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Spanner Approximations in Practice [article]

Markus Chimani, Finn Stutzenstein
2021 arXiv   pre-print
While many algorithms have been developed to find good spanners in terms of approximation guarantees, no experimental studies comparing different approaches exist.  ...  A multiplicative α-spanner H is a subgraph of G=(V,E) with the same vertices and fewer edges that preserves distances up to the factor α, i.e., d_H(u,v)≤α· d_G(u,v) for all vertices u, v.  ...  We are interested in the computation of spanners in practice.  ... 
arXiv:2107.02018v1 fatcat:zhpmtperwvfvnfh6v53m56cloq

Approximating geometrical graphs via "spanners" and "banyans"

Satish B. Rao, Warren D. Smith
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
For large s comparible to N the approximation is exact and NP-Hard problems are assumed not soluble in time  ...  Create a (1+ )-spanner of known length ( ) Don't need to rely on the points after the spanner is constructed (r does not depend on N) Can average in one dimension (bound length increase in the graph and  ...  In-practice performance is not known (for d=2 faster practical algorithms exist) factor could be large even for d=2 and reasonable s Could combine with heuristics (tour "cleaning up", solving small subproblems  ... 
doi:10.1145/276698.276868 dblp:conf/stoc/RaoS98 fatcat:ztxupj3qczagbmygaecjnr25qy

Multi-level Weighted Additive Spanners [article]

Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Stephen Kobourov, Richard Spence
2021 arXiv   pre-print
By analyzing our experimental results we developed a new technique of changing an initialization parameter value that provides better performance in practice.  ...  Spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs.  ...  As mentioned earlier, in practice we use an approximation algorithm to compute the subsetwise spanner instead of computing the minimum spanner.  ... 
arXiv:2102.05831v3 fatcat:culm5zs7zrfxfgrd3utsajyg44

Construction of Minimum-Weight Spanners [chapter]

Mikkel Sigurd, Martin Zachariasen
2004 Lecture Notes in Computer Science  
Recently spanners have found important practical applications in metric space searching and message distribution in networks.  ...  In this paper we give an exact algorithm for constructing minimum-weight spanners in arbitrary graphs.  ...  Thus the greedy spanner algorithm appears to be an excellent choice for constructing approximate minimum-weight spanners in practice.  ... 
doi:10.1007/978-3-540-30140-0_70 fatcat:n357bg47gbdtdlliejhftd5yd4

Experimental study of geometrict-spanners

Mohammad Farshi, Joachim Gudmundsson
2009 ACM Journal of Experimental Algorithmics  
Recently low-weight spanners found interesting practical  ...  v in G.  ...  Thus a comparison in practice between the two graphs is interesting.  ... 
doi:10.1145/1498698.1564499 fatcat:5kr3clk6pvcpdhrt6orp2g5uuq

Experimental Study of Geometric t-Spanners [chapter]

Mohammad Farshi, Joachim Gudmundsson
2005 Lecture Notes in Computer Science  
Recently low-weight spanners found interesting practical  ...  v in G.  ...  Thus a comparison in practice between the two graphs is interesting.  ... 
doi:10.1007/11561071_50 fatcat:dkbk5xgtyza4jcnc6m4n4ewwiy

Approximating Maximum Flow in Polygonal Domains using Spanners

Joondong Kim, Joseph S. B. Mitchell, Jingyu Zou
2009 Canadian Conference on Computational Geometry  
We show that Euclidean spanners offer a means of computing approximately optimal solutions.  ...  Further, we show experimentally that using a spanner (e.g., Delaunay graph) yields approximation ratios very close to one.  ...  We also conduct experiments, using the Delaunay graph as spanner, to validate the effectiveness of the approximation in practice on both randomly generated data and actual weather data. 21st Canadian Conference  ... 
dblp:conf/cccg/KimMZ09 fatcat:f6d6lufiizhkxbjvttanr6mlsa

t-Spanners for metric space searching

Gonzalo Navarro, Rodrigo Paredes, Edgar Chávez
2007 Data & Knowledge Engineering  
This property holds in most real-world metric spaces, so we expect that t-spanners will display good behavior in most practical applications.  ...  A t-spanner is a subgraph G ′ (V, E) of a graph G(V, A), such that E ⊆ A and G ′ approximates the shortest path costs over G within a precision factor t.  ...  In practice, t-Spanner 1, 3 and 4 can make good distance approximations between the clusters by using few edges.  ... 
doi:10.1016/j.datak.2007.05.002 fatcat:t73cdcgftjcnvnuawrnxcb35ne

The Greedy Spanner is Existentially Optimal [article]

Arnold Filtser, Shay Solomon
2020 arXiv   pre-print
Further, we observe that approximate-greedy spanners are existentially near-optimal as well.  ...  as good) as the worst performance of an optimal spanner over all graphs in G.  ...  In many practical applications one is required to construct a spanner that satisfies a number of useful properties, while preserving a small stretch.  ... 
arXiv:1605.06852v2 fatcat:hnfwncky75f4jor5vxmfiowg7y

t-Spanners as a Data Structure for Metric Space Searching [chapter]

Gonzalo Navarro, Rodrigo Paredes, Edgar Chávez
2002 Lecture Notes in Computer Science  
A t-spanner, a subgraph that approximates graph distances within a precision factor t, is a well known concept in graph theory.  ...  The key idea is to consider the t-spanner as an approximation of the complete graph of distances among the objects, and use it as a compact device to simulate the large matrix of distances required by  ...  This becomes a feasible approximation to AESA, which in its original form cannot be implemented in practice because of its quadratic memory requirements.  ... 
doi:10.1007/3-540-45735-6_26 fatcat:tip64p3chffupjs7xoaq6med6u

Optimal Spanners for Unit Ball Graphs in Doubling Metrics [article]

David Eppstein, Hadi Khodabandeh
2021 arXiv   pre-print
Resolving an open question from 2006, we prove the existence of light-weight bounded-degree spanners for unit ball graphs in the metrics of bounded doubling dimension, and we design a simple 𝒪(log^*n)  ...  in G to the length of the shortest edge.  ...  In other words, a t-spanner approximates the pairwise distances within a factor of t.  ... 
arXiv:2106.15234v1 fatcat:qoh6b2p7djaxvd4kphycyzclz4

Spectral vertex sparsifiers and pair-wise spanners over distributed graphs

Chunjiang Zhu, Qinqing Liu, Jinbo Bi
2021 International Conference on Machine Learning  
We further provide algorithms for constructing pair-wise spanners which approximate the shortest distances between each pair of vertices in a target set, instead of all pairs, and incur communication costs  ...  Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over graphs.  ...  For a set of vertex pairs P ⊆ V × V , a P -pairwise spanner F (V, E ⊆ E) of G only approximates distances between pairs (u, v) ∈ P in G up to a small stretch.  ... 
dblp:conf/icml/ZhuLB21 fatcat:xo4j26r3yzaxfbctewzw4wiyn4

Approximation algorithms and an integer program for multi-level graph spanners [article]

Reyan Ahmed, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence
2019 arXiv   pre-print
Given a weighted graph G(V,E) and t > 1, a subgraph H is a t--spanner of G if the lengths of shortest paths in G are preserved in H up to a multiplicative factor of t.  ...  The subsetwise spanner problem aims to preserve distances in G for only a subset of the vertices.  ...  We showed that both the approximation algorithms and the heuristics work well in practice on several different types of graphs, with different number of levels and different stretch factors.  ... 
arXiv:1904.01135v1 fatcat:vcadmu7k2faa7jlvcejbeut7f4

Page 4160 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
Lower bounds are also es- tablished for various generalisations of spanners, including Steiner spanners and ft-approximators.  ...  However, in many practical instances, there is a ‘level’ structure which may be imposed on the underlying graph.  ... 

Applications of Geometric Spanner Networks [chapter]

Joachim Gudmundsson, Giri Narasimhan, Michiel Smid
2008 Encyclopedia of Algorithms  
Problem Definition Given a geometric graph in d-dimensional space, it is useful to preprocess it so that distance queries, exact or approximate, can be answered efficiently.  ...  Algorithms that can report distance queries in constant time are also referred to as "distance oracles".  ...  Practical implementations of distance oracles in geometric networks have also been investigated [15] .  ... 
doi:10.1007/978-0-387-30162-4_15 fatcat:zsclqoek3vexbl2ydzk3d4ncxe
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