Abstract
We address the following problem: Given a complete k-partite geometric graph K whose vertex set is a set of n points in ℝd, 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.
Research partially supported by NSERC, MRI, CFI, and MITACS.
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Bose, P., Carmi, P., Couture, M., Maheshwari, A., Morin, P., Smid, M. (2008). Spanners of Complete k-Partite Geometric Graphs. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_15
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DOI: https://doi.org/10.1007/978-3-540-78773-0_15
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