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Approximation algorithms and an integer program for multi-level graph spanners
[article]
2019
arXiv
pre-print
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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. ...
In the pairwise spanner problem [11] , distances only need to be preserved for a subset P ⊆ V × V of pairs of vertices. ...
arXiv:1904.01135v1
fatcat:vcadmu7k2faa7jlvcejbeut7f4
On Pairwise Spanners
2013
Symposium on Theoretical Aspects of Computer Science
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Here we present pairwise spanners which are at the same time sparser than the best known preservers (on the same P) and of the best known spanners (with the same f (·)). ...
We show that there exists an (S × S)-spanner of size O(n |S|) with f (d) = d + 2, and an (S × V )-spanner of size O(n |S| log n) with f (d) = d + 2 log n. ...
in [8] are at the same time more accurate and sparser than our spanners for small enough values of |P|. ...
doi:10.4230/lipics.stacs.2013.209
dblp:conf/stacs/CyganGK13
fatcat:qmfqkwfkhndyxgdsufqvohxehe
On Pairwise Spanners
[article]
2013
arXiv
pre-print
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Here we present pairwise spanners which are at the same time sparser than the best known preservers (on the same ) and of the best known spanners (with the same f(·)). ...
We show that there exists an (S× S)-spanner of size O(n√(|S|)) with f(d)=d+2, and an (S× V)-spanner of size O(n√(|S| n)) with f(d)=d+2 n. ...
An (α, β) spanner is a spanner with stretch functions f (d) = α · d + β. (α and β are the multiplicative stretch and additive stretch of the spanner, respectively). ...
arXiv:1301.1999v1
fatcat:y5pdjxbifze2fn25ki46sakguu
Approximating Spanners and Directed Steiner Forest: Upper and Lower Bounds
[article]
2016
arXiv
pre-print
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We give an O(n^3/5 + ϵ)-approximation for distance preservers and pairwise spanners (for arbitrary constant ϵ > 0). ...
in which demand pairs have their distance preserved exactly), and pairwise spanners (subgraphs in which demand pairs have their distance preserved up to a multiplicative or additive stretch) [Abboud-Godwin ...
In this paper we bring together these lines of work, by studying the approximability of distance preservers, pairwise spanners, and additive spanners. ...
arXiv:1607.06068v1
fatcat:q5owvfqnrjcozmglkx3qb5tngy
New Pairwise Spanners
2016
Theory of Computing Systems
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We show sparse pairwise spanners with additive stretch 4 and with additive stretch 6. ...
A subgraph H of G is called an (all-pairs) purely additive spanner with stretch β if for every (u, v) The problem of computing sparse spanners with small stretch β is well-studied. ...
[9] were the first to study a variant of pairwise preservers -they studied D-preservers where the problem was to compute a sparse pairwise preserver for the set P = {(u, v) : δ G (u, v) ≥ D}. ...
doi:10.1007/s00224-016-9736-7
fatcat:n3e7nn2c4jauvh3wi6nymnrapa
Graph Spanners: A Tutorial Review
[article]
2020
arXiv
pre-print
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It reviews the current literature covering various research streams about graph spanners, such as different formulations, sparsity and lightness results, computational complexity, dynamic algorithms, and ...
As an additional contribution, we offer a list of open problems on graph spanners. ...
Small stretch pairwise spanners. In International Colloquium on Automata, Languages, and Programming (ICALP), pages 601-612. Springer, 2013 [116] Telikepalli Kavitha. New pairwise spanners. ...
arXiv:1909.03152v2
fatcat:vqme4ewuvbbd5ac5erinyykwsy
Improved Purely Additive Fault-Tolerant Spanners
[chapter]
2015
Lecture Notes in Computer Science
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one such spanner that preserves all pairwise distances. ...
On one hand, we show how to augment (by adding a small number of edges) a fault-tolerant additive sourcewise spanner (that approximately preserves distances only from a given set of source nodes) into ...
We show that, by carefully choosing S and by augmenting A S with a conveniently selected small subset of edges, it is possible to construct a fault-tolerant spanner (approximately preserving all pairwise ...
doi:10.1007/978-3-662-48350-3_15
fatcat:lqwrqjtwfvbtfehw7hjnsttu7i
Distributed Construction of Purely Additive Spanners
[article]
2016
arXiv
pre-print
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We complement our algorithms with a lower bound on the number of rounds required for computing pairwise spanners. ...
Instead, to obtain our lower bound, we define a new communication complexity problem that reduces to computing a sparse spanner, and prove a lower bound on its communication complexity using information ...
Acknowledgements We thank Merav Parter for a helpful discussion on the lower bound, and the anonymous referees of DISC 2016 for valuable comments. ...
arXiv:1607.05597v1
fatcat:rwrhqal3gbfvhddnjvnmponbee
Improved Purely Additive Fault-Tolerant Spanners
[article]
2015
arXiv
pre-print
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one such spanner that preserves all pairwise distances. ...
On one hand, we show how to augment (by adding a small number of edges) a fault-tolerant additive sourcewise spanner (that approximately preserves distances only from a given set of source nodes) into ...
We show that, by carefully choosing S and by augmenting A S with a conveniently selected small subset of edges, it is possible to construct a fault-tolerant spanner (approximately preserving all pairwise ...
arXiv:1507.00505v1
fatcat:4egrechb3ve4fhv6mez3p7zunm
A Note on Distance-Preserving Graph Sparsification
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2001.07741v2 fatcat:mnen642r5vfyjl7vqy3nzj2hbqOther Versions
Examples include pairwise spanners, distance preservers, reachability preservers, etc. ...
This simplifies and unifies a few proofs in the area, and it improves the size of the +4 pairwise spanner from O(np^2/7) [Kavitha Th. Comp. Sys. '17] to O(np^2/7). ...
Not pictured: there is also a +0 pairwise spanner (distance preserver) by Coppersmith and Elkin [11] on O(n+ n 1/2 p) edges, which improves on these pairwise spanners in some regime of small p. some ...
arXiv:2001.07741v3
fatcat:23eqk3j5jfdpnf64o73d5f4k64
Better Distance Preservers and Additive Spanners
2015
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
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We then develop a new graph clustering technique, based on distance preservers, and we apply this technique to show new upper bounds for additive (standard) spanners, in which all pairwise distances must ...
be preserved up to an additive error function, and for subset spanners, in which only distances within a given node subset must be preserved up to an error function. ...
These are: a +2 pairwise spanner onÕ(n|P | 1/3 ) edges due to Kavitha & Varma [KV13] , a +4 pairwise spanner onÕ(n|P | 2/7 ) edges due to Kavitha [Kav15] , and a +6 pairwise spanner on O(n|P | 1/4 ) ...
doi:10.1137/1.9781611974331.ch61
dblp:conf/soda/BodwinW16
fatcat:66i75jt6tjfd3iprey47bp4f4y
Locality-Sensitive Orderings and Applications to Reliable Spanners
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:2101.07428v2 fatcat:7ilqkggarra4vmjfpz7izredguOther Versions
Afterwards, we use our new LSO's to construct reliable spanners with improved stretch and sparsity parameters. ...
Most prominently, we construct Õ(n)-size reliable spanners for trees and planar graphs with the optimal stretch of 2. ...
They used their LSO to design simple dynamic algorithms for approximate nearest neighbor search, approximate bichromatic closest pair, approximate MST, spanners, and fault-tolerant spanners. ...
arXiv:2101.07428v3
fatcat:6iwemadvkncu7hgfwd2ym6fk3q
Multi-Level Graph Sketches via Single-Level Solvers
[article]
2019
arXiv
pre-print
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Examples include Steiner trees (preserving connectivity among T) and subsetwise spanners (preserving shortest path distances up to a stretch factor). ...
This is the first algorithm and weight guarantee for a multiplicative subsetwise spanner for nonplanar graphs. ...
The research for this paper was partially supported by NSF grants CCF-1740858 and DMS-1839274. ...
arXiv:1905.00536v2
fatcat:ynptxpg3engvdlsxww6kb66ar4
Very Sparse Additive Spanners and Emulators
[article]
2021
arXiv
pre-print
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2015 pre-print arXiv:1505.05630v1 fatcat:qqsj4mj3w5gwrjdspsq3tw2ywi
The second part of this paper leverages these distance preservers in a new construction of additive spanners, which are subgraphs that preserve all pairwise distances up to an additive error function. ...
split apart, and then intersect again later. ...
Much of the initial theoretical work on spanners studied multiplicative stretch spanners, that is, all pairwise distances are preserved up to a small multiplicative factor. Althofer et al. ...
arXiv:1505.05630v2
fatcat:eqcs5cposrhxxikyixpd6fbfvy
Online Directed Spanners and Steiner Forests
[article]
2021
arXiv
pre-print
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We present online algorithms for directed spanners and Steiner forests. ...
Our results include the following: For the pairwise spanner problem, in which the pairs of vertices to be spanned arrive online, we present an efficient randomized Õ(n^4/5)-competitive algorithm for graphs ...
Acknowledgements We thank the anonymous reviewers for comments and suggestions that helped improve the presentation. ...
arXiv:2103.04543v2
fatcat:r54ordqp7vc37f6kmsrhfvzjqe
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