Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
The Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Approximation algorithms for the watchman route and zookeeper's problems
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
A linear-time approximation algorithm for weighted matchings in graphs
ACM Transactions on Algorithms (TALG)
On The Approximability Of The Traveling Salesman Problem
Combinatorica
Fast minimum-weight double-tree shortcutting for metric TSP
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
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Given a metric graph G = (V ,E ) of n vertices, i.e., a complete graph with an edge cost function c :V ×V ****** *** 0 satisfying the triangle inequality, the metricity degree of G is defined as $\beta=\max_{x,y,z \in V} \big\{ \frac{c(x,y)}{c(x,z)+c(y,z)}\big\} \in \big[\frac{1}{2},1\big]$. This value is instrumental to establish the approximability of several NP-hard optimization problems definable on G , like for instance the prominent traveling salesman problem , which asks for finding a Hamiltonian cycle of G of minimum total cost. In fact, this problem can be approximated quite accurately depending on the metricity degree of G , namely by a ratio of either $\frac{2-\beta}{3(1-\beta)}$ or $\frac{3\beta^2}{3 \beta^2-2\beta+1}$, for $\beta or $\beta \geq \frac{2}{3}$, respectively. Nevertheless, these approximation algorithms have O (n 3) and O (n 2.5 log1.5 n ) running time, respectively, and therefore they are superlinear in the *** (n 2) input size. Thus, since many real-world problems are modeled by graphs of huge size, their use might turn out to be unfeasible in the practice, and alternative approaches requiring only O (n 2) time are sought. However, with this restriction, all the currently available approaches can only guarantee a 2-approximation ratio for the case ß = 1, which means a $\frac{2\beta^2}{2\beta^2-2\beta+1}$-approximation ratio for general ß double-MST heuristic, in order to obtain a 2ß -approximate solution. This improvement is effective, since we show that the double-MST heuristic has in general a performance ratio strictly larger that 2 ß , and we further show that any re-elaboration of the shortcutting phase therein provided, cannot lead to a performance ratio better than 2ß .