C. S. Helvig, G. Robins, and A. Zelikovsky. Moving-target TSP and related problems. In Proc. 6th Annual European Symposium on Algorithms (ESA), 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and both theoretically and practically important generalization of TSP (e.g. several scheduling problems can be reduced to solving variants of kinetic TSP) The complexity status of the problem, especially with respect to approximation, is a paradigmatic question. Helvig, Robins and Zelikovsky [6] give a polynomial time algorithm to solve the problem when the moving points are restricted to lie on the real line. They also give a 2 approximation algorithm for the Kinetic TSP if the number of points with nonzero speed is small. We prove the following results. 1. If the points all move ....

....to this mapping we were able to generalize their result. If the speeds are bounded by a constant, then the algorithm is a true PTAS. 4 Two Reductions for KTSP The kinetic traveling salesman problem is in general not as easily approximated as the translational TSP. Helvig, Robins and Zelikovsky [6] give a 2 approximation algorithm for kinetic TSP instances with n points of which O( log n log log n ) are moving. The simple construction described in Figure 2 shows that their algorithm is close to optimal. The gure contains a GGJ instance, chosen as Type a in Figure 1, at distance D ....

C. S. Helvig, G. Robins, and A. Zelikovsky. Moving-target TSP and related problems. In Proc. 6th Annual European Symposium on Algorithms (ESA), 1998.

....that two dioeerent points may have dioeerent velocities. Rote [13] calls this problem the mice collecting Traveling Salescat Problem and gives a polynomial time algorithm to solve the problem when the moving points (the mice) are restricted to lie on the real line. Helvig, Robins and Zelikovsky [8] give another algorithm to solve the same problem, improving the running time somewhat. They also give a 2 ffl algorithm for the Kinetic TSP if the number of points with non zero speed is small. We prove the following results. 1. If the points all move with the same speed and in the same ....

....optimal path. Using this in the proof of Theorem 6 shows that the tour computed is at most 1 ffl times the optimal salesman tour. ut 4 Two Reductions for KTSP The kinetic traveling salesman problem is in general not as easily approximated as the translational TSP. Helvig, Robins and Zelikovsky [8] give a 2 ffl approximation algorithm for kinetic TSPinstances with n points of which O( log n log log n ) are moving. The simple construction described in Figure 2 shows that their algorithm is close to optimal. The gure contains a GGJ instance at distance D from the origin and two moving ....

C. S. Helvig, G. Robins, and A. Zelikovsky. Moving-target TSP and related problems. In Proc. 6th Annual European Symposium on Algorithms (ESA), 1998.

....in time, all targets would have left the origin simultaneously. Finally, we present an exact algorithm for the case when all targets have the same speed, and conclude in Section 5 with some future research directions. Some proofs are condensed or altogether omitted due to page limitations. See [2] or our Web site http: www.cs.virginia.edu robins for a more complete version of this paper. 2 Special Instances of Moving Target TSP Since unrestricted Moving Target TSP is NP hard 3 , and because non optimal tours can have unbounded error, we consider special variants where MovingTarget ....

C. H. Helvig, G. Robins, and A. Zelikovsky. Moving target tsp and related problems. Technical Report CS-98-07, Department of Computer Science, University of Virginia, December 1997.

....in time, all targets would have left the origin simultaneously. Finally, we present an exact algorithm for the case when all targets have the same speed, and conclude in Section 5 with some future research directions. Some proofs are condensed or altogether omitted due to page limitations. See [2] or our Web site http: www.cs.virginia.edu robins for a more complete version of this paper. 2 Special Instances of Moving Target TSP Since unrestricted Moving Target TSP is NP hard 3 , and because non optimal tours can have unbounded error, we consider special variants where MovingTarget ....

C. H. Helvig, G. Robins, and A. Zelikovsky. Moving target tsp and related problems. Technical Report CS-98-07, Department of Computer Science, University of Virginia, December 1997.

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