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Page 1864 of Mathematical Reviews Vol. , Issue 98C
[page]
1998
Mathematical Reviews
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; 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
1995
SIAM Journal on Discrete Mathematics
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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]
2009
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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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
2012
SIAM journal on computing (Print)
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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]
2001
Lecture Notes in Computer Science
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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
2005
Theoretical Computer Science
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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]
2008
arXiv
pre-print
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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]
2009
Lecture Notes in Computer Science
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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]
2022
arXiv
pre-print
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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
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., 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
2003
Proceedings of the twenty-second annual symposium on Principles of distributed computing - PODC '03
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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
2008
Journal of computer and system sciences (Print)
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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]
2022
arXiv
pre-print
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2022 pre-print arXiv:2203.00671v1 fatcat:z54sixr2drb63a3w7vpdgxtsku
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]
2021
arXiv
pre-print
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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
2021
Algorithmica
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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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