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Spanner Approximations in Practice
[article]

2021
*
arXiv
*
pre-print

While many algorithms have been developed to find good

arXiv:2107.02018v1
fatcat:zhpmtperwvfvnfh6v53m56cloq
*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*. ...##
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Approximating geometrical graphs via "spanners" and "banyans"

1998
*
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
*

For large s comparible to N the

doi:10.1145/276698.276868
dblp:conf/stoc/RaoS98
fatcat:ztxupj3qczagbmygaecjnr25qy
*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 ...##
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Multi-level Weighted Additive Spanners
[article]

2021
*
arXiv
*
pre-print

By analyzing our experimental results we developed a new technique of changing an initialization parameter value that provides better performance

arXiv:2102.05831v3
fatcat:culm5zs7zrfxfgrd3utsajyg44
*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*. ...##
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Construction of Minimum-Weight Spanners
[chapter]

2004
*
Lecture Notes in Computer Science
*

Recently

doi:10.1007/978-3-540-30140-0_70
fatcat:n357bg47gbdtdlliejhftd5yd4
*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*. ...##
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Experimental study of geometrict-spanners

2009
*
ACM Journal of Experimental Algorithmics
*

Recently low-weight

doi:10.1145/1498698.1564499
fatcat:5kr3clk6pvcpdhrt6orp2g5uuq
*spanners*found interesting*practical*... v*in*G. ... Thus a comparison*in**practice*between the two graphs is interesting. ...##
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Experimental Study of Geometric t-Spanners
[chapter]

2005
*
Lecture Notes in Computer Science
*

Recently low-weight

doi:10.1007/11561071_50
fatcat:dkbk5xgtyza4jcnc6m4n4ewwiy
*spanners*found interesting*practical*... v*in*G. ... Thus a comparison*in**practice*between the two graphs is interesting. ...##
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Approximating Maximum Flow in Polygonal Domains using Spanners

2009
*
Canadian Conference on Computational Geometry
*

We show that Euclidean

dblp:conf/cccg/KimMZ09
fatcat:f6d6lufiizhkxbjvttanr6mlsa
*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 ...##
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t-Spanners for metric space searching

2007
*
Data & Knowledge Engineering
*

This property holds

doi:10.1016/j.datak.2007.05.002
fatcat:t73cdcgftjcnvnuawrnxcb35ne
*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. ...##
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The Greedy Spanner is Existentially Optimal
[article]

2020
*
arXiv
*
pre-print

Further, we observe that

arXiv:1605.06852v2
fatcat:hnfwncky75f4jor5vxmfiowg7y
*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. ...##
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t-Spanners as a Data Structure for Metric Space Searching
[chapter]

2002
*
Lecture Notes in Computer Science
*

A t-

doi:10.1007/3-540-45735-6_26
fatcat:tip64p3chffupjs7xoaq6med6u
*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. ...##
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Optimal Spanners for Unit Ball Graphs in Doubling Metrics
[article]

2021
*
arXiv
*
pre-print

Resolving an open question from 2006, we prove the existence of light-weight bounded-degree

arXiv:2106.15234v1
fatcat:qoh6b2p7djaxvd4kphycyzclz4
*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. ...##
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Spectral vertex sparsifiers and pair-wise spanners over distributed graphs

2021
*
International Conference on Machine Learning
*

We further provide algorithms for constructing pair-wise

dblp:conf/icml/ZhuLB21
fatcat:xo4j26r3yzaxfbctewzw4wiyn4
*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. ...##
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Approximation algorithms and an integer program for multi-level graph spanners
[article]

2019
*
arXiv
*
pre-print

Given a weighted graph G(V,E) and t > 1, a subgraph H is a t--

arXiv:1904.01135v1
fatcat:vcadmu7k2faa7jlvcejbeut7f4
*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. ...##
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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. ...##
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Applications of Geometric Spanner Networks
[chapter]

2008
*
Encyclopedia of Algorithms
*

Problem Definition Given a geometric graph

doi:10.1007/978-0-387-30162-4_15
fatcat:zsclqoek3vexbl2ydzk3d4ncxe
*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] . ...
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