Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation Algorithms for Time-Dependent Orienteering
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Pickup and delivery for moving objects on broken lines
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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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. 1. If the points all move with the same velocity, then there is a PTAS for the Kinetic TSP. 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. 3. The Kinetic TSP cannot be approximated better than by a factor of 2Ω(√n) 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.