N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-865, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....some stronger assumptions on the curves: We assume that all pieces of the curve are algebraic of degree bounded by a constant. This is needed in the analysis of the algorithm to ensure that only a limited number of obstacles can appear in a cell. We apply Megiddo s parametric search technique [8]. We will closely follow the approach of [1] for polygonal curves, except that the technical details are a little bit more involved. By Theorem 2, we know that we can solve the decision problem for a given threshold # it we know all obstacles and their extreme points in all four directions in ....

N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. Assoc. Comput. Mach. 30, 852--865. 13

....and discusses some of them in more detail. The first technique that we present is called parametric searching. Although restricted versions of parametric searching already existed earlier (see e.g. 112] the full scale technique was presented by Megiddo in the late 1970s and early 1980s [209, 210]. The technique was originally motivated by so called parametric optimization problems in combinatorial optimization, and did not receive much attention by the computational geometry community until the late 1980s. In the last seven years, though, it has become one of the major techniques for ....

....Searching We begin by outlining the parametric searching technique, and then illustrate the technique by giving an example where this technique is applied. Finally, we discuss various extensions of parametric searching. 2. 1 Outline of the technique The parametric searching technique of Megiddo [209, 210] can be described in the following general terms (which are not as general as possible, but suffice for our purposes) Suppose we have a decision problem P( that depends on a real parameter , and is monotone in , meaning that if P( 0 ) is true for some 0 , then P( is true for all 0 . Our ....

N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. ACM, 30 (1983), 852--865.

....problem for P in Q, with the additional advantage of nding a high clearance motion, where P aims to stay as far away from the boundary of Q as possible; see [17] for a more precise de nition of high clearance. Sharir and Toledo [37] proposed another algorithm that combines parametric searching [29] with a construction of the entire con guration space for the xed size case, as in the preceding paragraph; the running time of their algorithm is close to O(m ) If only translation and scaling are allowed, the largest homothetic placement of P inside Q can be computed in time O(mn log n) ....

.... there exists one, we can return such a path in time proportional to its complexity, which is at most O(mn 6 (mn) Finding the Largest Placement of P inside Q 19 4 Finding the Largest Placement of P inside Q As mentioned in the introduction, we use the parametric searching technique of Megiddo ([29]; see also [5, 7] to compute a largest free similar placement of P inside Q. The parametric searching paradigm requires an oracle procedure to determine, for a given scaling factor s 0 of P , whether C s , the free con guration space corresponding to sP moving within Q, is nonempty. Using ....

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N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. ACM 30 (1983), 852-865.

....problem f r (e) B we have several possibilities as in the case of capacity expansion problems. One possibility is Radzik s nite Newton method [14] If the problem can be solved by an algorithm which uses only additions and comparisons, then one can also use one of Megiddo s methods [11, 12] for parametric programming. 3 Complexity of capacity expansion problems vs. weight reduction problems In this section we rst consider the decision versions of capacity expansion and weight reduction problems. The decision version of the capacity expansion problem has the following ....

N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, Journal of the ACM 30, 1983, 852-865.

.... are in NC [98] Algorithms for the TVPI problem were developed partly in the search for polynomial algorithms for the general linear programming problem [5] It was shown by Megiddo [87] that the TVPI problem could be solved in strongly polynomial time using parametric techniques (see also [86]) The strongly polynomial algorithms for TVPI given in [55, 20] and for the the generalized shortest path problem [95] are all based on the parametric binary search techniques of Megiddo [87] There is an interesting correspondence between satis ability problems and linear feasibility problems ....

N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. Assoc. Comput. Mach., 30:852-865, 1983.

.... for the works of Jaromczyk and Kowaluk, the general approach in solving the above covering problems is to first solve the corresponding decision problem, and then to apply an optimization scheme, such as the sorted matrices technique [9] the expander based technique [15] or parametric search [16]. In what follows we employ a variety of techniques to solve our problems using this general approach. The decision algorithm of Problem 1 searches for the centers of a solution pair (of squares) in an implicit special matrix, using a technique that has recently been used in [7, 21] To find an ....

....a search in a collection of sorted matrices [9] is performed. The decision algorithm of Problem 2 involves maintenance of dynamically changing convex hulls, and maintenance of an orthogonal range search tree that must adapt to a rotating axes system. For the optimization, we apply Megiddo s [16] parametric search. However, since our decision algorithm is not parallelizable, we had to find an algorithm that solves a completely dif3 ferent problem, but is both parallelizable and enables to generate the optimal square area when the parametric search technique is applied to it. In the ....

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N. Megiddo, "Applying parallel computation algorithms in the design of serial algorithms", J. ACM 30 (1983), 852--865.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-865, 1983.

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N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, Journal of the Association for Computing Machinery 30 (1983), 852-866. 4

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-- 865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM, 30:852--865, 1983.

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N. Megiddo, \Applying parallel computation algorithms in the design of serial algorithms, " Journal of the ACM, 30, 852-865, 1983. 11

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Nimrod Megiddo. Applying parallel computation algorithms in the design of serial algorithms. Journal of the Association for Computing Machinery, 30(4):852-865, October 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM, 30:852--865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852--865, 1983.

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Megiddo, N., Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM, 30(1983)852-865.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30:852--865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM, 30(4):852--865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30(4):852-865, 1983.

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Megiddo, N. Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30 (1983), 852-865.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30:852-865, 1983.

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N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30:852-865, 1983.

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N. Megiddo, Applying Parallel Computation Algorithms in the Design of Serial Algorithms, J. ACM 30 (1983), 852--865.

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N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. ACM 30 (1983), 852--865. 5

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