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Title: On the performance of a simple approximation algorithm for the longest path problem
Authors: Nguyen, Thi Phuong
Tran, Vinh Duc
Le, Cong Thanh
Keywords: Path
Hamiltonian path
Approximation algorithm an performance ratio
Issue Date: 2019
Series/Report no.: Journal of Computer Science and Cybernetics;Vol.35 (01) .- P.57–68
Abstract: The longest path problem is known to be NP-hard. Moreover, it cannot be approximated within a constant ratio, unless P = NP. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithms of the optimum. In this paper we investigate the performance of an approximation algorithm for this problem in almost every case. We show that a simple algorithms, based on depth-first search, finds on almost every undirected graph G = (V,E) a path of length more than |V| - 3√(|V|log⁡|V|)and so has performance ratio less than 1+4√(log⁡|V|/|V|)1. Mathematics Subject Classification (2010): 68Q17.
ISSN: 1813-9663
Appears in Collections:Tin học và Điều khiển học (Journal of Computer Science and Cybernetics)

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