Near―perfect non-crossing harmonic matchings in randomly labeled points on a circle - Archive ouverte HAL
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Near―perfect non-crossing harmonic matchings in randomly labeled points on a circle

Abstract

Consider a set $S$ of points in the plane in convex position, where each point has an integer label from $\{0,1,\ldots,n-1\}$. 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 non―crossing $\textit{harmonic}$ 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 nearly―perfect matching, a matching of size $n/2 - O(n^{1/3}\ln n)$.
Fichier principal
Vignette du fichier
dmAD0103.pdf (143.97 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01184038 , version 1 (12-08-2015)

Identifiers

Cite

József Balogh, Boris Pittel, Gelasio Salazar. Near―perfect non-crossing harmonic matchings in randomly labeled points on a circle. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.17-26, ⟨10.46298/dmtcs.3366⟩. ⟨hal-01184038⟩

Collections

TDS-MACS
81 View
630 Download

Altmetric

Share

More