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Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems
1999
SIAM journal on computing (Print)
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), and the k-MST problem. ...
The method is based on the concept of an "m-guillotine subdivision," a simple extension of the recent approximation method of Mitchell [9] , which considered the case m = 1. ...
I thank Esther Arkin, Rafi Hassin, Samir Khuller, Günter Rote, and the referees for several useful comments and suggestions that improved the presentation of the paper. ...
doi:10.1137/s0097539796309764
fatcat:qkugndrzgjanfonb3bwgrtdx5m
A Constant-Factor Approximation Algorithm for the Geometrick-MST Problem in the Plane
1998
SIAM journal on computing (Print)
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We introduce a new technique that can be used to obtain simple approximation algorithms for geometric network design problems. The method is based on the concept of a \guillotine subdivision". ...
To illustrate the power of the method, we show how it can be used to give a very simple constant-factor approximation algorithm for the geometric k-MST problem, obtaining a substantially better factor ...
Mata for comments and suggestions that improved this paper. ...
doi:10.1137/s0097539796303299
fatcat:fibg35t3arh73dpft2roqat73q
Page 7914 of Mathematical Reviews Vol. , Issue 96m
[page]
1996
Mathematical Reviews
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B. (1-SUNYS-S; Stony Brook, NY)
Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric kK-MST problem. ...
In particular, a consequence of our main theorem is a very simple proof that the k-MST problem in the plane has a constant factor polynomial-time approximation al-
,
909 ECONOMICS, OPERATIONS RESEARCH, ...
Page 4944 of Mathematical Reviews Vol. , Issue 99g
[page]
1999
Mathematical Reviews
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for the geometric k-MST problem in the plane. ...
In particular, a consequence of our main theorem is a very simple proof that the A-MST problem in the plane has a constant-factor polynomial-time approximation algo- rithm: we obtain a factor of 2 [resp ...
Spanning Trees and Spanners
[chapter]
2000
Handbook of Computational Geometry
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We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and low-dilation graphs. ...
We describe the 2 √ 2 approximation algorithm, but the other results use similar methods. For related work on non-geometric k-MST problems see [13, 22, 30, 97, 116] . ...
Up to constant factors in the approximation ratio, the k-MST problem is equivalent to the problem of finding a path connecting k points (the k-TSP problem) or a Steiner tree connecting k points. ...
doi:10.1016/b978-044482537-7/50010-3
fatcat:gitonpgfozgfribivszd6gf5cy
A constant-factor approximation algorithm for the k MST problem (extended abstract)
1996
Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
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In the Euclidean TSP with neighborhoods (TSPN) problem we seek a shortest tour that visits a given set of n neighborhoods. The Euclidean TSPN generalizes the standard TSP on points. ...
We present the first constant-factor approximation algorithm for TSPN on an arbitrary set of disjoint, connected neighborhoods in the plane. ...
We convert T into a polygonal subdivision, G, each of whose faces are histograms; this 2 increases the total length of T by only a constant factor. 4 . ...
doi:10.1145/237814.237992
dblp:conf/stoc/BlumRV96
fatcat:ubcvflvuu5c33g5j5kdp4t4ksu
9707-Computational Geometry
unpublished
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The aim of this workshop was twofold: Firstly, to provide a forum for discussions about the interplay between the theory and practice of geometric computing. ...
In particular it gave a chance to hear about (and maybe influence) the nascent efforts of various groups to create libraries of geometric algorithms. ...
A Simple Polynomial-Type Approximation Scheme for Geometric Network Optimization
Joe Mitchell We present a simple polynomial-time approximation scheme for geometric instances of the k-MST problem, the ...
fatcat:7m52stmf7vbwbosir6zcbjnosi
Page 1523 of Mathematical Reviews Vol. 28, Issue Index
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Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric kK-MST problem. ...
(English summary) 96a:68041
Bhavnagri, Burzin A method for representing shape based on an equivalence relation on polygons. ...
Page 1911 of Mathematical Reviews Vol. 32, Issue Index
[page]
Mathematical Reviews
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Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. ...
(with Rao, Satish) A nearly linear-time approximation scheme for the Euclidean &-median problem. ...
Page 988 of Mathematical Reviews Vol. 28, Issue Index
[page]
Mathematical Reviews
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Counting convex polygons in planar point sets. (English summary) 96h:68212
— Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric kK-MST problem. ...
B.; et al., 96h:68212
Wu, Hui An optimal algorithm for finding the internal common tangent of two simple planar polygons. (Chinese. ...
TSP on manifolds
[article]
2021
arXiv
pre-print
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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. ...
In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. ...
Given a series of metric spaces d k : {1, . . . , n k } → R for k ∈ N one can estimate the 1 C approximation of the TSP problem on d k (with probability ≥ 1 2 ). ...
arXiv:2110.01093v1
fatcat:umnnrvmxyrccdka5yiyept3vdi
Page 1275 of Mathematical Reviews Vol. 32, Issue Index
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Mathematical Reviews
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(see 2000j:68006) 68U0S
— Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. ...
Sweeping simple polygons with a chain of guards. ...