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Abstract: . An algebraic approach to the Traveling Salesman Problem is described which results in an algorithm for counting Hamiltonian circuits in a graph and in an approximation polynomial time algorithm for computing the longest Hamiltonian circuit with the given vertices in a normed space. For a graph with n vertices the counting algorithm has 2 n+O(logn) time complexity whereas the space complexity is polynomial in n. For any norm in a Euclidean space and for any number ffi ? 0 we present a... (Update)
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BibTeX entry: (Update)
A. I. Barvinok. Two algorithmic results for the traveling salesman problem, April 1994. Unpublished manuscript. http://citeseer.ist.psu.edu/barvinok94two.html More
@article{ barvinok96two,
author = "Barvinok",
title = "Two Algorithmic Results for the Traveling Salesman Problem",
journal = "MOR: Mathematics of Operations Research",
volume = "21",
year = "1996",
url = "citeseer.ist.psu.edu/barvinok94two.html" }
Citations (may not include all citations):4212 Computers and Intractability: a Guide to the Theory of NP-co.. (context) - Garey, Johnson - 1979
1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
333 Geometric Algorithms and Combinatorial Optimization (context) - Grotschel, Lov'asz et al. - 1988
106 The Traveling Salesman Problem: a guided tour of combinatori.. (context) - Lawler - 1985
88 The traveling salesman problem with distances one and two (context) - Papadimitriou, Yannakakis - 1993
30 Expected computation time for Hamiltonian Path Problem (context) - Gurevich, Shelah - 1987
12 An analysis of approximations for finding a maximum weight h.. (context) - Fisher, Nemhauser et al. - 1979
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