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Distributed Construction of Purely Additive Spanners [article]

Keren Censor-Hillel, Telikepalli Kavitha, Ami Paz, Amir Yehudayoff
2016 arXiv   pre-print
This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases.  ...  We complement our algorithms with a lower bound on the number of rounds required for computing pairwise spanners.  ...  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

The Sparsest Additive Spanner via Multiple Weighted BFS Trees

Keren Censor-Hillel, Ami Paz, Noam Ravid
2020 Theoretical Computer Science  
Distributed constructions of spanners are also abundant.  ...  However, for additive spanners, while there were algorithms constructing (+2) and (+4)-all-pairs spanners, the sparsest case of (+6)-spanners remained elusive.  ...  Acknowledgements We thank Shiri Chechik and Pierre Fraigniaud for discussions regarding (+6)-spanners.  ... 
doi:10.1016/j.tcs.2020.05.035 fatcat:gcbxtnmua5bxbnmlv5u5yddnbm

The Sparsest Additive Spanner via Multiple Weighted BFS Trees [article]

Keren Censor-Hillel, Ami Paz, Noam Ravid
2018 arXiv   pre-print
Distributed constructions of spanners are also abundant.  ...  However, for additive spanners, while there were algorithms constructing (+2) and (+4)-all-pairs spanners, the sparsest case of (+6)-spanners remained elusive.  ...  Acknowledgement We thank Shiri Chechik and Pierre Fraigniaud for discussions about (+6)-spanners.  ... 
arXiv:1811.01997v1 fatcat:ef6gbs5gqnhd3kwmnigxubuyze

Graph Spanners: A Tutorial Review [article]

Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Richard Spence
2020 arXiv   pre-print
As an additional contribution, we offer a list of open problems on graph spanners.  ...  This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners.  ...  [55] study the complexity of distributed constructions of purely additive spanners.  ... 
arXiv:1909.03152v2 fatcat:vqme4ewuvbbd5ac5erinyykwsy

Distributed algorithms for ultrasparse spanners and linear size skeletons

Seth Pettie
2008 Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing - PODC '08  
In particular, any distance preservers, purely additive spanners, or spanners with sublinear additive distortion must either be very dense, slow to construct, or have very weak guarantees on distortion  ...  Our second result is a new class of efficiently constructible (α, β)-spanners called Fibonacci spanners whose distortion improves with the distance being approximated.  ...  Acknowledgments We would like to thank the anonymous referees for spotting several errors and greatly improving the readability of the paper.  ... 
doi:10.1145/1400751.1400786 dblp:conf/podc/Pettie08 fatcat:yzcw6thetbf5rj2rde7wgh5ql4

Distributed algorithms for ultrasparse spanners and linear size skeletons

Seth Pettie
2009 Distributed computing  
In particular, any distance preservers, purely additive spanners, or spanners with sublinear additive distortion must either be very dense, slow to construct, or have very weak guarantees on distortion  ...  Our second result is a new class of efficiently constructible (α, β)-spanners called Fibonacci spanners whose distortion improves with the distance being approximated.  ...  Acknowledgments We would like to thank the anonymous referees for spotting several errors and greatly improving the readability of the paper.  ... 
doi:10.1007/s00446-009-0091-7 fatcat:isl3aja6ordz5ikuw6pbcttmzm

On the locality of distributed sparse spanner construction

Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot
2008 Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing - PODC '08  
The paper presents a deterministic distributed algorithm that, given k 1, constructs in k rounds a (2k−1, 0)-spanner of O(kn 1+1/k ) edges for every n-node unweighted graph.  ...  It is also shown that for every k > 1, any (randomized) distributed algorithm that constructs a spanner with fewer than n 1+1/k+ edges in at most n expected rounds must stretch some distances by an additive  ...  Only few constructions for pure additive spanners, i.e., for which the stretch is of the form (1, β), are known, even in the sequential setting.  ... 
doi:10.1145/1400751.1400788 dblp:conf/podc/DerbelGPV08 fatcat:uj6zgq3mwvegrl5hix5cjjnteq

Spanners and message distribution in networks

Arthur M. Farley, Andrzej Proskurowski, Daniel Zappala, Kurt Windisch
2004 Discrete Applied Mathematics  
We illustrate that by varying the value of k a spanner can be made to gradually favor cost over delay.  ...  We investigate the applicability of spanners as substructures that o er both low cost and low delay for broadcast and multicast.  ...  Acknowledgements We would like to thank Iyer Sivaramakrishna for producing appealing plots from an unappealing slew of numbers, and Nita Viswanath for running the program producing those numbers.  ... 
doi:10.1016/s0166-218x(03)00259-2 fatcat:zjxalityhvf57op7nvax5gupcy

Additive spanners and (α, β)-spanners

Surender Baswana, Telikepalli Kavitha, Kurt Mehlhorn, Seth Pettie
2010 ACM Transactions on Algorithms  
However no other additive spanners are known to exist. In this paper we develop a couple of new techniques for constructing (α, β)-spanners.  ...  Our first result is an additive (1, 6)-spanner of size O(n 4/3 ).  ...  We would like to thank Uri Zwick, Mikkel Thorup, and Michael Elkin for some helpful comments on an earlier draft of this paper.  ... 
doi:10.1145/1868237.1868242 fatcat:lpui4f4qhjha7kf5ky4ztbtwvy

New Additive Spanners [chapter]

Shiri Chechik
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n 3/2 ) and the other for 6-additive spanner of size O(n 4/3  ...  This paper considers additive and purely additive spanners. We present a new purely additive spanner of sizẽ O(n 7/5 ) with additive stretch 4.  ...  The first construction for purely additive spanners was presented by Aingworth et al. [1] .  ... 
doi:10.1137/1.9781611973105.36 dblp:conf/soda/Chechik13 fatcat:dvthkauynbd7ra3bybmwjvh3pi

Efficient Algorithms for Constructing Very Sparse Spanners and Emulators [article]

Michael Elkin, Ofer Neiman
2017 arXiv   pre-print
All previous constructions of (1+ϵ,β)-spanners and emulators employ a superlinear number of edges, for all choices of parameters.  ...  The distributed algorithm with these properties is implicit in MPVX15.] algorithm in the CONGEST model, that given a parameter k = 1,2,..., constructs an O(k)-spanner of an input unweighted n-vertex graph  ...  Spanners with purely additive error and lower bounds concerning them were given in [ACIM99, EP04, BCE05, BKMP10, Che13, Woo06, BW15, AB16].  ... 
arXiv:1607.08337v2 fatcat:qsjmcw555zflzayalrfgqk7tlq

Very Sparse Additive Spanners and Emulators

Gregory Bodwin, Virginia Vassilevska Williams
2015 Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15  
We obtain new upper bounds on the additive distortion for graph emulators and spanners on relatively few edges.  ...  [1] gave a construction for spanners on O(n 3/2 ) edges with additive error of 2, Chechik [9] showed how to construct spanners oñ O(n 7/5 ) 1 edges with additive distortion of 4, and Baswana et al  ...  There are three known constructions that produce spanners of constant additive error. Aingworth et al.  ... 
doi:10.1145/2688073.2688103 dblp:conf/innovations/BodwinW15 fatcat:2updxxzliragtdemnu2phbwzvq

Multi-level Weighted Additive Spanners [article]

Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Stephen Kobourov, Richard Spence
2021 arXiv   pre-print
We experimentally measure the performance of this and several other algorithms for weighted additive spanners, both in terms of runtime and sparsity of output spanner, when applied at each level of the  ...  Given a graph G = (V,E), a subgraph H is an additivespanner if _H(u,v) ≤_G(u,v) + β for all u, v ∈ V.  ...  For very large graphs, purely additive error is arguably a much more appealing paradigm.  ... 
arXiv:2102.05831v3 fatcat:culm5zs7zrfxfgrd3utsajyg44

New sparseness results on graph spanners

Barun Chandra, Gautam Das, Giri Narasimhan, José Soares
1992 Proceedings of the eighth annual symposium on Computational geometry - SCG '92  
For the spanners constructed by the greedy algo~rithm this clustering is purely for the purposes of analysis, but in the case of the transformational technique (Lemma 4.4) we act uall y construct the spanner  ...  The primary focus of most of these papers was to clesign efficient algorithms for spanner construction.  ... 
doi:10.1145/142675.142717 dblp:conf/compgeom/ChandraDNS92 fatcat:55sm4t2uebeblgblvbfoiad26u

NEW SPARSENESS RESULTS ON GRAPH SPANNERS

BARUN CHANDRA, GAUTAM DAS, GIRI NARASIMHAN, JOSE SOARES
1995 International journal of computational geometry and applications  
For the spanners constructed by the greedy algo~rithm this clustering is purely for the purposes of analysis, but in the case of the transformational technique (Lemma 4.4) we act uall y construct the spanner  ...  The primary focus of most of these papers was to clesign efficient algorithms for spanner construction.  ... 
doi:10.1142/s0218195995000088 fatcat:bznsd55lzfb5lprfvepczq5uze
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