Abstract
We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results.
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1.
If the points all move with the same velocity, then there is a PTAS for the Kinetic TSP.
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2.
The Kinetic TSP cannot be approximated better than by a factor of two by a polynomial time algorithm unless P=NP, even if there are only two moving points in the instance.
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3.
The Kinetic TSP cannot be approximated better than by a factor of \( 2^{\Omega \left( {\sqrt n } \right)} \) by a polynomial time algorithm unless P=NP, even if the maximum velocity is bounded. The n denotes the size of the input instance.
Especially the last result is surprising in the light of existing polynomial time approximation schemes for the static version of the problem.
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© 1999 Springer-Verlag Berlin Heidelberg
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Hammar, M., Nilsson, B.J. (1999). Approximation Results for Kinetic Variants of TSP. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_36
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DOI: https://doi.org/10.1007/3-540-48523-6_36
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