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One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as the Christofides algorithm. Recently, some authors started calling it Christofides-Serdyukov algorithm, pointing out that it was published independently in the USSR in 1978. We provide some historic background on Serdyukovs findings and a translation of his article from Russian into English.
We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus.
We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum
Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides algorithm for the TSP, called the Best-of-Many Christofides algorithm. The algorithm involves sampling a spanni
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the pr
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other disciplines.