Linear-space algorithms for distance preserving embedding

Tetsuo Asano, Prosenjit Bose, Paz Carmi, Anil Maheshwari, Chang Shu, Michiel Smid, Stefanie Wuhrer

Research output: Contribution to conferencePaperpeer-review

2 Scopus citations


The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O(√n) such that the minimum inter cluster distance is maximized among all possible such partitions.

Original languageEnglish
Number of pages4
StatePublished - 1 Dec 2007
Externally publishedYes
Event19th Annual Canadian Conference on Computational Geometry, CCCG 2007 - Ottawa, ON, Canada
Duration: 20 Aug 200722 Aug 2007


Conference19th Annual Canadian Conference on Computational Geometry, CCCG 2007
CityOttawa, ON

ASJC Scopus subject areas

  • Geometry and Topology


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