Near―perfect non-crossing harmonic matchings in randomly labeled points on a circle
| Autor: | József Balogh, Boris Pittel, Gelasio Salazar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2005 |
| Předmět: |
harmonic graph
noncrossing harmonious labeling graceful convex position matching average case behavior algorithm [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] [info.info-hc] computer science [cs]/human-computer interaction [cs.hc] Mathematics QA1-939 |
| Zdroj: | Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AD,..., Iss Proceedings (2005) |
| Druh dokumentu: | article |
| ISSN: | 1365-8050 |
| DOI: | 10.46298/dmtcs.3366 |
| Popis: | 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 $n/2 - O(n^{1/3}\ln n)$. |
| Databáze: | Directory of Open Access Journals |
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