Abstract
In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n ∈-separated segments in two dimensional space. Our results are based on a number of geometric observations and an interesting generalization of Arora’s technique 5 for Euclidean TSP (of a set of points). The randomized version of our algorithm takes \( O(n^2 (\log n)^{O(1/\varepsilon ^4 )} ) \) time to compute a (1 + ∈)-approximation with probability ≥ 1/2, and can be derandomized with an additional factor of O(n 2). Our technique is likely applicable to TSP problems of certain Jordan arcs and related problems.
Keywords
- Dynamic Programming
- Entry Point
- Travel Salesman Problem
- Polynomial Time Approximation Scheme
- Optimal Tour
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This research was supported in part by an IBM faculty partnership award, and an award from NYSTAR (New York state office of science, technology, and academic research) through MDC (Microelectronics Design Center).
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Xu, J., Yang, Y., Lin, Z. (2003). Traveling Salesman Problem of Segments. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_6
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DOI: https://doi.org/10.1007/3-540-45071-8_6
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