A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Roundtrip spanners and roundtrip routing in directed graphs

2008
*
ACM Transactions on Algorithms
*

The

doi:10.1145/1367064.1367069
fatcat:flgu5f2gfnfhfjk4dknmqgnnnq
*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 ...##
###
Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners
[article]

2018
*
arXiv
*
pre-print

Our main technical contribution to achieve these results is the first nearly linear time algorithm for computing

arXiv:1611.00721v2
fatcat:buf4rgd3rjedvo67nci2hdypk4
*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*. ...##
###
Compact roundtrip routing with topology-independent node names

2003
*
Proceedings of the twenty-second annual symposium on Principles of distributed computing - PODC '03
*

As observed by Cowen

doi:10.1145/872035.872042
dblp:conf/podc/AriasCL03
fatcat:edidzu433jfehiqlvp5mrpkkle
*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. ...##
###
Compact roundtrip routing with topology-independent node names

2008
*
Journal of computer and system sciences (Print)
*

As observed by Cowen

doi:10.1016/j.jcss.2007.09.001
fatcat:cbmtt73q5vg63cyatup7k4wnnm
*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. ...##
###
A Fast Algorithm for Source-wise Round-trip Spanners
[article]

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*. ...

##
###
Multipath Spanners
[chapter]

2010
*
Lecture Notes in Computer Science
*

This paper concerns

doi:10.1007/978-3-642-13284-1_17
fatcat:bxp7qsjat5b2fbsg7a676rjh2a
*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. ...##
###
Relaxed Spanners for Directed Disk Graphs

2011
*
Algorithmica
*

The disk

doi:10.1007/s00453-011-9580-8
fatcat:3mnz6pgghzcovcvngdm7wt3a4i
*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*...##
###
Relaxed spanners for directed disk graphs
[article]

2010
*
arXiv
*
pre-print

The disk

arXiv:0912.2815v2
fatcat:daocmpaivrd7dpotuqwgtwlkjy
*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*...##
###
Transitive-Closure Spanners
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Given a

doi:10.1137/1.9781611973068.101
fatcat:ttojgncqejdgzfy6nwbkeqxjua
*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. ...##
###
Transitive-Closure Spanners

2012
*
SIAM journal on computing (Print)
*

Given a

doi:10.1137/110826655
fatcat:uqb7un2onracjeh4v3jgfwbyjq
*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. ...##
###
Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations
[chapter]

1999
*
Lecture Notes in Computer Science
*

The

doi:10.1007/3-540-48747-6_2
fatcat:nbkzf3rldrhk5pim4nzehnplom
*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. ...##
###
Node-Disjoint Multipath Spanners and Their Relationship with Fault-Tolerant Spanners
[chapter]

2011
*
Lecture Notes in Computer Science
*

Given a weighted

doi:10.1007/978-3-642-25873-2_11
fatcat:gkkrferctzcxpec4ffymmrnty4
*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*. ...##
###
Transitive-Closure Spanners: A Survey
[chapter]

2010
*
Lecture Notes in Computer Science
*

Given a

doi:10.1007/978-3-642-16367-8_10
fatcat:vwinrex67rcwfk5kfwwxvwglpy
*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 ...##
###
Graph Spanners: A Tutorial Review
[article]

2020
*
arXiv
*
pre-print

It reviews the current literature covering various research streams about

arXiv:1909.03152v2
fatcat:vqme4ewuvbbd5ac5erinyykwsy
*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*. ...##
###
Transitive-Closure Spanners
[article]

2008
*
arXiv
*
pre-print

Given a

arXiv:0808.1787v1
fatcat:nvslbec64nd3tl2mneevnpksou
*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. ...
« Previous

*Showing results 1 — 15 out of 30 results*