2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 1726
author:  József Balogh, Boris Pittel and Gelasio Salazar 

title:  Nearperfect noncrossing harmonic matchings in randomly labeled points on a circle 
keywords:  Graceful, harmonious labeling, noncrossing, harmonic graph, convex position, matching, algorithm, average case behavior 
abstract: 
Consider a set
S
of points in the plane in convex position, where each
point has an integer label from
{0,1,…,n1}
. This naturally induces a labeling of the edges:
each edge
(i,j)
is assigned label
i+j
, modulo
n
. We propose the algorithms for finding large
noncrossing harmonic matchings or paths, i. e.
the matchings or paths in which no two edges have the same
label. When the point labels are chosen uniformly at
random, and independently of each other, our matching
algorithm with high probability (w.h.p.) delivers a
nearlyperfect matching, a matching of size
n/2  O(n
.
1/3
lnn)

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reference:  József Balogh and Boris Pittel and Gelasio Salazar (2005), Nearperfect noncrossing harmonic matchings in randomly labeled points on a circle, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 1726 
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