Spanners of complete k-partite geometric graphs

Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Pat Morin, Michiel Smid

Research output: Contribution to journalArticlepeer-review

Abstract

We address the following problem: Given a complete k-partite geometric graph K whose vertex set is a set of n points in Rdbl; 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 ≤ k ≤ n - Θ( √ 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.

Original languageEnglish
Pages (from-to)1803-1820
Number of pages18
JournalSIAM Journal on Computing
Volume38
Issue number5
DOIs
StatePublished - 1 Dec 2008
Externally publishedYes

Keywords

  • Computational geometry
  • K-partite geometric graphs
  • Spanners

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