J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput., 28(4):1298--1309, 1999. Home/Search Document Details and Download
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Balanced Partition of Minimum Spanning Trees.. - Andersson.. (Correct)
....tour of shortest length that visits all of the buyers neighborhoods and finally returns to his initial departure point. Both these problems are related to the problem known in the literature as the Traveling Salesperson problem with Neighborhoods (TSPN) and which has been extensively studied [2, 4, 6, 7, 8, 9]. The problem (TSPN) asks for the shortest tour that visits each of the neighborhoods. The problem was recently shown to be APX hard[7] Interesting generalizations of the TSPN problem arise when additional resources (k 1 robots in the sheet cutting problem, or k 1 salespersons in the second ....
J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric tsp, k-mst, and related problems. SIAM Journal on Computing, 28(4):1298--1309, 1999.
A Polynomial Time Approximation Scheme for the Symmetric - Rectilinear Steiner.. (Correct)
....In this paper, we provide a polynomial time approximation scheme (PTAS) for the SRStA problem. A PTAS for a problem of size n is an algorithm that, for every constant 0, finds an approximate solution with an approximation factor of 1 in time polynomial in n. We apply the method proposed in [3, 7, 8, 9]. For the sake of completeness, we briefly review the results of m guillotine in Section 3. 1.1 Motivations and Applications The SRStA and the RStA problems have a number of applications. An application that is mentioned quite often comes from VLSI design, where a RStA or SRStA is needed to ....
....that any rectangular subdivision with cost L can be converted into a guillotine rectangular subdivision with cost at most 2L by adding a set of new edges whose total length is at most L. Moreover, the cost of the new edges is charged off to the original edge set of the subdivision. Mitchell [7, 8, 9] extended these concepts and ideas by defining m guillotine subdivision and proving that an m guillotine subdivision with cost at most (1 ) Delta L can be obtained from a rectilinear subdivision whose cost is L. With m guillotine subdivision, Mitchell [8, 9] found PTASs for various geometric ....
J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem. Proc. 7th ACM-SIAM Sympos. Discrete Algorithms, 1996, pp. 402-408.
Asymptotic Relations Between Minimal Graphs and alpha-entropy - Hero, Costa, Ma (2003) (Correct)
....convergence rate may be derived if a better m dependent analog to the concentration inequality (25) can be found. 4 Convergence Rates for Fixed Partition Approximations Partitioning approximations to minimal graphs have been proposed by many authors, including Karp [5] Ravi etal [25] Mitchell [26], and Arora [27] as ways to reduce computational complexity. The fixed partition approximation is a simple example whose convergence rate has been studied by Karp [5, 28] Karp and Steele [29] and Yukich [2] in the context of a uniform density f . Fixed partition approximations to a minimal graph ....
J. Mitchell, "Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem," in Proc. of ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 402--408.
On the Competitive Complexity of Navigation Tasks - Icking, Kamphans, Klein.. (2002) (Correct)
....known. This amounts to constructing a shortest traveling salesperson (TSP) tour on the cells. 252 Christian Icking et al. If the polygonal environment contains obstacles, the problem of finding such a minimum length tour is known to be NP hard [25] and there are some approximation schemes [2,3,18,36]. In a simple polygon without obstacles, the complexity of constructing offline a minimum length tour seems to be open. There are, however, some results concerning the related Hamiltonian cycle and path problems [14,44] and approximations [2,38] 3.1 The Competitive Complexity The following ....
J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem. In Proc. 7th ACM-SIAM Sympos. Discrete Algorithms, pages 402--408, 1996.
Guillotine Subdivisions Approximate Polygonal Subdivisions: A.. - Mitchell (1996) (92 citations) Self-citation (Mitchell) (Correct)
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J. S. B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: Part III -- Faster polynomial-time approximation schemes for geometric network optimization, Manuscript, April 1997, available at http://www.ams.sunysb.edu/~jsbm/jsbm.html
Guillotine Subdivisions Approximate Polygonal Subdivisions: A.. - Mitchell (1996) (92 citations) Self-citation (Mitchell) (Correct)
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J. S. B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem, Proc. 7th ACM-SIAM Sympos. Discrete Algorithms (1996), pp. 402--408.
Guillotine Subdivisions Approximate Polygonal Subdivisions: Part .. - Mitchell (1997) (92 citations) Self-citation (Mitchell) (Correct)
....how a modification to our earlier results on guillotine subdivisions leads to an n time (deterministic) PTAS for Euclidean versions of various geometric network optimization problems on a set of n points in the plane. This improves the previous n time algorithms of Arora [1] and Mitchell [10]. Arora [2] has recently obtained even better bounds than our own: He obtains a randomized algorithm with expected running time O(n log n) However, our new theorem on approximating guillotine subdivisions may be interesting in its own right, and may lead to yet further improvements or ....
....running time O(n log n) However, our new theorem on approximating guillotine subdivisions may be interesting in its own right, and may lead to yet further improvements or generalizations. Our methods are based on the concept of an m guillotine subdivision , which were introduced by Mitchell [9, 10]. Roughly speaking, an m guillotine subdivision is a polygonal subdivision with the property that there exists a line ( cut ) whose intersection with the subdivision edges consists of a small number (O(m) of connected components, and the subdivisions on either side of the line are also ....
[Article contains additional citation context not shown here]
J. S. B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: Part II --- A simple polynomial-time approximation scheme for geometric k-MST, TSP, and related problems, SIAM J. Comp., to appear.
Guillotine Subdivisions Approximate Polygonal Subdivisions: Part .. - Mitchell (1997) (92 citations) Self-citation (Mitchell) (Correct)
....running time O(n log n) However, our new theorem on approximating guillotine subdivisions may be interesting in its own right, and may lead to yet further improvements or generalizations. Our methods are based on the concept of an m guillotine subdivision , which were introduced by Mitchell [9, 10]. Roughly speaking, an m guillotine subdivision is a polygonal subdivision with the property that there exists a line ( cut ) whose intersection with the subdivision edges consists of a small number (O(m) of connected components, and the subdivisions on either side of the line are also ....
....the geometric optimization problems considered here are known to be NP hard, polynomialtime approximation algorithms have been known previously that get within a constant factor of optimal. Further, polynomial time approximation schemes were discovered last year, by Arora [1] and by Mitchell [9, 10]. This paper represents a continuation of our previous work on guillotine subdivisions ( 9, 10, 11] which in turn is based on the concept of division trees introduced by Blum, Chalasani, and Vempala [3, 11] and the guillotine rectangular subdivision methods of Mata and Mitchell [8] Here, we ....
[Article contains additional citation context not shown here]
J. S. B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem, Proc. 7th ACM-SIAM Sympos. Discrete Algorithms (1996), pp. 402--408.
Fast Approximation Schemes for Euclidean - Multi-Connectivity Problems.. (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput., 28(4):1298--1309, 1999.
Exploring Simple Grid Polygons - Icking, Kamphans, Klein, Langetepe (2005) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput., 28:1298--1309, 1999.
Exploring Grid Polygons Online - Icking, Kamphans, Klein, Langetepe (2005) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem. In Proc. 7th ACM-SIAM Sympos. Discrete Algorithms, pages 402--408, 1996.
A Quasi-Polynomial Time Approximation Scheme for Minimum.. - Remy, Steger (2006) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem. In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 402--408, 1996.
Approximation Schemes For Node-Weighted Geometric Steiner Tree .. - Remy, Steger (2005) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST and related problems. SIAM Journal on Computing, 28(4):1298--1309, 1999.
Approximation Schemes For Node-Weighted Geometric Steiner Tree .. - Remy, Steger (2005) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem. In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 402--408, 1996.
Approximation Schemes for Node-Weighted - Geometric Steiner Tree (2005) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST and related problems. SIAM Journal on Computing, 28(4):1298--1309, 1999.
Differential Approximation of NP-Hard Problems with Equal Size.. - Monnot (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: Part II--a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comp., 28:1298--1309, 1999.
A nearly linear-time approximation scheme for the Euclidean.. - Kolliopoulos, Rao (1999) (141 citations) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM Journal on Computing, 28:1298-1309, 1999.
Approximation Schemes for Degree-restricted MST and Red-Blue.. - Arora, Chang (2003) (7 citations) (Correct)
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J. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple PTAS for geometric k-MST, TSP, and related problems. SIAM J. Comp., 28, 1999.
Approximation Algorithms for the Single-Sink Edge Installation.. - Jothi (2004) (Correct)
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J.S.B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: Part II---a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Computing, 28:1298--1309, 1999.
Euclidean Bounded-Degree Spanning Tree Ratios - Timothy Chan School (2003) (3 citations) (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput., 28:1298-1309, 1999.
Degree-Bounded Minimum Spanning Trees - Jothi, Raghavachari (2004) (Correct)
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J.S.B. Mitchell, Guillotine Subdivisions Approximate Polygonal Subdivisions: Part II { A simple polynomialtime approximation scheme for geometric TSP, kMST, and related problems, SIAM J. Computing, 28, pp. 1298-1309, 1999. 4
Degree-Bounded Minimum Spanning Trees - Raja Jothi Balaji (2004) (Correct)
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J.S.B. Mitchell, Guillotine Subdivisions Approximate Polygonal Subdivisions: Part II { A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems, SIAM J. Computing, 28, pp. 1298-1309, 1999.
The UPS Problem - Fernandes, Nierhoff (Correct)
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J. Mitchell, Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems, SIAM Journal on Computing 28, 1298-1309 (1999).
Convergence Rates of Minimal Graphs with Random Vertices - Hero, Costa, Ma (2003) (Correct)
No context found.
J. Mitchell, "Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem," in Proc. of ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 402--408.
On the Complexity of Approximating TSP with Neighborhoods and .. - Safra, Schwartz (Correct)
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J. S. B. Mitchell. Guillotine subdivisions approximate polygonal subdivisions: A simple new method for the geometric k-MST problem. In Proceedings of the Seventh Annual ACMSIAM Symposium on Discrete Algorithms, pages 402--408, Atlanta, Georgia, 28--30 January 1996.
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