Skip to main content
Article thumbnail
Location of Repository

Estimating the weight of metric minimum spanning trees in sublinear time

By Artur Czumaj and Christian Sohler

Abstract

In this paper we present a sublinear-time $(1+\varepsilon)$-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an $n$-point metric space. The running time of the algorithm is $\widetilde{\mathcal{O}}(n/\varepsilon^{\mathcal{O}(1)})$. Since the full description of an $n$-point metric space is of size $\Theta(n^2)$, the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in $o(n)$ time the weight of the minimum spanning tree to within any factor. We also show that no deterministic algorithm can achieve a $B$-approximation in $o(n^2/B^3)$ time. Furthermore, it has been previously shown that no $o(n^2)$ algorithm exists that returns a spanning tree whose weight is within a constant times the optimum

Topics: QA76
Publisher: Society for Industrial and Applied Mathematics
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:2416

Suggested articles

Citations

  1. (1995). A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields, doi
  2. (2000). A minimum spanning tree algorithm with inverse-Ackermann type complexity, doi
  3. (2003). A sublinear algorithm for weakly approximating edit distance, doi
  4. (1998). A sublinear time approximation scheme for clustering in metric spaces, doi
  5. (2002). An optimal minimum spanning tree algorithm,J doi
  6. (2006). Approximating average parameters of graphs, doi
  7. (2005). Approximating the minimum spanning tree weight in sublinear time, doi
  8. (2007). Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms, doi
  9. (2005). Approximating the weight of the Euclidean minimum spanning tree in sublinear time, doi
  10. (2001). Approximation Algorithms, doi
  11. (2004). Fast Monte-Carlo algorithms for finding low-rank approximations, doi
  12. (2005). Finding frequent patterns in a string in sublinear time, doi
  13. (1995). K a r g e r ,P .N .K l e i n ,a n dR .E .T a r j a n , A randomized linear-time algorithm to find minimum spanning trees, doi
  14. (1982). On constructing minimum spanning trees in k-dimensional spaces and related problems, doi
  15. (1970). Proof of a conjecture of P. Erd˝ os,
  16. (1998). Property testing and its connection to learning and approximation, doi
  17. (2000). Spanning trees and spanners, doi
  18. (2006). Sublinear geometric algorithms, doi
  19. (2004). Sublinear methods for detecting periodic trends in data streams, doi
  20. (1999). Sublinear time algorithms for metric space problems, doi
  21. (2001). Sublinear time approximate clustering,
  22. (2006). Sublinear-time algorithms, doi
  23. (2003). Testing of clustering,S I A MJ .D i s c r e t eM a t h . doi
  24. (1996). The regularity lemma and approximation schemes for dense problems, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.