M. I. Shamos and D. Hoey. Closest-point problems. In Proceedings of the 16th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 151--162, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in computational geometry and has been extensively studied in the literature for more than two decades. It is easy to see that to find the EMST of n points, O(dn ) time suffices, by reducing it to the MST problem in dense graphs. In the simplest case where d = 2 (on the plane) Shamos and Hoey [29] show that the EMST problem can be solved in O(n log n) time. For d 3, no e O(n) time algorithm is known and it is a major open question whether an O(n log n) time algorithm exists even for d = 3 [17] Yao [32] was the first who broke the O(n ) time barrier for d 3 and designed an e O(n ....

....O(n L n) O(n ) A note on the running time is due here. We use O( queries in the course of constructing the quad tree. Next, we have to find the minimum spanning tree (or any (1 ) approximation to it for any fixed ) In the two dimensional case this can be done in n) time ([29]) and this term dominates the total complexity. As it turns out, the above quality of approximation is optimal for the given time bound as shown by the following claim whose proof is deferred to the full version of the paper. CLAIM 3.2. Any algorithm with O( n) orthogonal range queries has an ....

M. I. Shamos and D. Hoey. Closest-point problems. In Proceedings of the 16th IEEE Symposium on Foundations of Computer Science, pp. 151--162, 1975.

....Hence, it is NP hard. WP3: Euclidean Spanning Tree Input: A set P of pin locations, P= x i ,y i )# 1 i n ; between two points (a,b) and (c,d) is the Euclidean metric [ a c) b d) Complexity: Polynomial. An O(n log n) algorithm to find the minimum spanning tree is presented in [SHAM75]. WP4: Manhattan Spanning Tree Input: P, as in WP3. between two points (a,b) and (c,d) is the Manhattan metric a c# #b d#. Complexity: Polynomial. An O(n log n) algorithm that finds the minimum spanning tree is presented in [HWAN79] WP5: Degree Constrained Wiring with Manhattan Distance ....

....which there do exist polynomial time absolute approximation algorithms. It has long been conjectured ( GILB68] that, under the Euclidean metric, 41 length of optimum Steiner tree = 2 3 Hence, fP(sr 3 2 fP(sr 3 0. 155 Hence, the O(n log n) minimum spanning tree algorithm in [SHAM75] can be used as a 0.155 approximate algorithm for the Euclidean Steiner tree problem. For the rectilinear Steiner tree problem, it is known ( HWAN79] 42 [LEE76] that length of optimum Steiner tree 3 2 Hence, 1 2 The O(n log n) spanning tree algorithm in [HWAN79a] can be used ....

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Shamos, M.I. and D.Hoey, "Closest Point Problems", 16th Annual IEEE Symposium on Found. of Comp. Sc., 1975, pp.151-163.

....area with many applications in computer graphics, robotics, VLSI design, geographic information systems, etc. From its first days as a separate research field in algorithmic research, computational geometry has aspired to two goals: solving practical problems and creating beautiful mathematics [SH75, SH76, SB77] Computational geometry has always concerned itself with the design of efficient data structures and algorithms for solving problems which involve geometric objects. Two decades after the landmark paper by M. I. Shamos in 1975 [Sha75] and only ten years after the publication of the ....

....solving practical problems and creating beautiful mathematics [SH75, SH76, SB77] Computational geometry has always concerned itself with the design of efficient data structures and algorithms for solving problems which involve geometric objects. Two decades after the landmark paper by M. I. Shamos in 1975 [Sha75] and only ten years after the publication of the first text book [PS85] entirely devoted to the topic, computational geometry has established itself as an important research field in computer science. Numerous papers have been produced by researchers all over the world. Several ....

M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16th Annu. IEEE Sympos. Found. Comput. Sci., pages 151--162, 1975.

....problem in computational geometry and it has been extensively studied in the literature for more than two decades. It is easy to see that this problem can be solved in time O(dn ) by reducing it to the MST problem in dense graphs. In the simplest case d = 2 (on the plane) Shamos and Hoey [26] show that the EMST problem can be solved in O(n log n) For d 3, no e O(n) time algorithm is known and it is a major open question whether an O(n log n) time algorithm exists even for d = 3 [14] Yao [29] was the first who broke the O(n ) time barrier for d 3 and designed an e O(n 1:8 ....

M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16th IEEE FOCS, pp. 151--162, 1975.

....or l d (S) as in dimension 2, is a far type vertex. To summarize, a close type vertex of a higher order Voronoi diagram remains in d successive diagrams. More generally, a h face remains in d Gamma h successive diagrams. Complexity results The order k Voronoi diagram has been introduced in [SH75] to deal with k closest points problems. Lee [Lee82] gives the following result : Property 1.3 In the plane, the size of the order k Voronoi diagram is O(k(n Gamma k) The size of orders k Voronoi diagrams is thus O(nk ) The random sampling technique (Section 2.3.1) shows the following ....

M.I. Shamos and D. Hoey. Closest-point problems. In IEEE Symposium on Foundations of Computer Science, pages 151--162, October 1975.

....the surveys by [Auren91] and [Okabe92] on various algorithms, applications, and generalizations of Voronoi diagrams. 2. 1 Voronoi Diagrams of Points Among the algorithms known for computing Voronoi diagrams of points in 2D, 3D, and higher dimensions are the divide andconquer algorithm proposed by [Shamo75] and Fortune s sweepline algorithm [Fortu86] Numerically robust algorithms for constructing topologically consistent Voronoi diagrams have been proposed by [Inaga92, Sugih94] A number of implementations in exact and floating point arithmetic are also available. Algorithms have been proposed for ....

M.I. Shamos and D.Hoey. Closest-point Problems. In Proc. 16th Annual IEEE Symposium on Foundations of Comp. Sci., pages 151-162, 1975.

....F lies entirely within some V (s i ) and such an s i can be identi ed in linear time. In summary, the outline of the algorithm to compute the minimum width annulus with outer radius r is as follows: 1. Compute the nearest point Voronoi diagram of the set of points S in O(n log n) time (e.g. [9, 23]) 2. Compute the intersection F of the n discs D(s i ; r) s i 2 S in O(n log n) time [4, 6] Aurenhammer uses power diagrams [4] in two dimensions to compute the intersection, whereas Brown [6] reduces the problem to the intersection of n halfspaces in three dimensions. 12 3. Identify the ....

M.I. Shamos and D. Hoey. Closest-point problems. In Proc. Sixteenth Annual IEEE Symposium on Foundations of Computer Science, pages 151-162, October 1975.

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M. I. Shamos and D. Hoey. Closest-point problems. In Proceedings of the 16th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 151--162, 1975.

No context found.

M. I. Shamos and D. Hoey. Closest-point problems. Proceedings of the 16th IEEE Symposium on Foundations of Computer Science, 1975, pp. 151-162.

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M. I. Shamos and D. Hoey. Closest-point problems. Proceedings of the 16th IEEE Symposium on Foundations of Computer Science, 1975, pp. 151-162.

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M. I. Shamos and D. Hoey. Closest-point problems. Proceedings of the 16th IEEE Symposium on Foundations of Computer Science, 1975, pp. 151-162.

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M. I. Shamos and D. Heoy. Closest-point Problems. Proc. 16th IEEE Annu. Symp. Found. Comput. Sci., pages 151---162, 1975.

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M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16th Annual Symp. Foundations of Computer Science, pages 151-162. IEEE Press, 1975.

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M. Shamos and D. Hoey, "Closest-point problems", Proc. 17th Annual IEEE FOCS, (Oct. 1975) pp. 151-162.

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M. I. Shamos and D. Hoey. Closest-point problems. In Proceedings of the 16th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 151-162, 1975.

No context found.

M. I. Shamos and D. Hoey, Closest-point problems, Proceedings of the 16-th Annual IEEE Symposium on Foundations of Computer Science, 1975, 151-162.

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M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16th Annu. IEEE Sympos. Found. Comput. Sci., pp. 151-162, 1975.

No context found.

M. I. Shamos and D. Hoey. Closest-point problems. Proceedings of the 16th IEEE Symposium on Foundations of Computer Science, 1975, pp. 151-162.

No context found.

Shamos, M. I., and Hoey, D. Closest-point problems. In Proc. 16th Annu. IEEE Sympos. Found. Comput. Sci. (1975), pp. 151-162.

No context found.

M.I. Shamos and D. Hoey. Closest point problems. Proc. 16th Annu. IEEE Sympos. Found. Comput. Sci., pages 152-162, 1975.

No context found.

M. I. Shamos and D. Hoey. Closest-point problems. In Proceedings of the 16th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 151--162, 1975.

No context found.

M. I. Shamos and D. Hoey. Closest-point problem. In Proc. 16th IEEE Annual Symposium on Foundations of Computer Science, pages 151-- 162, Berkeley, CA, Oct 1975.

No context found.

M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16th Annu. IEEE Sympos. Found. Comput. Sci., pages 151--162, 1975.

No context found.

Shamos, M. I. and Hoey D., "Closest point problems", Proc. of 16th Annual IEEE Symposium on Foundations of Computer Science, FOCS'75, pp. 151-162, 1975.

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Shamos, M I and Hoey, D. "Closest-point problems," i6th Annual IEEE Symposium on. Foundation of Computer Science (1975).

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