We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and low-dilation graphs. 1 Introduction This survey covers topics in geometric network design theory. The problem is easy to state: connect a collection of sites by a "good" network. For instance, one may wish to connect components of a VLSI circuit by networks of wires, in a way that uses little surface area on the chip, draws little power, and propagates signals quickly. Similar problems come up in other applications such as telecommunications, road network design, and medical imaging [1]. One network design problem, the Traveling Salesman problem, is sufficiently important to have whole books devoted to it [79]. Problems involving some form of geometric minimum or maximum spanning tree also arise in the solution of other geometric problems such as clustering [12], mesh generation [56], and robot motion planning [93]. One can vary the network design problem in many w...
|
7271
|
Computers and Intractability - A Guide to the Theory of NP-Completeness
– Garey, Johnson
- 1979
|
|
218
|
A data structure for dynamic trees
– SLEATOR, TARJAN
- 1981
|
|
204
|
Optimal search in planar subdivisions
– Kirkpatrick
- 1983
|
|
204
|
The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
– Lawler, Lenstra, et al.
- 1985
|
|
184
|
A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields
– Callahan, Kosaraju
- 1995
|
|
179
|
Worst-case analysis of a new heuristic for the travelling salesman problem
– Christofides
- 1976
|
|
171
|
Algorithms for VLSI Physical Design Automation: Second Edition
– Sherwani
- 1995
|
|
162
|
Mesh generation and optimal triangulation
– Bern, Eppstein
- 1992
|
|
156
|
Closest-Point problems
– SHAMOS, HOEY
- 1975
|
|
138
|
Planar point location using persistent search trees
– Sarnak, Tarjan
- 1986
|
|
137
|
On constructing minimum spanning trees in kdimensional spaces and related problems
– Yao
- 1982
|
|
133
|
Optimal point location in a monotone subdivision
– Edelsbrunner, Guibas, et al.
- 1986
|
|
132
|
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
– Fredman, Willard
- 1994
|
|
125
|
Guillotine Subdivisions Approximate Polygonal Subdivisions: Part II - A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems
– Mitchell
- 1999
|
|
123
|
On sparse spanners of weighted graphs
– Althöfer, Das, et al.
- 1993
|
|
123
|
Randomized incremental construction of Delaunay and Voronoi diagrams
– Guibas, Knuth, et al.
- 1992
|
|
123
|
Applications of a planar separator theorem
– Lipton, Tarjan
- 1977
|
|
104
|
Sparsification—a technique for speeding up dynamic graph algorithms
– Eppstein, Galil, et al.
- 1997
|
|
85
|
A randomized linear-time algorithm to find minimum spanning trees
– Karger, Klein, et al.
- 1995
|
|
83
|
Decomposable searching problems I: static-to-dynamic transformation
– Bentley, Saxe
- 1980
|
|
82
|
Delaunay graphs are almost as good as complete graphs
– Dobkin, Friedman, et al.
- 1990
|
|
80
|
A retraction method for planning the motion of a disc
– O'Dunlaing, Yap
- 1982
|
|
78
|
There is a planar graph almost as good as the complete graph
– Chew
- 1986
|
|
71
|
Approximation Algorithms for Geometric Problems
– Bern, Eppstein
- 1995
|
|
67
|
New sparseness results on graph spanners
– Chandra, Das, et al.
- 1995
|
|
64
|
Efficient algorithms for finding minimum spanning trees in directed and undirected graphs
– Gabow, Galil, et al.
- 1986
|
|
59
|
Finding minimum spanning trees
– Cheriton, Tarjan
- 1976
|
|
58
|
Approximation Algorithms for Geometric Tour and Network Design Problems
– Mata, Mitchell
- 1995
|
|
56
|
R.L.S.Drysdale Voronoi diagrams based on convex distance functions
– Chew
- 1985
|
|
56
|
Maintenance of a minimum spanning forest in a dynamic plane graph
– Eppstein, Italiano, et al.
- 1992
|
|
51
|
Euclidean minimum spanning trees and bichromatic closest pairs
– Agarwal, Edelsbrunner, et al.
- 1991
|
|
50
|
Spanning trees short or small
– Ravi, Sundaram, et al.
- 1994
|
|
50
|
Exact Zero Skew
– Tsay
- 1991
|
|
49
|
Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen
– Awerbuch, Azar, et al.
- 1999
|
|
49
|
Tree spanners
– Cai, Corneil
- 1995
|
|
49
|
Iterated nearest neighbors and finding minimal polytopes
– Eppstein, Erickson
- 1994
|
|
49
|
Constructing multidimensional spanner graphs
– Salowe
- 1991
|
|
47
|
Which triangulations approximate the complete graph
– Das, Joseph
- 1989
|
|
43
|
A fast algorithm for constructing sparse Euclidean spanners
– DAS, NARASIMHAN
- 1997
|
|
43
|
Minimal triangulations of polygonal domains
– Klincsek
- 1980
|
|
42
|
Parallel construction of quadtrees and quality triangulations
– Bern, Eppstein, et al.
- 1993
|
|
41
|
A Linear Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon, Discrete and Computational Geometry 4
– Aggarwal, Guibas, et al.
- 1989
|
|
41
|
A sparse graph almost as good as the complete graph on points in k dimensions
– Vaidya
- 1991
|
|
40
|
Static and dynamic algorithms for k-point clustering problems
– Datta, Lenhof, et al.
- 1993
|
|
40
|
On Two Geometric Problems Related to the Traveling Salesman Problem
– Papadimitriou, Vazirani
- 1984
|
|
37
|
Clock routing for high-performance ICs
– Jackson, Srinivasan, et al.
- 1990
|
|
37
|
Approximating the d-dimensional complete euclidean graph
– Ruppert, Seidel
- 1991
|
|
36
|
Randomized multidimensional search trees: lazy balancing and dynamic shuffling
– Mulmuley
- 1991
|
|
35
|
The Delaunay triangulation closely approximates the complete Euclidean graph
– KEIL, GUTWIN
- 1989
|
|
34
|
A constant-factor approximation algorithm for the k-MST problem
– Blum, Ravi, et al.
- 1996
|
