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Roundtrip spanners and roundtrip routing in directed graphs

Iam Roditty, Mikkel Thorup, Uri Zwick
2008 ACM Transactions on Algorithms  
The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs  ...  We show that for every integer k ≥ 1 and any > 0, any directed graph on n vertices with edge weights in the range [1, W ] has a (2k + )-roundtrip-spanner with O(min{(k 2 / ) n 1+1/k log (nW ) , (k/ ) 2  ...  Roundtrip Spanners and Roundtrip Routing in Directed Graphs Removing the Dependence on the Edge Weights In the previous section, we showed that any directed graph on n vertices with edge weights in the  ... 
doi:10.1145/1367064.1367069 fatcat:flgu5f2gfnfhfjk4dknmqgnnnq

Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners [article]

Jakub Pachocki, Liam Roditty, Aaron Sidford, Roei Tov, Virginia Vassilevska Williams
2018 arXiv   pre-print
Our main technical contribution to achieve these results is the first nearly linear time algorithm for computing roundtrip covers, a directed graph decomposition concept key to previous roundtrip spanner  ...  Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted m-edge and n-node graphs require Ω({n^ω, mn}) time (for 2≤ω<2.373).  ...  Roundtrip distances were studied by Cowen and Wagner [CW04] in the context of routing.  ... 
arXiv:1611.00721v2 fatcat:buf4rgd3rjedvo67nci2hdypk4

Compact roundtrip routing with topology-independent node names

Marta Arias, Lenore J. Cowen, Kofi A. Laing
2003 Proceedings of the twenty-second annual symposium on Principles of distributed computing - PODC '03  
As observed by Cowen and Wagner [11, 13] , sparse roundtrip spanners do exist in this model, and can be used as a basis for compact roundtrip routing schemes in directed networks where they presented the  ...  For example, it is shown in [16] that distinguishing between pairs of vertices at distances 2 and ∞ even in unweighted directed graphs is at least as hard as Boolean matrix multiplication.  ...  Lenore Cowen was supported in part by the National Science Foundation under Grant No. CCR-0208629. Kofi Laing was supported in part by NSF grant EHR-0227879.  ... 
doi:10.1145/872035.872042 dblp:conf/podc/AriasCL03 fatcat:edidzu433jfehiqlvp5mrpkkle

Compact roundtrip routing with topology-independent node names

Marta Arias, Lenore J. Cowen, Kofi A. Laing
2008 Journal of computer and system sciences (Print)  
As observed by Cowen and Wagner [11, 13] , sparse roundtrip spanners do exist in this model, and can be used as a basis for compact roundtrip routing schemes in directed networks where they presented the  ...  For example, it is shown in [16] that distinguishing between pairs of vertices at distances 2 and ∞ even in unweighted directed graphs is at least as hard as Boolean matrix multiplication.  ...  Lenore Cowen was supported in part by the National Science Foundation under Grant No. CCR-0208629. Kofi Laing was supported in part by NSF grant EHR-0227879.  ... 
doi:10.1016/j.jcss.2007.09.001 fatcat:cbmtt73q5vg63cyatup7k4wnnm

A Fast Algorithm for Source-wise Round-trip Spanners [article]

Chun Jiang Zhu, Song Han, Kam-Yiu Lam
2021 arXiv   pre-print
In this paper, we study the problem of fast constructions of source-wise round-trip spanners in weighted directed graphs.  ...  For a source vertex set S⊆ V in a graph G(V,E), an S-sourcewise round-trip spanner of G of stretch k is a subgraph H of G such that for every pair of vertices u,v∈ S× V, their round-trip distance in H  ...  Conclusion and Future Work In this paper, we propose a fast algorithm for constructing source-wise roundtrip spanners in weighted directed graphs.  ... 
arXiv:2004.05721v2 fatcat:bj2go2mo2fdybbrvkndf7su6pu

Multipath Spanners [chapter]

Cyril Gavoille, Quentin Godfroy, Laurent Viennot
2010 Lecture Notes in Computer Science  
This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with n vertices.  ...  Interestingly, these solutions lead to compact routing scheme in directed graphs. Dragan and Yan [9] study the complexity of computing spanners approximating maximum flow between any two vertices.  ...  In weighted directed graphs, the one-way distance is not a graph metric.  ... 
doi:10.1007/978-3-642-13284-1_17 fatcat:bxp7qsjat5b2fbsg7a676rjh2a

Relaxed Spanners for Directed Disk Graphs

D. Peleg, L. Roditty
2011 Algorithmica  
The disk graph that corresponds to V and r(·) is a directed graph I(V, E, r), whose vertices are the points of V and whose edge set includes a directed edge from p to q if δ(p, q) ≤ r(p).  ...  In particular, we show that if it is allowed to use edges of the disk graph I(V, E, r1+ǫ), where r1+ǫ(p) = (1+ǫ)·r(p) for every p ∈ V , then it is possible to get a (1 + ǫ)-spanner of size O(n/ǫ d ) for  ...  It is shown by Cowen and Wagner [5] and later by Roditty, Thorup and Zwick [6] that methods of path approximations from undirected graphs can work using more ideas also in directed graphs when roundtrip  ... 
doi:10.1007/s00453-011-9580-8 fatcat:3mnz6pgghzcovcvngdm7wt3a4i

Relaxed spanners for directed disk graphs [article]

David Peleg, Liam Roditty
2010 arXiv   pre-print
The disk graph that corresponds to V and r(·) is a directed graph I(V,E,r), whose vertices are the points of V and whose edge set includes a directed edge from p to q if δ(p,q)≤ r(p).  ...  In particular, we show that if it is allowed to use edges of the disk graph I(V,E,r_1+), where r_1+(p) = (1+)· r(p) for every p∈ V, then it is possible to get a (1+)-spanner of size O(n/^d) for I(V,E,r  ...  It is shown by Cowen and Wagner [5] and later by Roditty, Thorup and Zwick [6] that methods of path approximations from undirected graphs can work using more ideas also in directed graphs when roundtrip  ... 
arXiv:0912.2815v2 fatcat:daocmpaivrd7dpotuqwgtwlkjy

Transitive-Closure Spanners [chapter]

Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, E H ) that has (1) the same transitive-closure as G and (2) diameter  ...  We define the notion of a transitive-closure spanner of a directed graph.  ...  Rubinfeld, and A. Smith for helpful discussions.  ... 
doi:10.1137/1.9781611973068.101 fatcat:ttojgncqejdgzfy6nwbkeqxjua

Transitive-Closure Spanners

Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff
2012 SIAM journal on computing (Print)  
Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, E H ) that has (1) the same transitive-closure as G and (2) diameter  ...  We define the notion of a transitive-closure spanner of a directed graph.  ...  Rubinfeld, and A. Smith for helpful discussions.  ... 
doi:10.1137/110826655 fatcat:uqb7un2onracjeh4v3jgfwbyjq

Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations [chapter]

Ofer Arieli, Arnon Avron
1999 Lecture Notes in Computer Science  
The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs  ...  Abstract We introduce the notion of roundtrip-spanners of weighted directed graphs and describe efficient algorithms for their construction.  ...  Presented at the ECG Workshop on Robustness and Efficiency Issues in Implementing Arrangements of Curves and Surfaces, Inria, France, December 18-19, 2002.  ... 
doi:10.1007/3-540-48747-6_2 fatcat:nbkzf3rldrhk5pim4nzehnplom

Node-Disjoint Multipath Spanners and Their Relationship with Fault-Tolerant Spanners [chapter]

Cyril Gavoille, Quentin Godfroy, Laurent Viennot
2011 Lecture Notes in Computer Science  
Given a weighted graph G, a subgraph H is a p-multipath s-spanner if for all u, v, the p-multipath cost between u and v in H is at most s times the p-multipath cost in G.  ...  Motivated by multipath routing, we introduce a multiconnected variant of spanners.  ...  We stress that there is a significant difference between proving the existence of short routes in a graph (or subgraph), and constructing and explicitly describing such short routes.  ... 
doi:10.1007/978-3-642-25873-2_11 fatcat:gkkrferctzcxpec4ffymmrnty4

Transitive-Closure Spanners: A Survey [chapter]

Sofya Raskhodnikova
2010 Lecture Notes in Computer Science  
Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, EH ) that has (1) the same transitive-closure as G and (2) diameter  ...  In this article, we survey combinatorial bounds on the size of sparsest TC-spanners, and algorithms and inapproximability results for the problem of computing the sparsest TC-spanner of a given directed  ...  In the directed setting, three notions of spanners have been proposed: the direct generalization of the above definition [PS89] , roundtrip spanners [CW04, RTZ02] and transitive-closure spanners [BGJ  ... 
doi:10.1007/978-3-642-16367-8_10 fatcat:vwinrex67rcwfk5kfwwxvwglpy

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
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.  ...  [140] study roundtrip spanners, and Zhu and Lam [155, 156] introduce the notion of sourcewise roundtrip spanners for directed graphs.  ... 
arXiv:1909.03152v2 fatcat:vqme4ewuvbbd5ac5erinyykwsy

Transitive-Closure Spanners [article]

Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff
2008 arXiv   pre-print
Given a directed graph G = (V,E) and an integer k>=1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, E_H) that has (1) the same transitive-closure as G and (2) diameter  ...  These spanners were implicitly studied in access control, data structures, and property testing, and properties of these spanners have been rediscovered over the span of 20 years.  ...  Jayram, Elad Hazan, Ronitt Rubinfeld, and Adam Smith for helpful discussions.  ... 
arXiv:0808.1787v1 fatcat:nvslbec64nd3tl2mneevnpksou
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