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Page 1864 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
; Barcelona) Spanners of underlying graphs of iterated line digraphs.  ...  In this paper, we study spanners with small dilation of graphs which are underlying graphs of iterated line digraphs.” 98c:68168 68R10 05C85 Hsu, Wen-Lian (RC-AST-I; Taipei) On-line recognition of interval  ... 

Tree Spanners

Leizhen Cai, Derek G. Corneil
1995 SIAM Journal on Discrete Mathematics  
The results for tree spanners on undirected graphs are extended to "quasi-tree spanners" on digraphs.  ...  A tree t-spanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most times their distance in G.  ...  Some material in this paper has previously appeared in the first author's Ph.D. dissertation under the supervision of the second author. The authors thank the referees for useful suggestions.  ... 
doi:10.1137/s0895480192237403 fatcat:wxag2mbkvnbzbbdvtkidhdm2gi

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  
We define the notion of a transitive-closure spanner of a directed graph.  ...  We study the approximability of the size of the sparsest k-TC-spanner for a given digraph.  ...  However, although the separators are paths, in our digraph they may be the union of many dipaths, and so we cannot efficiently recurse using the sparse k-TC-spanners for the directed line of Alon and Schieber  ... 
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)  
We define the notion of a transitive-closure spanner of a directed graph.  ...  We study the approximability of the size of the sparsest k-TC-spanner for a given digraph.  ...  However, although the separators are paths, in our digraph they may be the union of many dipaths, and so we cannot efficiently recurse using the sparse k-TC-spanners for the directed line of Alon and Schieber  ... 
doi:10.1137/110826655 fatcat:uqb7un2onracjeh4v3jgfwbyjq

Approximating k-Spanner Problems for k > 2 [chapter]

Michael Elkin, David Peleg
2001 Lecture Notes in Computer Science  
The basic k-spanner problem is to find a k-spanner of a given graph G with the smallest possible number of edges.  ...  Given a graph G = (V , E), a subgraph G = (V , H ), H ⊆ E is a k-spanner of G if for any pair of vertices u, w ∈ V it satisfies d H (u, w) kd G (u, w).  ...  A subgraph (V , T ) is a quasi-tree if the underlying graph (V , under(T )) is a tree. Let SP k (QTREE) be the family of digraphs that have a quasi-tree k-spanner.  ... 
doi:10.1007/3-540-45535-3_8 fatcat:q32xzzhq4bdonjkjmpu6gmjvla

Approximating k-spanner problems for k>2

Michael Elkin, David Peleg
2005 Theoretical Computer Science  
The basic k-spanner problem is to find a k-spanner of a given graph G with the smallest possible number of edges.  ...  Given a graph G = (V , E), a subgraph G = (V , H ), H ⊆ E is a k-spanner of G if for any pair of vertices u, w ∈ V it satisfies d H (u, w) kd G (u, w).  ...  A subgraph (V , T ) is a quasi-tree if the underlying graph (V , under(T )) is a tree. Let SP k (QTREE) be the family of digraphs that have a quasi-tree k-spanner.  ... 
doi:10.1016/j.tcs.2004.11.022 fatcat:pw5dbl6iyzbtnghfk4va7mtxnq

Transitive-Closure Spanners [article]

Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff
2008 arXiv   pre-print
We initiate the study of approximability of the size of the sparsest k-TC-spanner for a given directed graph.  ...  Finally, we study the size of the sparsest k-TC-spanners for H-minor-free graph families.  ...  A digraph G is called an s-path separable digraph if the undirected graph underlying T R(G ) is s-path separable.  ... 
arXiv:0808.1787v1 fatcat:nvslbec64nd3tl2mneevnpksou

Local Computation of Nearly Additive Spanners [chapter]

Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot
2009 Lecture Notes in Computer Science  
This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β)-spanner H for a given graph G and distortion parameters α and β.  ...  It first presents a generic distributed algorithm that in constant number of rounds constructs, for every n-node graph and integer k ≥ 1, an (α, β)-spanner of O(βn 1+1/k ) edges, where α and β are constants  ...  Stretch: The stretch analysis is similar to the one of Proposition 7. One consider two distinct nodes u, v in G, and let P be a shortest path from u to v in G.  ... 
doi:10.1007/978-3-642-04355-0_20 fatcat:fw6ejlbworfzvd2rfbmf7vqwz4

Nearly Tight Spectral Sparsification of Directed Hypergraphs by a Simple Iterative Sampling Algorithm [article]

Kazusato Oko, Shinsaku Sakaue, Shin-ichi Tanigawa
2022 arXiv   pre-print
Our algorithm can be regarded as an extension of the spanner-based graph sparsification by Koutis and Xu (2016).  ...  To exhibit the power of the spanner-based approach, we also examine a natural extension of Koutis and Xu's algorithm to undirected hypergraphs.  ...  [26] obtained such a scheme by looking at underlying clique digraphs.  ... 
arXiv:2204.02537v1 fatcat:ui5darnmubevxit4m46fpkomoq

Master index

2002 Discrete Mathematics  
., Digraph embedding 233 (2001) 321}328 Hasunuma, T., Completely independent spanning trees in the underlying graph of a line digraph (Note) 234 (2001) 149}157 Havet, F., Channel assignment and  ...  RyjaH c\ ek, Clique covering and degree conditions for hamiltonicity in claw-free graphs 236 (2001) 65}180 vulnerability of iterated line digraphs 233 (2001) 103}113 Fiala, J., Computational complexity  ... 
doi:10.1016/s0012-365x(01)00417-4 fatcat:cf6rcjdhrrb7xexabp2gbedq6q

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  
Roditty et al. [35] observe that sparse spanners do not exist for all digraphs, and there is further discussion in [13, 41] .  ...  Cowen and Wagner [11, 13] made the observation that in directed graphs, instead of bounding the length of a one-way path from node x to node y in terms of the shortest distance d(x, y), we could bound  ...  Acknowledgments We thank the anonymous referees for suggestions that greatly improved the presentation of this paper. Marta Arias was partly supported by NSF grant IIS-0099446.  ... 
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)  
Roditty et al. [35] observe that sparse spanners do not exist for all digraphs, and there is further discussion in [13, 41] .  ...  Cowen and Wagner [11, 13] made the observation that in directed graphs, instead of bounding the length of a one-way path from node x to node y in terms of the shortest distance d(x, y), we could bound  ...  Acknowledgments We thank the anonymous referees for suggestions that greatly improved the presentation of this paper. Marta Arias was partly supported by NSF grant IIS-0099446.  ... 
doi:10.1016/j.jcss.2007.09.001 fatcat:cbmtt73q5vg63cyatup7k4wnnm

Maximum Flow and Minimum-Cost Flow in Almost-Linear Time [article]

Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, Sushant Sachdeva
2022 arXiv   pre-print
Our algorithm builds the flow through a sequence of m^1+o(1) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m^o(1) time using a new dynamic graph data  ...  We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m^1+o(1) time.  ...  Acknowledgments We thank the 2021 Hausdorff Research Institute for Mathematics Program Discrete Optimization during which part of this work was developed.  ... 
arXiv:2203.00671v2 fatcat:hwdtmht5mjc4fn73pb3zg5tyte

The Computational Complexity of Finding Temporal Paths under Waiting Time Constraints [article]

Arnaud Casteigts, Anne-Sophie Himmel, Hendrik Molter, Philipp Zschoche
2021 arXiv   pre-print
to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which  ...  For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth  ...  We thank the referees for their careful reading and constructive comments which significantly improved the presentation of these results.  ... 
arXiv:1909.06437v5 fatcat:wetm454dp5gw7dbflspu5lgqtm

Finding Temporal Paths Under Waiting Time Constraints

Arnaud Casteigts, Anne-Sophie Himmel, Hendrik Molter, Philipp Zschoche
2021 Algorithmica  
to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finer-grained temporal features of the input temporal graph, and which  ...  For example, it is W[1]-hard when parameterized by the distance to disjoint path of the underlying graph, which implies W[1]-hardness for many other parameters like feedback vertex number and pathwidth  ...  Furthermore, let H i,w be the running time of Lines (5)-(7) in iteration i of the forloop in Line (3), and R i,w be the number of operations over of Line (8) in iteration i of the for-loop in Line  ... 
doi:10.1007/s00453-021-00831-w fatcat:li6o75ankvcmbmasakjkclw3ty
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