M. Hammar and B. J. Nilsson, Approximation Results for Kinetic Variants of TSP, in Proc. International Colloquium on Automata, Languages, and Programming, 1999, pp. 392--401. Lecture Notes in computer Science 1644.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... paper has appeared in [5] formulations generalize TSP without the triangle inequality, which admits no approximation bounds unless P = NP [2] Applicability of dynamic programming to related formulations was also considered in [7] The approximation complexity of Moving Target TSP was studied in [4], where it was shown that Moving Target TSP cannot be approximated better than by a factor of 2 Omega Gamma p n) times optimal within polynomial time unless P = NP . In this paper, we propose and address several natural variants of Moving Target TSP. In Section 2, we show that unlike the ....

....line) is not trivial, and we give an exact O(n ) time algorithm. For Moving Target TSP instances where the number of moving targets is sufficiently small, we develop a (1 ff) approximation algorithm, where ff denotes the approximation ratio of the best classical TSP heuristic. It was shown in [4] that the (2 Gamma ffl) approximation is NP hard even in the case when only two targets are moving. Thus, combining our approach with the polynomial time approximation scheme for Euclidean TSP [1] yields almost optimal (2 ffl) approximation algorithms for Moving Target TSP when enough of ....

M. Hammar and B. J. Nilsson, Approximation Results for Kinetic Variants of TSP, in Proc. International Colloquium on Automata, Languages, and Programming, 1999, pp. 392--401. Lecture Notes in computer Science 1644.

....generalizations of TSP (e.g. several scheduling problems can be reduced to solving variants of these problems) The complexity status of these problems, especially with respect to approximation, is a paradigmatic question. We have proved such results for di erent variants of these problems in [30]. In case of the Kinetic TSP, we have looked at TSP for moving points in the Euclidean plane, considering instances in which each point moves with a xed speci c velocity. We have proved that the Kinetic TSP cannot be approximated better than by a factor of 2 p n) by a polynomial time algorithm ....

....considering instances in which each point moves with a xed speci c velocity. We have proved that the Kinetic TSP cannot be approximated better than by a factor of 2 p n) by a polynomial time algorithm unless P=NP, even if the maximum speed is bounded (n denotes the size of the input instance) [30]. 2 A polynomial time approximation scheme (PTAS) for a minimization problem is a family of algorithms fA g such that for each xed 0, A runs in time polynomial in the size of the input and produces a (1 ) approximate solution. TSP with neighborhoods (J. Gudmundsson and C. Levcopoulos) ....

M. Hammar and B.J. Nilsson. Approximation Results for Kinetic Variants of TSP. Proc. 26th International Colloquium on Automata, Languages, and Programming (ICALP'99). Lecture Notes in Computer Science 1644, 1999, pp. 392-401.

.... Diskrete Probleme , No. Ot 64 8 1. 2 The lower bound for searching in m rays has proved to be a very useful tool for proving lower bounds for searching in a number of classes of simple polygons, such as star shaped polygons [13] generalized streets [6, 15] HV streets [5] and streets [5, 8]. In this paper we are interested in obtaining upper and lower bounds for the competitive ratio of parallel searching on m concurrent rays. This problem has been adressed before in two contexts. The rst context is the on line construction of hybrid algorithms the setting of which can be described ....

....Note that two di erent points may have di erent 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 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 ....

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M. Hammar and B. J. Nilsson. Approximation results for kinetic variants of TSP. ICALP, 1999.

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