K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proceedings of the 5th International Symposium on Algorithms and Computation, volume 834 of Lecture Notes in Computer Science, pages 29--37. Springer, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to obtain results for BCCMED with metric c cost. However, our results apply without this restriction and give a slightly better approximation guarantee. 4 Past Work and Relationship with Other Problems In the past, several service constrained minimum cost network problems have been considered in [1, 8, 17, 22, 21]. These papers consider the variant that prescribes a budget on the service distance for each node. The goal is to determine a solution subgraph (which in some of the cited papers is a salesperson tour and in others is a subtree) subject to the budget constraints of the vertices not in the ....

....customers and the service radius represents the distance a customer is willing to travel to meet the salesperson. The goal is to find a minimum length salesperson tour so that all the (customer) nodes are strictly serviced. Restrictions of the problems to geometric instances were considered in [1, 17, 24]. These problems are similar to BCCMED studied here, the primary difference being in the way the location theoretic constraint is formulated. In the current paper, we put a budget on the sum of the costs of the nodes not in the tree while the papers referred to above consider a budget on the ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proceedings of the 5th International Symposium on Algorithms and Computation, volume 834 of Lecture Notes in Computer Science, pages 29--37. Springer, 1994.

....a survey and for applications of computational geometry to the problem. The algorithmic study of the problem has focused on the problem of minimizing the length of a milling tour: Arkin et al. 5, 6] show that the problem is NP hard in general. Constant factor approximation algorithms are given in [5, 6, 23], with the best current factor being a 2.5 approximation for min length milling (11 5 approximation for orthogonal simple polygons) For the closely related lawn mowing problem (also known as the traveling cameraman problem [23] in which the covering tour is not constrained to stay within P , ....

....general. Constant factor approximation algorithms are given in [5, 6, 23] with the best current factor being a 2. 5 approximation for min length milling (11 5 approximation for orthogonal simple polygons) For the closely related lawn mowing problem (also known as the traveling cameraman problem [23]) in which the covering tour is not constrained to stay within P , the best current approximation factor is (3 ) utilizing PTAS results for TSP) Also closely related is the watchman route problem with limited visibility (or d sweeper problem ) as studied by Ntafos [31] who provides a ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., Vol. 834 LNCS, pp. 29-37. Springer-Verlag, 1994.

....a survey and for applications of computational geometry to the problem. The algorithmic study of the problem has focussed on the problem of minimizing the length of a milling tour: Arkin et al. 5, 6] show that the problem is NPhard in general. Constant factor approximation algorithms are given in [5, 6, 23], with the best current factor being a 2.5 approximation for min length milling (11 5approximation for orthogonal simple polygons) For the closely related lawn mowing problem (also known as the traveling cameraman problem [23] in which the covering tour is not constrained to stay within P , ....

....general. Constant factor approximation algorithms are given in [5, 6, 23] with the best current factor being a 2. 5 approximation for min length milling (11 5approximation for orthogonal simple polygons) For the closely related lawn mowing problem (also known as the traveling cameraman problem [23]) in which the covering tour is not constrained to stay within P , the best current approximation factor is (3 ) utilizing PTAS results for TSP) Also closely related is the watchman route problem with limited visibility (or d sweeper problem ) as studied by Ntafos [31] who provides a ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., volume 834 of Lecture Notes Comput. Sci., pages 29--37. Springer-Verlag, 1994.

....algorithm from [20] we get a (1 ; 2(1 1= O(log 3 m log log m) approximation for BCCMED. Our algorithm given in Section 6 uses the techniques from [20] directly and improves this result. 3.2. Related Work. Other service constrained minimum cost network problems have been considered in [1, 6, 12, 16, 17]. These papers consider the variant that prescribes a budget on the service distance for each node not in the tree. The goal is to find a minimum length salesperson tour (or a tree as may be the case) so that all the (customer) nodes are strictly serviced. Restrictions of the problems to geometric ....

....that prescribes a budget on the service distance for each node not in the tree. The goal is to find a minimum length salesperson tour (or a tree as may be the case) so that all the (customer) nodes are strictly serviced. Restrictions of the problems to geometric instances were considered in [1,12,19]. Finally, the problem BCCMED can be seen as a generalization of the classical k Median Problem, where we require the set of medians to be connected. 4. HARDNESS RESULTS Theorem 3. The problem BCCMED is weakly NP hard even on trees. This result continues to hold even if we require the two cost ....

K. Iwano, P. Raghavan, and H. Tamaki, The traveling cameraman problem, with applications to automatic optical inspection, Proceedings of the 5th International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, vol. 834, Springer, 1994, pp. 29--37.

....be thought of as a dual: minimize the amount of re milling, subject to no retractions of the cutter. In [1] we showed that the milling and lawn mower problems are NP hard, in general. We also provided existence proofs of constant factor approximation algorithms for these problems. Iwano et al. [13] independently obtained an approximation algorithm for a version of the lawn mower problem; they provide, for any fixed # 0, a (9 #) approximation for the case of rectilinear grass regions. Main Results This paper represents a continuation and extension of our earlier work [1] with several ....

....work [1] with several substantial new results: For the lawnmowing problem, we give improved approximation algorithms that not only cut the previous best factor by up to a factor of 2, but also substantially improve the running time. Further, our 3 method greatly simplifies the proof of [13]. For the milling problem, we give a 2.5 approximation algorithm, with worst case time O(n log n) for a (possibly multiply connected) pocket whose boundary complexity is n. We give new results for the TSP on grid graphs, and applications of these results to related instances of the ....

[Article contains additional citation context not shown here]

K. Iwano, P. Raghavan, and H. Tamaki, The traveling cameraman problem, with applications to automatic optical inspection. Proceedings of the 5th Annual International Symposium on Algorithms and Computing (ISAAC 1994), Lecture Notes in Computer Science, Springer-Verlag, 1994.

....of length no more than 2L , even if the boundary of P Phi R is disconnnected. This result is also of importance in the more general situation where we have to search a polygonal area A with a scanning device of shape R. This so called lawn mowing problem is NP hard and was considered in [9] and [1] As it was shown in [1] our inequality allows the construction of approximation algorithms with small approximation factors. 2 The Inequality We will make use of the following proposition, following from Cauchy s formula see [4, 5, 3, 14] Proposition 2.1 (Cauchy 1841) Let C 1 and C ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. Proc. 5th Annu. Internat. Sympos. Algorithms Comput. (ISAAC 94), Lecture Notes in Computer Science, Springer-Verlag, 1994.

....of milling heuristics from a computational geometry perspective. For the single tool case, he presented efficient algorithms to find a feasible tool path, given the shape of the pocket to be milled and the size of the tool. On the theoretical side, Arkin, et al. AFM93, AFM95] and Iwano, et al. IRT94] have given constant factor approximation algorithms for finding shortest paths for the single tool milling problem and for the closely related problem of lawnmowing. Arkin, et al. AHS96] have also given approximation algorithms for minimizing the number of retractions for the zig zag milling ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., Lecture Notes Comput. Sci., Beijing, 1994. Springer-Verlag.

....They show that this problem is NP hard, no matter whether the object is constrained to the interior of the pocket or whether it may cross the pocket s boundary during moving. Furthermore, they give constant factor approximations. Very recently, these results have been improved by Iwano et al. [17], and further improved by the original authors [3] A general survey of pocketing requirements is given by Guyder [12] Gupta et al. 11] present an interesting algorithm for determining a good orientation of a workpiece (for 4D 5D machining) For further readings, also on 3D 5D machining, we ....

K. Iwano, P. Raghavan, and H. Tamaki. The Traveling Cameraman Problem, with Applications to Automatic Optical Inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput.('94), Lecture Notes Comput. Sci., Beijing, PR China, 1994. Springer-Verlag.

....be thought of as a dual: minimize the amount of re milling, subject to no retractions of the cutter. In [1] we showed that the milling and lawn mower problems are NP hard, in general. We also provided existence proofs of constant factor approximation algorithms for these problems. Iwano et al. [13] independently obtained an approximation algorithm for a version of the lawn mower problem; they provide, for any fixed ffl 0, a (9 ffl) approximation for the case of rectilinear grass regions. Main Results This paper represents a continuation and extension of our earlier work [1] with ....

....earlier work [1] with several substantial new results: ffl For the lawnmowing problem, we give improved approximation algorithms that not only cut the previous best factor by up to a factor of 2, but also substantially improve the running time. Further, our method greatly simplifies the proof of [13]. ffl For the milling problem, we give a 2.5 approximation algorithm, with worst case time O(n log n) for a (possibly multiply connected) pocket whose boundary complexity is n. ffl We give new results for the TSP on grid graphs, and applications of these results to related instances of the ....

[Article contains additional citation context not shown here]

K. Iwano, P. Raghavan, and H. Tamaki, The traveling cameraman problem, with applications to automatic optical inspection. Proc. 5th Annu. Internat. Sympos. Algorithms Comput. 1994), Lecture Notes in Computer Science, Springer-Verlag, 1994.

....of milling heuristics from a computational geometry perspective. For the single tool case, he presented efficient algorithms to find a feasible tool path, given the shape of the pocket to be milled and the size of the tool. On the theoretical side, Arkin, et al. AFM93, AFM95] and Iwano, et al. IRT94] have given constant factor approximation algorithms for finding shortest paths for the single tool milling problem and for the closely related problem of lawnmowing. Arkin, et al. AHS96] have also given approximation algorithms for minimizing the number of retractions for the zig zag milling ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., Lecture Notes Comput. Sci., Beijing, 1994. SpringerVerlag.

....of milling heuristics from a computational geometry perspective. For the single tool case, he presented efficient algorithms to find a feasible tool path, given the shape of the pocket to be milled and the size of the tool. On the theoretical side, Arkin, et al. AFM93, AFM95] and Iwano, et al. IRT94] have given constant factor approximation algorithms for finding shortest paths for the single tool milling problem and for the closely related problem of lawnmowing. Arkin, et al. AHS96] have also given approximation algorithms for minimizing the number of retractions for the zig zag milling ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., Lecture Notes Comput. Sci., Beijing, 1994. Springer-Verlag.

....They show that this problem is NP hard, no matter whether the object is constrained to the interior of the pocket or whether it may cross the pocket s boundary during moving. Furthermore, they give constant factor approximations. Very recently, these results have been improved by Iwano et al. [21], and further improved by the original authors [3] A general survey of pocketing requirements is given by Guyder [15] Gupta et al. 14] present an interesting algorithm for determining a good orientation of a workpiece (for 4D 5D machining) For further readings, also on 3D 5D machining, we ....

K. Iwano, P. Raghavan, and H. Tamaki. The Traveling Cameraman Problem, with Applications to Automatic Optical Inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput.('94), Lecture Notes Comput. Sci., Beijing, PR China, 1994. Springer-Verlag.

....and Lenhart [376] who have shown that one can determine Hamiltonicity of a solid grid graph (a grid graph induced by the points that lie inside a simply connected region) in polynomial time. Approximation algorithms for the lawnmowing problem allow one to get within a constant factor of optimal [24, 25, 224]; the best current factor is (3 ffl) based on the algorithm of Arkin, Fekete, and Mitchell [25] together with recent PTAS results for TSP. They also give a 2.5 approximation algorithm for the milling problem; the approximation factor becomes 11 5 if R is a rectilinear simple polygon. The model ....

K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., volume 834 of Lecture Notes Comput. Sci., pages 29--37. Springer-Verlag, 1994.

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K. Iwano, P. Raghavan, and H. Tamaki. The traveling cameraman problem, with applications to automatic optical inspection. In Proc. 5th Annu. Internat. Sympos. Algorithms Comput., Lecture Notes Comput. Sci., Beijing, 1994. Springer-Verlag. 33

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