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191
Roundtrip Spanners and Roundtrip Routing in Directed Graphs
"... We introduce the notion of roundtripspanners of weighted directed graphs and describe ecient algorithms for their construction. For every integer k 1 and any > 0, we show that any directed graph on n vertices with edge weights in the range [1; W ] has a (2k + )roundtripspanner with O( ..."
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Cited by 38 (0 self)
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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. Our roundtrip routing schemes substantially improve previous results of Cowen and Wagner. Our results are obtained by combining ideas of Cohen
Compact roundtrip routing with topologyindependent node names
 In Proceedings of the TwentySecond Annual Symposium on Principles of Distributed Computing
, 2003
"... This paper presents compact roundtrip routing schemes with local tables of size Õ( √ n) and stretch 6 for any directed network with arbitrary edge weights; and with local tables of size Õ(ǫ−1 n 2/k) and stretch min((2 k/2 − 1)(k + ǫ),16k 2 + 8k − 8), for any directed network with polynomiallysized ..."
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Cited by 6 (0 self)
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This paper presents compact roundtrip routing schemes with local tables of size Õ( √ n) and stretch 6 for any directed network with arbitrary edge weights; and with local tables of size Õ(ǫ−1 n 2/k) and stretch min((2 k/2 − 1)(k + ǫ),16k 2 + 8k − 8), for any directed network with polynomially
Multipath Spanners
"... This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with n vertices. Classically, a spanner H of stretch s for a graph G is a spanning subgraph such that the distance in H between any two vertices is at most s times the distance in G. We s ..."
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Cited by 3 (2 self)
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This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with n vertices. Classically, a spanner H of stretch s for a graph G is a spanning subgraph such that the distance in H between any two vertices is at most s times the distance in G. We
Additive Spanners and (α, β)Spanners
"... An (α, β)spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a (multiplicative) (2k − 1, 0)spanner of size O(n 1+1/k) and an (additive) (1, 2)spanner of size O(n 3/2). How ..."
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Cited by 13 (3 self)
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An (α, β)spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a (multiplicative) (2k − 1, 0)spanner of size O(n 1+1/k) and an (additive) (1, 2)spanner of size O(n 3
Transitiveclosure spanners
, 2008
"... We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanner ..."
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Cited by 38 (11 self)
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We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k
ALMI: An Application Level Multicast Infrastructure
, 2001
"... The IP multicast model allows scalable and efficient multiparty communication, particularly for groups of large size. However, deployment of IP multicast requires substantial infrastructure modifications and is hampered by a host of unresolved open problems. To circumvent this situation, we have de ..."
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Cited by 335 (11 self)
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The IP multicast model allows scalable and efficient multiparty communication, particularly for groups of large size. However, deployment of IP multicast requires substantial infrastructure modifications and is hampered by a host of unresolved open problems. To circumvent this situation, we have designed and implemented ALMI, an application level group communication middleware, which allows accelerated application deployment and simplified network configuration, without the need of network infrastructure support. ALMI is tailored toward support of multicast groups of relatively small size (several I Os of members) with many to many semantics. Session participants are connected via a vir tual multicast tree, which consists of unicast connections between end hosts and is formed as a minimum spanning tree (MST) using applicationspecific performance metric. Using simulation, we show that the performance penalties, introduced by this shift of multicast to end systems, is a relatively small increase in traffic load and that ALMI multicast trees approach the efficiency of IP multicast trees. We have also implemented ALMi as a Java based middleware package and performed experiments over the Internet. Experimental results show that ALMI is able to cope with network dynamics and keep the mul ticast tree efficient.
Transitive closure spanners
 IN PROCEEDINGS OF THE 18TH ANNUAL SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2009
"... We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanner ..."
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We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k
IDMaps: A Global Internet Host Distance Estimation Service
 IN PROCEEDINGS OF IEEE INFOCOM
, 2000
"... There is an increasing need to quickly and efficiently learn network distances, in terms of metrics such as latency or bandwidth, between Internet hosts. For example, Internet content providers often place data and server mirrors throughout the Internet to improve access latency for clients, and it ..."
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Cited by 300 (13 self)
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, and it is necessary to direct clients to the closest mirrors based on some distance metric in order to realize the benefit of mirrors. We suggest a scalable Internetwide architecture, called IDMaps, which measures and disseminates distance information on the global Internet. Higherlevel services can collect
TransitiveClosure Spanners: A Survey
"... We survey results on transitiveclosure spanners and their applications. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanner ..."
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Cited by 9 (5 self)
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We survey results on transitiveclosure spanners and their applications. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k
www.stacsconf.org RELAXED SPANNERS FOR DIRECTED DISK GRAPHS
, 2010
"... Abstract. Let (V, δ) be a finite metric space, where V is a set of n points and δ is a distance function defined for these points. Assume that (V, δ) has a constant doubling dimension d and assume that each point p ∈ V has a disk of radius r(p) around it. The disk graph that corresponds to V and r(· ..."
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(·) 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 [8] we presented an algorithm for constructing a (1 + ǫ)spanner of size O(n/ǫ d log M), where M is the maximal radius r(p). The current paper presents two
Results 1  10
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191