O(n \log n)$ edges in $O(n \log n)$ time. The latter result is optimal: We show that for any $2 \leq k \leq n - Θ(\sqrt{n \log n})$, spanners with $O(n \log n)$ edges and stretch factor less than 3 do not exist for all complete $k$-partite geometric graphs. | |
| dc.identifier | https://arxiv.org/abs/0712.0554 | |
| dc.identifier | http://arxiv.org/abs/0712.0554 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143535 | |
| dc.subject | Computational Geometry | |
| dc.title | Spanners of Complete $k$-Partite Geometric Graphs | |
| dc.type | text |