The Directed Minimum Latency Problem
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Asymmetric traveling salesman path and directed latency problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Reordering rows for better compression: Beyond the lexicographic order
ACM Transactions on Database Systems (TODS)
An improved integrality gap for asymmetric TSP paths
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
A comprehensive taxonomy for multi-robot task allocation
International Journal of Robotics Research
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In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the objective is to find a minimum cost walk from the source to destination visiting all cities at least once. We first characterize traveling salesman walk perfect graphs, graphs for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities. We show these graphs have a description by way of forbidden minors and also characterize them constructively. We also address the asymmetric traveling salesman path problem (ATSPP) and give a factor $$O(\sqrt{n})$$-approximation algorithm for this problem.