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107
AllPairs SmallStretch Paths
 Journal of Algorithms
, 1997
"... Let G = (V; E) be a weighted undirected graph. A path between u; v 2 V is said to be of stretch t if its length is at most t times the distance between u and v in the graph. We consider the problem of finding smallstretch paths between all pairs of vertices in the graph G. It is easy to see that f ..."
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Cited by 37 (7 self)
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Let G = (V; E) be a weighted undirected graph. A path between u; v 2 V is said to be of stretch t if its length is at most t times the distance between u and v in the graph. We consider the problem of finding smallstretch paths between all pairs of vertices in the graph G. It is easy to see
AllPairs SmallStretch Paths
"... Abstract Let G = (V; E) be a weighted undirected graph. A path between u; v 2 V is said to be of stretch t if its length is at most t times the distance between u and v in the graph. We consider the problem of finding smallstretch paths between all pairs of vertices in the graph G. It is easy to se ..."
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Abstract Let G = (V; E) be a weighted undirected graph. A path between u; v 2 V is said to be of stretch t if its length is at most t times the distance between u and v in the graph. We consider the problem of finding smallstretch paths between all pairs of vertices in the graph G. It is easy
Faster Algorithms for Approximate Distance Oracles and AllPairs Small StretchPaths
"... ffi(u, v) < = ^ffi(u, v) < = t * ffi(u, v). The most efficient algorithms known for computing small stretch distances in Gare the approximate distance oracles of [16] and the three algorithms in [9] to compute allpairs stretch t distancesfor t = 2, 7/3, and 3. We present faster algorithms fo ..."
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ffi(u, v) < = ^ffi(u, v) < = t * ffi(u, v). The most efficient algorithms known for computing small stretch distances in Gare the approximate distance oracles of [16] and the three algorithms in [9] to compute allpairs stretch t distancesfor t = 2, 7/3, and 3. We present faster algorithms
Compact routing schemes
 in SPAA ’01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
"... We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extrem ..."
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Cited by 229 (4 self)
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, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a near
S4: Small State and Small Stretch Routing Protocol for Large Wireless Sensor Networks
 IN PROC. OF THE USENIX NSDI CONF
, 2007
"... Routing protocols for wireless sensor networks must address the challenges of reliable packet delivery at increasingly large scale and highly constrained node resources. Attempts to limit node state can result in undesirable worstcase routing performance, as measured by stretch, which is the ratio ..."
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Cited by 60 (2 self)
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of the hop count of the selected path to that of the optimal path. We present a new routing protocol, Small State and Small Stretch (S4),which jointly minimizes the state and stretch. S4 uses a combination of beacon distancevector based global routing state and scoped distancevector based local routing
Independent Spanning Trees with Small Stretch Factors
, 1996
"... A pair of spanning trees rooted at a vertex r are independent if for every vertex v the pair of unique tree paths from v to the root r are disjoint. This paper presents the first analysis of the path lengths involved in independent spanning trees in 2edgeconnected and 2vertexconnected graphs. We ..."
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Cited by 1 (0 self)
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. We present upper and lower bounds on the stretch factors of pairs of independent spanning trees, where the stretch factor of a spanning tree is defined to be the maximum ratio between the length of paths in the tree to the root to the length of the shortest path in the graph to the root. We prove
A Tradeoff between Space and Efficiency for Routing Tables
, 1989
"... Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use paths that are as short as possible for routing messages in the network, while keeping the routing information stored in the processors’ local memory as succinct as pos ..."
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Cited by 157 (7 self)
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as possible. The efficiency of a routing scheme is measured in terms of its stretch factorthe maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices. Most previous work has concentrated on finding good routing schemes (with a small
Polylogarithmic network navigability using compact metrics with small stretch
 IN: 20TH ANNUAL ACM SYMP. ON PARALLEL ALGORITHMS AND ARCHITECTURES (SPAA
, 2008
"... Graph augmentation theory is a general framework for analyzing navigability in social networks. It is known that, for large classes of graphs, there exist augmentations of these graphs such that greedy routing according to the shortest path metric performs in polylogarithmic expected number of steps ..."
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Cited by 4 (0 self)
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consuming to encode locally the shortest path distances to all the other nodes, and, second, greedy routing according to the shortest path metric performs poorly in some graphs. We prove that, using semimetrics of small stretch results in a huge positive impact, in both encoding space and efficiency of greedy routing
Path Vector Face Routing: Geographic Routing with Local Face Information
"... Existing geographic routing algorithms depend on the planarization of the network connectivity graph for correctness, and the planarization process gives rise to a welldefined notion of “faces”. In this paper, we demonstrate that we can improve routing performance by storing a small amount of loc ..."
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Cited by 63 (4 self)
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path stretch and hop stretch than existing geographic routing algorithms by exploiting available local face information. Our simulations demonstrate that GPVFR/PVEX achieves significantly reduced path and hop stretch than Greedy Perimeter Stateless Routing (GPSR) and somewhat better performance than
S4: Small state and small stretch compact routing protocol for large static wireless networks
 IEEE/ACM TRANS. NETW
, 2010
"... Routing protocols for large wireless networks must address the challenges of reliable packet delivery at increasingly large scales and with highly limited resources. Attempts to reduce routing state can result in undesirable worstcase routing performance, as measured by stretch, which is the ratio ..."
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Cited by 7 (0 self)
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is the ratio of the hop count of the selected path to that of the optimal path. We present a new routing protocol, Small State and Small Stretch (S4), which jointly minimizes the state and stretch. S4 uses a combination of beacon distancevectorbased global routing state and scoped distancevectorbased local
Results 1  10
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107