A partitioning algorithm for the Euclidean matching problem in is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time and approximates the optimal matching in the probabilistic sense.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-5, author = {Birgit Anthes and Ludger R\"uschendorf}, title = {On the weighted Euclidean matching problem in $$\mathbb{R}$^d$ }, journal = {Applicationes Mathematicae}, volume = {28}, year = {2001}, pages = {181-190}, zbl = {1052.68055}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-5} }
Birgit Anthes; Ludger Rüschendorf. On the weighted Euclidean matching problem in $ℝ^d$ . Applicationes Mathematicae, Tome 28 (2001) pp. 181-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-5/