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Probabilistic analysis of the longest hamiltonian tour problem
Author(s) -
Vohra Rakesh V.
Publication year - 1988
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230180103
Subject(s) - probabilistic logic , combinatorics , heuristic , hamiltonian (control theory) , mathematics , probabilistic analysis of algorithms , hamiltonian path , random graph , graph , enhanced data rates for gsm evolution , discrete mathematics , travelling salesman problem , computer science , mathematical optimization , statistics , artificial intelligence
In this paper we study the probabilistic behavior of the farthest neighbor heuristic for finding the longest Hamiltonian tour in a graph. We assume the edge weights are independent random variables uniformly distributed in [0,1]. If F, is the length of the heuristic tour and L, the optimal tour then F n /L n → 1 a.s. as n → α. We also show that L n /n → 1 a.s. as n → ∞.