New references related to Geometric Spanner Networks
- M. A. Abam.
Spanners for geodesic graphs and visibility graphs.
Algorithmica, volume 80, 2018, pages 515-529.
- M. A. Abam, M. Adeli, H. Homapour, and P. Z. Asadollahpoor.
Geometric spanners for points inside a polygonal domain.
Proceedings of the 31st International Symposium on Computational
Geometry, 2015, pages 186-197.
- M. A. Abam and M. de Berg.
Kinetic Spanners in R^d.
Discrete & Computational Geometry, volume 45, 2011, pages 723-736.
- M. A. Abam, M. de Berg, M. Farshi, and J. Gudmundsson.
Region-fault tolerant geometric spanners.
Discrete & Computational Geometry, volume 41, 2009, pages 556-582.
- M. A. Abam, M. de Berg, M. Farshi, J. Gudmundsson, and M. Smid.
Geometric spanners for weighted point sets.
Algorithmica, volume 61, 2011, pages 207-225.
- M. A. Abam, M. de Berg, and J. Gudmundsson.
A simple and efficient kinetic spanner.
Computational Geometry: Theory and Applications, volume 43, 2010,
pages 251-256.
- M. A. Abam, M. de Berg, and M. J. R. Seraji.
Geodesic spanners for
points on a polyhedral terrain.
Proceedings of the 28th ACM-SIAM Symposium on Discrete Algorithms,
2017, pages 2434-2442.
- M. A. Abam and M. S. Borouny.
Local geometric spanners.
Algorithmica, volume 83, 2021, pages 3629-3648.
- M. A. Abam, P. Carmi, M. Farshi, and M. Smid.
On the power of the semi-separated pair decomposition.
Computational Geometry: Theory and Applications, volume 46, 2013,
pages 631-639.
- M. A. Abam and S. Har-Peled.
New constructions of SSPDs and their applications.
Computational Geometry: Theory and Applications, volume 45, 2012,
pages 200-214.
- M. A. Abam and M. J. R. Seraji.
Geodesic spanners for
points in R^3 amid axis-parallel boxes.
- A. K. Abu-Affash, R. Aschner, P. Carmi, and M. J. Katz.
The MST of symmetric disk graphs is light.
Computational Geometry: Theory and Applications, volume 45, 2012,
pages 54-61.
- R. Ahmed, G. Bodwin, F. D. Sahneh, K. Hamm, M. J. Latifi Jebelli,
S. Kobourov, and R. Spence.
Graph spanners:
a tutorial review.
- H.-K. Ahn, M. Farshi, C. Knauer, M. Smid, and Y. Wang.
Dilation-optimal edge deletion in polygonal cycles.
International Journal of Computational Geometry & Applications,
volume 20, 2010, pages 69-87.
- O. Aichholzer, S. W. Bae, L. Barba, P. Bose, M. Korman,
A. van Renssen, P. Taslakian, and S. Verdonschot.
Theta-3 is connected.
Computational Geometry: Theory and Applications, volume 47, 2014,
pages 910-917.
- O. Aichholzer, M Borrazzo, P. Bose, J. Cardinal, F. Frati,
P. Morin, and B. Vogtenhuber.
Drawing graphs as
spanners.
- S. Alamdari, T. M. Chan, E. Grant, A. Lubiw, and V. Pathak.
Self-approaching
graphs.
Proceedings of the 20th International Symposium on Graph Drawing.
Lecture Notes in Computer Science, volume 7704, Springer-Verlag,
Berlin, 2013, pages 260-271.
- D. Aldous and T. Lando.
The stretch - length
tradeoff in geometric networks: Average case and worst case
study.
- S. P. A. Alewijnse, Q. W. Bouts, A. P. ten Brink, and K. Buchin.
Computing the greedy
spanner in linear space.
Algorithmica, volume 73, 2015, pages 589-606.
- S. P. A. Alewijnse, Q. W. Bouts, A. P. ten Brink, and K. Buchin.
Distribution-sensitive
construction of the greedy spanner.
Algorithmica, volume 78, 2017, pages 209-231.
- N. Alon and B. Schieber.
Optimal preprocessing
for answering on-line product queries.
This manuscript appeared originally as TR 71/87, the Moise and
Frida Eskenasy Institute of Computer Science, Tel Aviv University
(1987).
- M. Amani, A. Biniaz, P. Bose, J.-L. De Carufel, A. Maheshwari,
and M. Smid.
A plane 1.88-spanner for points in convex position.
Journal of Computational Geometry, volume 7(1), 2016,
pages 520-539.
- N. Amarnadh and P. Mitra.
Upper bound on dilation of triangulations of cyclic polygons.
Proceedings of Computational Science and its Applications.
Lecture Notes in Computer Science, volume 3980, Springer-Verlag,
Berlin, 2006, pages 1-9.
- F. Anderson, A. Ghosh, M. Graham, L. Mougeot, and D. Wisnosky.
Bounded-degree plane
geometric spanners in practice.
- A. Andoni and H. Zhang.
Sub-quadratic
(1+eps)-approximate Euclidean spanners, with applications.
- B. Aronov, K. Buchin, M. Buchin, B. Jansen, T. de Jong,
M. van Kreveld, M. L\"offler, J. Luo, R. I. Silveira, and
B. Speckmann.
Connect the dot: Computing feed-links for network extension.
Journal of Spatial Information Science, number 3, 2011,
pages 3-31.
- T. Asano, M. de Berg, O. Cheong, H. Everett, H. Haverkort,
N. Katoh, and A. Wolff.
Optimal spanners for axis-aligned rectangles.
Computational Geometry: Theory and Applications, volume 30, 2005,
pages 59-77.
- S. Ashur and S. Har-Peled.
Local spanners
revisited.
- V. Ashvinkumar, J. Gudmundsson, C. Levcopoulos, B. J. Nilsson,
and A. van Renssen.
Local routing in
sparse and lightweight geometric graphs.
Algorithmica, volume 84, 2022, pages 1316-1340.
- J. Augustine, D. Eppstein, and K. A. Wortman.
Approximate weighted farthest neighbors and minimum dilation
stars.
Proceedings of the 16th Annual International Computing and
Combinatorics Conference.
Lecture Notes in Computer Science, volume 6196, Springer-Verlag,
Berlin, 2010, pages 90-99.
- D. Bakhshesh, L. Barba, P. Bose, J.-L. De Carufel, M. Damian,
R. Fagerberg, M. Farshi, A. van Renssen, P. Taslakian, and
S. Verdonschot.
Continuous Yao graphs.
Computational Geometry: Theory and Applications, volume 67,
2018, pages 42-52.
- D. Bakhshesh and M. Farshi.
Some properties of continuous Yao graph.
Proceedings of the 1st IFIP International Conference on Topics in
Theoretical Computer Science (TTCS 2015).
Lecture Notes in Computer Science, volume 9541, Springer-Verlag,
Berlin, 2016, pages 44-55.
- D. Bakhshesh and M. Farshi.
Geometric spanners merging and its applications.
Proceedings of the 28th Canadian Conference on Computational
Geometry, 2016, pages 133-139.
- D. Bakhshesh and M. Farshi.
Improving space and time complexity of the gap-greedy spanner
algorithm.
The CSI Journal on Computer Science and Engineering, volume 14,
number 1, 2016, pages 6-18.
- D. Bakhshesh and M. Farshi.
Angle-constrained spanners with angle at least pi/3.
Information Processing Letters, volume 120, 2017, pages 44-46.
- D. Bakhshesh and M. Farshi.
Fault tolerancy of continuous Yao graph of angle less than
2pi/5.
Information Processing Letters, volume 148, 2019, pages 13-18.
- L. Barba, P. Bose, J.-L. De Carufel, A. van Renssen, and
S. Verdonschot.
On the stretch
factor of the Theta-4 graph.
Proceedings of the 13th Algorithms and Data Structures Symposium.
Lecture Notes in Computer Science, volume 8037, Springer-Verlag,
Berlin, 2013, pages 109-120.
- L. Barba, P. Bose, M. Damian, R. Fagerberg, W. L. Keng,
J. O'Rourke, A. van Renssen, P. Taslakian, S. Verdonschot,
and G. Xia.
New and improved
spanning ratios for Yao graphs.
Journal of Computational Geometry, volume 6, number 2, 2015,
pages 19-53.
- Y. Bartal and L.-A. Gottlieb.
A linear time approximation scheme for Euclidean TSP.
Proceedings of the 54th IEEE Symposium on Foundations of
Computer Science, 2013.
- M. Bauer and M. Damian.
Some sparse Yao graphs are spanners.
Proceedings of the 28th European Workshop on Computational
Geometry, 2012, pages 229-232.
- M. Bauer and M. Damian.
An infinite class of
sparse-Yao spanners.
Proceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms,
2013, pages 184-196.
- M. Benkert, J. Gudmundsson, H. Haverkort, and A. Wolff.
Constructing minimum-interference networks.
Computational Geometry: Theory and Applications, volume 40, 2008,
pages 179-194.
- S. de Berg, M. van Kreveld, and F. Staals.
The complexity of
geodesic spanners.
- S. de Berg, T. Ophelders, I. Parada, F. Staals, and J. Wulms.
The complexity of
geodesic spanners using Steiner points.
- S. Bhattacharjee and R. Inkulu.
Fault-tolerant
additive weighted geometric spanners.
- S. Bhattacharjee and R. Inkulu.
Vertex fault-tolerant
geometric spanners for weighted points.
- S. Bhore, A. Filtser, H. Khodabandeh, and C. D. Toth.
Online spanners in
metric spaces.
- S. Bhore, B. Keszegh, A. Kupavskii, H. Le, A. Louvet,
D. Palvolgyi, and C. D. Toth.
Spanners in planar
domains via Steiner spanners and non-Steiner tree covers.
- S. Bhore and C. D. Toth.
On Euclidean Steiner
(1+epsilon)-spanners.
- S. Bhore and C. D. Toth.
Light Euclidean Steiner
spanners in the plane.
- S. Bhore and C. D. Toth.
Online Euclidean
spanners.
- S. Bhore and C. D. Toth.
Euclidean Steiner
spanners: light and sparse.
- A. Biniaz, P. Bose, J.-L. De Carufel, C. Gavoille, A.Maheshwari,
and M. Smid.
Towards plane spanners
of degree 3.
Journal of Computational Geometry, volume 8(1), 2017,
pages 11-31.
- A. Biniaz, J.-L. De Carufel, A. Maheshwari, and M. Smid.
Metric and geometric
spanners that are resilient to degree-bounded edge faults.
- B. Bollob{\'a}s and A. Scott.
On separating systems.
European Journal of Combinatorics, volume 28, 2007,
pages 1068-1071.
- The results in this paper imply that for any WSPD/SSPD of
any point set, \sum_i (|A_i|+|B_i|) = Omega (n log n).
This was first proved by Hansel in 1964.
- In "Proofs from THE BOOK", third edition, pages 55-56, there
is a nice proof that any WSPD/SSPD of any point set consists
of at least n-1 pairs.
- N. Bonichon, P. Bose, P. Carmi, I. Kostitsyna, A. Lubiw, and
S. Verdonschot.
Gabriel triangulations
and angle-monotone graphs: local routing and recognition.
- N. Bonichon, P. Bose, J.-L. De Carufel, V. Despré,
D. Hill, and M. Smid
Improved routing on the Delaunay triangulation.
Discrete & Computational Geometry, volume 70, 2023, pp. 495-549.
- N. Bonichon, P. Bose, J.-L. De Carufel, L. Perkovic, and
A. van Renssen.
Upper and lower bounds
for competitive online routing on Delaunay triangulations.
- N. Bonichon, C. Gavoille, N. Hanusse, and D. Ilcinkas.
Connections between Theta-graphs, Delaunay triangulations, and
orthogonal surfaces.
Proceedings of the 36th International Workshop on Graph-Theoretic
Concepts in Computer Science.
Lecture Notes in Computer Science, volume 6410, Springer-Verlag,
Berlin, 2010, pages 266-278.
- N. Bonichon, C. Gavoille, N. Hanusse, and L. Perkovic.
Plane spanners of maximum degree six.
Proceedings of the 37th International Colloquium on Automata,
Languages and Programming.
Lecture Notes in Computer Science, volume 6198, Springer-Verlag,
Berlin, 2010, pages 19-30.
- N. Bonichon, C. Gavoille, N. Hanusse, and L. Perkovic.
Tight stretch factors for $L_1$- and $L_{\infty}$-Delaunay
triangulations.
Computational Geometry: Theory and Applications, volume 48, 2015,
pages 237-250.
- N. Bonichon, I. Kanj, L. Perkovic, and G. Xia.
There are plane spanners
of degree 4 and moderate stretch factor.
Discrete & Computational Geometry, volume 53, 2015, pages 514-546.
- G. Borradaile and D. Eppstein.
Near-linear-time deterministic plane Steiner spanners and TSP
approximation for well-spaced point sets.
Proceedings of the 24th Canadian Conference on Computational
Geometry, 2012, pages 297-302.
- G. Borradaile, H. Le, and C. Wulff-Nilsen.
Greedy spanners are optimal in doubling metrics.
Proceedings of the 30th ACM-SIAM Symposium on Discrete
Algorithms, 2019, pages 2371-2379.
- P. Bose, J. Cardinal, S. Collette, E. D. Demaine, B. Palop,
P. Taslakian, and N. Zeh.
Relaxed Gabriel graphs.
Proceedings of the 21st Canadian Conference on Computational
Geometry, 2009, pages 169-172.
- P. Bose, P. Carmi, and L. Chaitman-Yerushalmi.
On bounded degree plane strong geometric spanners.
Journal of Discrete Algorithms, volume 15, 2012, pages 16-31.
- P. Bose, P. Carmi, L. Chaitman-Yerushalmi, S. Collette,
M. J. Katz, and S. Langerman.
Stable roommates spanner.
Computational Geometry: Theory and Applications, volume 46, 2013,
pages 120-130.
- P. Bose, P. Carmi, S. Collette, and M. Smid.
On the stretch factor of convex Delaunay graphs.
Journal of Computational Geometry, volume 1, 2010, pages 41-56.
- P. Bose, P. Carmi, and M. Couture.
Spanners of additively weighted point sets.
Journal of Discrete Algorithms, volume 9, 2011, pages 287-298.
- P. Bose, P. Carmi, M. Couture, A. Maheshwari, M. Smid, and N. Zeh.
Geometric spanners with small chromatic number.
Computational Geometry: Theory and Applications, volume 42, 2009,
pages 134-146.
- P. Bose, P. Carmi, M. Couture, A. Maheshwari, P. Morin, and
M. Smid.
Spanners of complete k-partite geometric graphs.
SIAM Journal on Computing, volume 38, 2009, pages 1803-1820.
- P. Bose, P. Carmi, M. Couture, M. Smid, and D. Xu.
On a family of strong geometric spanners that admit local routing
strategies.
Computational Geometry: Theory and Applications, volume 44, 2011,
pages 319-328.
- P. Bose, P. Carmi, M. Damian, J.-L. De Carufel, D. Hill,
A. Maheshwari, Y. Liu, and M. Smid.
On the stretch factor
of convex polyhedra whose vertices are (almost) on a sphere.
Journal of Computational Geometry, volume 7(1), 2016,
pages 444-472.
- P. Bose, P. Carmi, V. Dujmović, and P. Morin.
Near-optimal
O(k)-robust geometric spanners.
- P. Bose, P. Carmi, M. Farshi, A. Maheshwari, and M. Smid.
Computing the greedy spanner in near-quadratic time.
Algorithmica, volume 58, 2010, pages 711-729.
- P. Bose, P. Carmi, M. Smid, and D. Xu.
Communication-efficient
construction of the plane localized Delaunay graph.
Proceedings of the 9th Latin American Theoretical Informatics
Symposium.
Lecture Notes in Computer Science, volume 6034, Springer-Verlag,
Berlin, 2010, pages 282-293.
- P. Bose, S. Collette, F. Hurtado, M. Korman, S. Langerman,
V. Sacristán, and M. Saumell.
Some properties of k-Delaunay and k-Gabriel graphs.
Computational Geometry: Theory and Applications, volume 46, 2013,
pages 131-139.
- P. Bose, M. Damian, K. Douïeb, J. O'Rourke, B. Seamone,
M. Smid, and S. Wuhrer.
pi/2-Angle Yao graphs are spanners.
International Journal of Computational Geometry & Applications,
volume 22, 2012, pp. 61-82.
- P. Bose, J.-L. De Carufel, and O. Devillers.
Expected complexity
of routing in $\Theta_6$ and half-$\Theta_6$-graphs.
- P. Bose, J.-L. De Carufel, and S. Njoo.
The exact spanning ratio
of the parallelogram Delaunay graph.
- P. Bose, J.-L. De Carufel, D. Hill, and M. Smid.
On the spanning and
routing ratio of the directed Theta-four.
Discrete & Computational Geometry, volume 71, 2024, pp. 872-892.
- P. Bose, J.-L. De Carufel, P. Morin, A. van Renssen, and
S. Verdonschot.
Towards tight bounds on theta-graphs: More is not always better.
Theoretical Computer Science, volume 616, 2016, pp. 70-93.
- P. Bose, J.-L. De Carufel, P. Morin, A. van Renssen, and
S. Verdonschot.
Towards tight bounds
on Theta-graphs.
- P. Bose, J.-L. De Carufel, and A. van Renssen.
Constrained empty-rectangle Delaunay graphs.
Proceedings of the 27th Canadian Conference on Computational
Geometry, 2015, pages 57-62.
- P. Bose, J.-L. De Carufel, and A. van Renssen.
Constrained generalized
Delaunay graphs are plane spanners.
- P. Bose, L. Devroye, M. L\"offler, J. Snoeyink, and V. Verma.
Almost all Delaunay triangulations have stretch factor greater
than $\pi/2$.
Computational Geometry: Theory and Applications, volume 44, 2011,
pages 121-127.
- P. Bose, V. Dujmović, P. Morin, and M. Smid.
Robust geometric
spanners.
SIAM Journal on Computing, volume 42, 2013, pages 1720-1736.
- P. Bose, R. Fagerberg, A. van Renssen, and S. Verdonschot.
Competitive routing in the half-$\theta_6$-graph.
Proceedings of the 23rd ACM-SIAM Symposium on Discrete
Algorithms, 2012, pages 1319-1328.
- P. Bose, R. Fagerberg, A. van Renssen, and S. Verdonschot.
On plane constrained
bounded-degree spanners.
Algorithmica, volume 81, 2019, pages 1392-1415.
- P. Bose, R. Fagerberg, A. van Renssen, and S. Verdonschot.
Competitive routing on a bounded-degree plane spanner.
Proceedings of the 24th Canadian Conference on Computational
Geometry, 2012, pages 285-290.
- P. Bose, D. Hill, and A. Ooms.
Improved spanning
on Theta-5.
- P. Bose, D. Hill, and M. Smid.
Improved spanning
ratio for low degree plane spanners.
Algorithmica, volume 80, 2018, pages 935-976.
- P. Bose and M. Keil.
On the stretch factor of the constrained Delaunay triangulation.
Proceedings of the 3rd International Symposium on Voronoi Diagrams
in Science and Engineering, 2006, pages 25-31.
- P. Bose, A. Lee, and M. Smid.
On generalized diamond spanners.
Proceedings of the 10th Workshop on Algorithms and Data Structures.
Lecture Notes in Computer Science, volume 4619,
Springer-Verlag, Berlin, 2007, pages 325-336.
- P. Bose, P. Morin, and A. van Renssen.
The price of order.
International Journal of Computational Geometry & Applications,
volume 26, 2016, pages 135-149.
- P. Bose, P. Morin, A. van Renssen, and S. Verdonschot.
The $\theta_5$-graph
is a spanner.
Computational Geometry: Theory and Applications, volume 48, 2015,
pages 108-119.
- P. Bose, S. Pratt, and M. Smid.
The convex hull of points on a sphere is a spanner.
Proceedings of the 26th Canadian Conference on Computational
Geometry, 2014, pages 244-250.
- P. Bose and M. Smid.
On plane geometric spanners: A survey and open problems.
Computational Geometry: Theory and Applications, volume 46, 2013,
pages 818-830.
- P. Bose and T. Tuttle.
Routing on heavy path
WSPD spanners.
- P. Bose and A. van Renssen.
Upper bounds on the
spanning ratio of constrained Theta-graphs.
Proceedings of the 11th Latin American Theoretical Informatics
Symposium.
Lecture Notes in Computer Science, volume 8392, Springer-Verlag,
Berlin, 2014, pages 108-119.
- P. Bose and A. van Renssen.
Spanning properties of
Yao and Theta-graphs in the presence of constraints.
- P. Bose, A. van Renssen, and S. Verdonschot.
On the spanning ratio of Theta-graphs.
Proceedings of the 13th Algorithms and Data Structures Symposium.
Lecture Notes in Computer Science, volume 8037, Springer-Verlag,
Berlin, 2013, pages 182-194.
- Q. W. Bouts, A. P. ten Brink, and K. Buchin.
A framework for computing the greedy spanner.
Proceedings of the 30th ACM Symposium on Computational Geometry,
2014, pages 11-19.
- A. F. Brandt, M. M. Gaiowski, C. C. de Souza, and
P. J. de Rezende
Minimum dilation triangulation: Reaching optimality efficiently
Proceedings of the 26th Canadian Conference on Computational
Geometry, 2014, pages 61-66.
- M. Brankovic, J. Gudmundsson, and A. van Renssen.
Local routing in a
tree metric 1-spanner.
- U. A. Brodowsky and S. Hougardy.
The approximation ratio
of the 2-opt heuristic for the Euclidean traveling salesman
problem.
- U. A. Brodowsky, S. Hougardy, and X. Zhong.
The approximation ratio
of the k-opt heuristic for the Euclidean traveling salesman
problem.
- K. Buchin, M. Buchin, J. Gudmundsson, and S. Wong.
Bicriteria approximation
for minimum dilation graph augmentation.
- K. Buchin, J. Gudmundsson, A. Kalb, A. Popov, C. Rehs,
A. van Renssen, and S. Wong.
Oriented spanners.
- K. Buchin, S. Har-Peled, and D. Olah.
A spanner for the
day after.
Discrete & Computational Geometry, volume 64, 2020, pages 1167-1191.
- K. Buchin, S. Har-Peled, and D. Olah.
Sometimes reliable
spanners of almost linear size.
Journal of Computational Geometry, volume 13, number 1, 2022,
pages 178-196.
- K. Buchin, T. Hulshof, and D. Olah.
O(k)-Robust spanners
in one dimension.
- S. Cabello and C. Knauer.
Algorithms for graphs of bounded treewidth via orthogonal range
searching.
Computational Geometry: Theory and Applications, volume 42, 2009,
pages 815-824.
- P. Carmi and L. Chaitman-Yerushalmi.
Minimum weight
Euclidean t-spanner is NP-hard.
Journal of Discrete Algorithms, volume 22, 2013, pages 30-42.
- P. Carmi and M. Smid.
An optimal algorithm for computing angle-constrained spanners.
Journal of Computational Geometry, volume 3, 2012, pages 196-221.
- T.-H. Chan and A. Gupta.
Small hop-diameter sparse spanners for doubling metrics.
Discrete & Computational Geometry, volume 41, 2009, pages 28-44.
- T.-H. Chan, M. Li, and L. Ning.
Sparse fault-tolerant spanners for doubling metrics with
bounded hop-diameter or degree.
Proceedings of the 39th International Colloquium on Automata,
Languages and Programming.
Lecture Notes in Computer Science, volume 7391, Springer-Verlag,
Berlin, 2012, pages 182-193.
- T.-H. Chan, M. Li, and L. Ning.
Incubators vs zombies:
fault-tolerant, short, thin and lanky spanners for doubling
metrics.
- T.-H. Chan, M. Li, L. Ning, and S. Solomon.
New doubling spanners: better and simpler.
SIAM Journal on Computing, volume 44, 2015, pages 37-53.
- T. M. Chan.
Well-separated pair decomposition in linear time?
Information Processing Letters, volume 107, 2008, pages 138-141.
- T. M. Chan, S. Har-Peled, and M. Jones.
On locality-sensitive
orderings and their applications.
- T. M. Chan and Z. Huang.
Constant-hop spanners for
more geometric intersection graphs, with even smaller size.
- H.-C. Chang, J. Conroy, H. Le, L. Milenkovic, S. Solomon, and
C. Than.
Optimal Euclidean tree
covers.
- K. Chen, A. Dumitrescu, W. Mulzer, and C. D. Toth.
On the stretch factor
of polygonal chains.
- S.-W. Cheng, C. Knauer, S. Langerman, and M. Smid.
Approximating the average stretch factor of geometric graphs.
Journal of Computational Geometry, volume 3, 2012, pages 132-153.
- O. Cheong and C. Lee.
Single-source
dilation-bounded minimum spanning trees.
International Journal of Computational Geometry & Applications,
volume 23, 2013, pages 159-170.
- K. Cho, J. Shin, and E. Oh.
Approximate distance and
shortest-path oracles for fault-tolerant geometric spanners.
- M. Couture.
Approximation algorithms for geometric networks.
Ph.D. Thesis. School of Computer Science, Carleton University,
Ottawa, Canada, 2008.
- S. Cui, I. A. Kanj, and G. Xia.
On the stretch factor of Delaunay triangulations of points in
convex position.
Computational Geometry: Theory and Applications, volume 44, 2011,
pages 104-109.
- M. Damian.
Cone-based spanners of constant degree.
Computational Geometry: Theory and Applications, volume 68,
2018, pages 48-61.
- M. Damian, J. Iacono, and A. Winslow.
Spanning properties
of Theta-Theta-6.
- M. Damian, N. Molla, and V. Pinciu.
Spanner properties of pi/2-angle Yao graphs.
Proceedings of the 25th European Workshop on Computational
Geometry, 2009, pages 21-24.
- M. Damian and N. Nelavalli.
Improved bounds on the
stretch factor of Y_4.
Computational Geometry: Theory and Applications, volume 62, 2017,
pages 14-24.
- M. Damian and K. Raudonis.
Yao graphs span Theta graphs.
Discrete Mathematics, Algorithms and Applications, volume 4,
issue 2, 2012.
- M. Damian and D. V. Voicu.
Spanning properties of
Theta-Theta graphs.
- M. Dennis, L. Perkovic, D. Turkoglu.
The stretch factor
of hexagon-Delaunay triangulations.
- L. Devroye, J. Gudmundsson, and P. Morin.
On the expected maximum degree of Gabriel and Yao graphs.
Advances in Applied Probability, volume 41, 2009,
pages 1123-1140.
- M. Dickerson, D. Eppstein, and K. A. Wortman.
Dilation, smoothed
distance, and minimization diagrams of convex functions.
- M. Dickerson, D. Eppstein, and K. A. Wortman.
Planar Voronoi diagrams for sums of convex functions, smoothed
distance and dilation.
Proceedings of the 7th International Symposium on Voronoi
Diagrams in Science and Engineering, 2010, pages 13-22.
- Y. Dinitz, M. Elkin, and S. Solomon.
Low-light trees, and tight lower bounds for Euclidean spanners.
Discrete & Computational Geometry, volume 43, 2010, pages
736-783.
- V. Dujmović, P. Morin, M. Smid.
Average stretch factor:
How low does it go?
Discrete & Computational Geometry, volume 53, 2015, pages
296-326.
- A. Dumitrescu, A. Ebbers-Baumann, A. Gr{\"u}ne, R. Klein, and
G. Rote.
On the geometric dilation of closed curves, graphs, and point sets.
Computational Geometry: Theory and Applications, volume 36, 2007,
pages 16-38.
- A. Dumitrescu and A. Ghosh.
Lower bounds on the
dilation of plane spanners.
Proceedings of the 2nd Conference on Algorithms and Discrete
Applied Mathematics.
Lecture Notes in Computer Science, volume 9602, Springer-Verlag,
Berlin, 2016, pages 139-151.
- A. Dumitrescu and A. Ghosh.
Lattice spanners of
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Proceedings of the 2nd Conference on Algorithms and Discrete
Applied Mathematics.
Lecture Notes in Computer Science, volume 9602, Springer-Verlag,
Berlin, 2016, pages 152-163.
- A. Dumitrescu and Cs. D. T{\'o}th.
Light orthogonal networks with constant geometric dilation.
Journal of Discrete Algorithms, volume 7, 2009, pages 112-129.
- M. Elkin and S. Solomon.
Narrow-shallow-low-light trees with and without Steiner points.
SIAM Journal on Discrete Mathematics, volume 25, 2011,
pages 181-210.
- M. Elkin and S. Solomon.
Steiner shallow-light trees are exponentially lighter than
spanning ones.
SIAM Journal on Computing, volume 44, 2015, pages 996-1025.
- M. Elkin and S. Solomon.
Optimal Euclidean
spanners: really short, thin and lanky.
Proceedings of the 45th ACM Symposium on the Theory of Computing,
2013, pages 645-654.
- D. Eppstein and H. Khodabandeh.
On the edge
crossings of the greedy spanner.
- D. Eppstein and H. Khodabandeh.
Optimal spanners for
unit ball graphs in doubling metrics.
- D. Eppstein and H. Khodabandeh.
Maintaining light
spanners via minimal updates.
- T. Farhana and M. J. Katz.
Spanners under the
Hausdorff and Frechet distances.
- M. Farshi.
A theoretical and experimental study of geometric networks.
Ph.D. Thesis. Department of Mathematics and Computer Science,
Eindhoven University of Technology, Eindhoven, The Netherlands,
2008.
- M. Farshi and J. Gudmundsson.
On algorithms for computing the diameter of a t-spanner.
Proceedings of the 37th Annual Iranian Mathematics Conference,
2006, pages 638-641.
- M. Farshi and J. Gudmundsson.
Experimental study of geometric t-spanners: a running time
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Proceedings of the 6th Workshop on Experimental Algorithms.
Lecture Notes in Computer Science, volume 4525, Springer-Verlag,
Berlin, 2007, pages 270-284.
- M. Farshi and J. Gudmundsson.
Experimental study of geometric t-spanners.
ACM Journal of Experimental Algorithmics, volume 14, 2009,
Article 1.3.
- M. Farshi and M. J. Hekmat Nasab.
Greedy spanner algorithms in practice.
Scientia Iranica D, volume 21, 2014, pages 2142-2152.
- M. Farshi and S. H. Hosseini.
Visualization of geometric spanner algorithms.
Proceedings of the 32nd International Symposium on Computational
Geometry, 2016, pages 67:1-67:4.
- M. Farshi and A. Poureidi.
A lower bound for computing geometric spanners.
Computational Geometry: Theory and Applications, volume 53, 2016,
pages 21-26.
- A. Filtser.
Labeled Nearest Neighbor
Search and Metric Spanners via Locality Sensitive Orderings.
- A. Filtser and H. Le.
Locality-sensitive
orderings and applications to reliable spanners.
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The greedy spanner is
existentially optimal.
Proceedings of the 35th ACM Symposium on Principles of
Distributed Computing, 2016, pages 9-17.
- D. Funke and P. Sanders.
Efficient Yao graph
construction.
- M. F{\"u}rer and S. P. Kasiviswanathan.
Spanners for geometric intersection graphs with applications.
Journal of Computational Geometry, volume 3, 2012, pages 31-64.
- D. Galant and C. Pilatte.
A note on optimal
degree-three spanners of the square lattice.
- J. Gao and D. Zhou.
The emergence of sparse spanners and well-separated pair
decomposition under anarchy.
Journal of Computational Geometry, volume 3, 2012, pages 1-19.
- Z. Gao and S. Har-Peled.
Almost optimal locality
sensitive orderings in Euclidean space.
- A. Ghosh, F. N. U. Shariful, and D. Wisnosky.
Visualizing WSPDs and
their applications.
- P. Giannopoulos, R. Klein, C. Knauer, M. Kutz, and D. Marx.
Computing geometric minimum-dilation graphs is NP-hard.
International Journal of Computational Geometry & Applications,
volume 20, 2010, pages 147-173.
- F. Gieseke, J. Gudmundsson, and J. Vahrenhold.
Pruning spanners and constructing well-separated pair
decompositions in the presence of memory hierarchies.
Journal of Discrete Algorithms, volume 8, 2010, pages 259-272.
- L.-A. Gottlieb.
A light metric
spanner.
Proceedings of the 56th IEEE Symposium on Foundations of
Computer Science, 2015, pages 759-772.
- L.-A. Gottlieb and L. Roditty.
Improved algorithms for fully dynamic geometric spanners and
geometric routing.
Proceedings of the 19th ACM-SIAM Symposium on Discrete Algorithms,
2008, pages 591-600.
- L.-A. Gottlieb and L. Roditty.
An optimal dynamic spanner for doubling metric spaces.
Proceedings of the 16th European Symposium on Algorithms.
Lecture Notes in Computer Science, volume 5193, Springer-Verlag,
Berlin, 2008, pages 478-489.
- L.-A. Gottlieb and S. Solomon.
Light spanners for
snowflake metrics.
Proceedings of the 30th ACM Symposium on Computational Geometry,
2014, pages 387-395.
- A. Gr{\"u}ne.
Geometric dilation and halving distance.
Ph.D. Thesis. University of Bonn, Bonn, Germany, 2006.
- A. Gr{\"u}ne and S. Kamali.
On the density of iterated line segment intersections.
Computational Geometry: Theory and Applications, volume 40, 2008,
pages 23-36.
- A. Gr{\"u}ne, T.-C. Lin, T.-K. Yu, R. Klein, E. Langetepe,
D. T. Lee, S.-H. Poon.
Spanning ratio and maximum detour of rectilinear paths in the
L_1 plane.
Proceedings of the 21st Annual International Symposium on
Algorithms and Computation (ISAAC), Part II.
Lecture Notes in Computer Science, volume 6507, Springer-Verlag,
Berlin, 2010, pages 121-131.
- J. Gudmundsson, Z. Huang, A. van Renssen, and S. Wong.
Spanner for the
0/1/infinity weighted region problem.
- J. Gudmundsson and S. Wong.
Improving the dilation
of a metric graph by adding edges.
- J. Gudmundsson and S. Wong.
A well-separated pair
decomposition for low density graphs.
- B. Hamedmohseni, Z. Rahmati, and D. Mondal.
Emanation graph: A new t-spanner.
Proceedings of the 30th Canadian Conference on Computational
Geometry, 2018, pages 311-317.
- S. Har-Peled, P. Indyk, and A. Sidiropoulos.
Euclidean spanners in high dimensions.
Proceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms,
2013, pages 804-809.
- S. Har-Peled and M. C. Lusardi.
Dependable spanners via
unreliable edges.
- S. Har-Peled, M. Mendel, and D. Olah.
Reliable spanners for
metric spaces.
- F. Hellweg, M. Schmidt, and C. Sohler.
Testing Euclidean Spanners.
Proceedings of the 18th European Symposium on Algorithms (ESA).
Lecture Notes in Computer Science, volume 6346, Springer-Verlag,
Berlin, 2010, pages 60-71.
- R. Inkulu and A. Singh.
Vertex fault-tolerant
spanners for weighted points in polygonal domains.
- N. Innami, B. H. Kim, Y. Mashiko, and K. Shiohama.
The Steiner ratio conjecture of Gilbert-Pollak may still be open.
Algorithmica, volume 57, 2010, pages 869-872.
- A. O. Ivanov and A. A. Tuzhilin.
The Steiner ratio Gilbert-Pollak conjecture is still open
(clarification statement).
Algorithmica, volume 62, 2012, pages 630-632.
- Y. Jin, J. Li, and W. Zhan.
Odd Yao-Yao graphs
are not spanners.
Proceedings of the 34st International Symposium on Computational
Geometry, 2018, pages 49:1-49:15.
- O. Kahalon, H. Le, L. Milenkovic, and S. Solomon.
Can't see the forest for the trees: navigating metric spaces by
bounded hop-diameter spanners.
- I. Kanj, L. Perkovic, and D. Turkoglu.
Degree four plane
spanners: simpler and better.
Proceedings of the 32nd International Symposium on Computational
Geometry, 2016, pages 45:1-45:15.
- I. A. Kanj, L. Perkovic, and G. Xia.
On spanners and lightweight spanners of geometric graphs.
SIAM Journal on Computing, volume 39, 2010, pages 2132-2161.
- I. A. Kanj and G. Xia.
Improved local algorithms for spanner construction.
Theoretical Computer Science, volume 453, 2012, pages 54-64.
- I. A. Kanj and G. Xia.
On certain geometric properties of the Yao-Yao graphs.
Journal of Combinatorial Optimization, volume 27, 2014,
pages 78-87.
- H. Kaplan, W. Mulzer, L. Roditty, and P. Seiferth.
Spanners and reachability
oracles for directed transmission graphs.
Proceedings of the 31st International Symposium on Computational
Geometry, 2015, pages 156-170.
- S. Kapoor and X.-Y. Li.
Geodesic spanners on polyhedral surfaces.
Proceedings of the 20th Annual International Symposium on
Algorithms and Computation.
Lecture Notes in Computer Science, volume 5878, Springer-Verlag,
Berlin, 2009, pages 213-223.
- W. L. Keng and G. Xia.
The Yao graph
Y_5 is a spanner.
- A. Khopkar and S. Govindarajan.
Hardness results for computing optimal locally Gabriel graphs.
Proceedings of the 24th Canadian Conference on Computational
Geometry, 2012, pages 149-154.
- J. Kim, J. S. B. Mitchell, and J. Zou.
Approximating maximum flow in polygonal domains using spanners.
Proceedings of the 21st Canadian Conference on Computational
Geometry, 2009, pages 115-118.
- S. Kisfaludi-Bak, J. Nederlof, and K. Wegrzycki.
A Gap-ETH-tight
approximation scheme for Euclidean TSP.
- R. Klein, C. Levcopoulos, and A. Lingas.
A PTAS for minimum vertex dilation triangulation of a simple
polygon with a constant number of sources of dilation.
Computational Geometry: Theory and Applications, volume 34, 2006,
pages 28-34.
- R. Klein and M. Kutz.
The density of iterated crossing points and a gap result for
triangulations of finite point sets.
Proceedings of the 22nd ACM Symposium on Computational Geometry,
2006, pages 264-272.
The full paper appeared as:
R. Klein, M. Kutz, and R. Penninger.
Most finite point sets in the plane have dilation > 1.
Discrete & Computational Geometry, volume 53, 2015, pages 80-106.
- C. Knauer and W. Mulzer.
An exclusion region for minimum dilation triangulations.
Proceedings of the 21st European Workshop on Computational
Geometry, 2005, pages 33-36.
- C. Knauer and W. Mulzer.
Minimum dilation triangulations.
Technical Report B-05-06, Fachbereich Mathematik und Informatik,
Freie Universit{\"a}t Berlin, 2005.
- E. Kranakis, O. M. Ponce, and L. Stacho.
Strong orientations of planar graphs with bounded stretch factor.
Discrete Applied Mathematics, volume 161, 2013, pages 176-183.
- A. La and H. Le.
Dynamic locality
sensitive orderings in doubling metrics.
- H. Le, L. Milenkovic, and S. Solomon.
Sparse Euclidean spanners with tiny diameter: a tight lower
bound.
- H. Le and S. Solomon.
Truly optimal Euclidean spanners.
- H. Le and S. Solomon.
Light Euclidean spanners with Steiner points.
- H. Le and S. Solomon.
- H. Le, S. Solomon, and C. Than.
Optimal fault-tolerant
spanners in Euclidean and doubling metrics: Breaking the
Omega(log n) lightness barrier.
- H. Le, S. Solomon, C. Than, C. D. Toth, and T. Zhang.
Towards instance-optimal
Euclidean spanners.
- H. Le and C. Than.
Greedy spanners in
Euclidean spaces admit sublinear separators.
- K. Lee and A. van Renssen.
Generalized sweeping
line spanners.
- J. Li and W. Zhan.
Almost all even
Yao-Yao graphs are spanners.
Proceedings of the 24th European Symposium on Algorithms (ESA).
Leibniz International Proceedings in Informatics (LIPIcs),
volume 57, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik,
2016, pages 62:1-62:13.
- X.-Y. Li.
Wireless Ad Hoc and Sensor Networks.
Cambridge University Press, 2008.
- J. Luo and C. Wulff-Nilsen.
Computing best and worst shortcuts of graphs embedded in metric
spaces.
Proceedings of the 19th Annual International Symposium on
Algorithms and Computation.
Lecture Notes in Computer Science, volume 5369, Springer-Verlag,
Berlin, 2008, pages 764-775.
- A. Maheshwari, M. Smid, and N. Zeh.
I/O-efficient algorithms for computing planar geometric spanners.
Computational Geometry: Theory and Applications, volume 40, 2008,
pages 252-271.
- A. Maheshwari, M. Smid, and N. Zeh.
Low-interference networks in metric spaces of bounded doubling dimension.
Information Processing Letters, volume 111, 2011, pages 1120-1123.
- H. Martini and S. Wu.
Geometric dilation of closed curves in normed planes.
Computational Geometry: Theory and Applications, volume 42, 2009,
pages 315-321.
- A. Mehrabian.
A randomly embedded random graph is not a spanner.
Proceedings of the 23rd Canadian Conference on Computational
Geometry, 2011, pages 373-374.
- A. Mehrabian and N. Wormald.
On the stretch factor
of randomly embedded random graphs.
- P. Morin and S. Verdonschot.
On the average number
of edges in Theta graphs.
Proceedings of the 11th Meeting on Analytic Algorithmics and
Combinatorics, 2014, pages 121-132.
- W. Mulzer.
Minimum dilation triangulations for the regular n-gon.
Master's Thesis, Freie Universit{\"a}t Berlin, 2004.
- M. Pătraşcu and T. M. Chan.
Voronoi diagrams in n times 2^{O(sqrt(lglg n))} time.
Proceedings of the 39th ACM Symposium on the Theory of Computing,
2007, pages 31-39.
- D. Peleg and L. Roditty.
Relaxed spanners for directed disk graphs.
Proceedings of the 27th Symposium on Theoretical Aspects of
Computer Science, 2010, pages 609-620.
- A. Poureidi and M. Farshi.
The well-separated
pair decomposition for balls.
- L. Roditty.
Fully dynamic geometric spanners.
Algorithmica, volume 62, 2012, pages 1073-1087.
- D. Russel and L. Guibas.
Exploring protein folding conformations using spanners.
Pacific Symposium on Biocomputing, 2005, pages 40-51.
- H. Salami and M. Nouri-Baygi.
$\alpha$-Gap Greedy Spanner.
Journal of Algorithms and Computation, volume 53, 2021, pages 41-56.
- D. Sarioz.
Generalized Delaunay
graphs with respect to any convex set are plane graphs.
- F. N. U. Shariful, J. Weathers, A. Ghosh, and G. Narasimhan.
Engineering an algorithm
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The weak gap property in metric spaces of bounded doubling
dimension.
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Lecture Notes in Computer Science, volume 5760, Springer-Verlag,
Berlin, 2009, pages 275-289.
- S. Solomon.
Sparse Euclidean spanners with tiny diameter.
ACM Transactions on Algorithms, volume 9, 2013, Article 28.
- S. Solomon.
The MST of symmetric disk graphs (in arbitrary metric spaces) is
light.
SIAM Journal on Discrete Mathematics, volume 26, 2012,
pages 250-262.
- S. Solomon.
Fault-tolerant spanners
for doubling metrics: better and simpler.
- S. Solomon.
From hierarchical
partitions to hierarchical covers: optimal fault-tolerant
spanners for doubling metrics.
- S. Solomon.
Euclidean Steiner shallow-light trees.
Journal of Computational Geometry, volume 6, number 2, 2015,
pages 113-139.
- S. Solomon and M. Elkin.
Balancing degree, diameter, and weight in Euclidean spanners.
SIAM Journal on Discrete Mathematics, volume 28, 2014,
pages 1173-1198.
- X. Tan, C. Sakthip, and B. Jiang
Improved stretch factor of Delaunay triangulations of points
in convex position.
COCOA 2019, LNCS 11949, pages 473–484.
- S. Temme and J. Vahrenhold.
Revisiting the construction of SSPDs in the presence of memory
hierarchies.
Proceedings of the 28th European Workshop on Computational
Geometry, 2012, pages 57-60.
- C. D. Toth.
Minimum weight Euclidean
(1+epsilon)-spanners.
- A. van Renssen.
On the spanning ratio of constrained Yao-graphs.
Proceedings of the 26th Canadian Conference on Computational
Geometry, 2014, pages 239-243.
- A. van Renssen.
Theta-graphs and other constrained spanners.
Ph.D. Thesis. School of Computer Science, Carleton University,
Ottawa, Canada, 2014.
- A. van Renssen, Y. Sha, Y. Sun, and G. Wong.
The tight spanning
ratio of the rectangle Delaunay triangulation.
- A. van Renssen and G. Wong.
Bounded-degree spanners
in the presence of polygonal obstacles.
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Flips and spanners.
Ph.D. Thesis. School of Computer Science, Carleton University,
Ottawa, Canada, 2015.
- W. Wang, X.-Y. Li, K. Moaveninejad, Y. Wang, and W.-Z. Song.
The spanning ratio of beta-skeletons.
Proceedings of the 15th Canadian Conference on Computational
Geometry, 2003, pages 35-38.
- C. Wulff-Nilsen.
Computing the dilation of edge-augmented graphs in metric spaces.
Computational Geometry: Theory and Applications, volume 43, 2010,
pages 68-72.
- C. Wulff-Nilsen.
Computing the maximum detour of a plane geometric graph in
subquadratic time.
Journal of Computational Geometry, volume 1, 2010, pages 101-122.
- C. Wulff-Nilsen.
Computing the stretch factor of paths, trees, and cycles in
weighted fixed orientation metrics.
Proceedings of the 20th Canadian Conference on Computational
Geometry, 2008, pages 59-62.
- C. Wulff-Nilsen, A. Gr{\"u}ne, R. Klein, E. Langetepe, D. T. Lee,
T.-C. Lin, S.-H. Poon, and T.-K. Yu.
Computing the stretch factor and maximum detour of paths, trees,
and cycles in the normed space.
International Journal of Computational Geometry & Applications,
volume 22, 2012, pp. 45-60.
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The stretch factor of the Delaunay triangulation is less than
1.998.
SIAM Journal on Computing, volume 42, 2013, pages 1620-1659.
- G. Xia and L. Zhang.
Toward the tight bound of the stretch factor of Delaunay
triangulations.
Proceedings of the 23rd Canadian Conference on Computational
Geometry, 2011, pages 175-180.
- J. Xu, Y. Yang, Y. Zhu, and N. Katoh.
A geometric spanner of segments.
International Journal of Computational Geometry & Applications,
volume 20, 2010, pages 43-67.
- J. Zeng and J. Gao.
A linear time Euclidean spanner on imprecise points.
Proceedings of the 26th Canadian Conference on Computational
Geometry, 2014, pages 118-124.