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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 196 (7 self)
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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 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 nearoptimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain: 1. A routing scheme that uses only ~ O(n 1=2) bits of memory at each node of an nnode network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that
Compact Routing with Minimum Stretch
 Journal of Algorithms
"... We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all node ..."
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Cited by 111 (5 self)
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We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use\Omega\Gamma n) local space at some vertex. 1 Introduction Let G = (V; E) with jV j = n be a labeled undirected network. Assuming that a positive cost, or distance is assigned with each edge, the stretch of path p(u; v) from node u to node v is defined as jp(u;v)j jd(u;v)j , where jd(u; v)j is the length of the shortest u \Gamma v path. The approximate allpairs shortest path problem involves a tradeoff of stretch against time short paths with stretch bounded by a constant are com...
Compact NameIndependent Routing with Minimum Stretch
 In Proceedings of the 16th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2004
, 2004
"... Given a weighted undirected network with arbitrary node names, we present a compact routing scheme, using a O(√n) space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the shortest paths. This is optimal in a very strong sense. It is known t ..."
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Cited by 64 (12 self)
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Given a weighted undirected network with arbitrary node names, we present a compact routing scheme, using a O(√n) space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the shortest paths. This is optimal in a very strong sense. It is known that no compact routing using o(n) space per node can route with stretch below 3. Also, it is known that any stretch below 5 requires Ω(√n) space per node.
Distance Estimation and Object Location via Rings of Neighbors
 In 24 th Annual ACM Symposium on Principles of Distributed Computing (PODC
, 2005
"... We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. Fo ..."
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Cited by 64 (4 self)
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We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors, which refers to a sparse distributed data structure that underlies all our constructions. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg’s small world model to doubling metrics, and a short proof of the main result in Chan et al. [14]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature. 1
On Hierarchical Routing in Doubling Metrics
, 2005
"... We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α ..."
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Cited by 57 (8 self)
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We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α if every set of diameter D can be covered by 2 α sets of diameter D/2. (A doubling metric is one whose doubling dimension dim(X) is a constant.) We show how to perform (1 + τ)stretch routing on metrics for any 0 < τ ≤ 1 with routing tables of size at most (α/τ) O(α) log 2 ∆ bits with only (α/τ) O(α) log ∆ entries, where ∆ is the diameter of the graph; hence the number of routing table entries is just τ −O(1) log ∆ for doubling metrics. These results extend and improve on those of Talwar (2004). We also give better constructions of sparse spanners for doubling metrics than those obtained from the routing tables above; for τ> 0, we give algorithms to construct (1 + τ)stretch spanners for a metric (X, d) with maximum degree at most (2 + 1/τ) O(dim(X)) , matching the results of Das et al. for Euclidean metrics.
Compact routing on Internetlike graphs
 In Proc. IEEE INFOCOM
, 2004
"... Abstract — The ThorupZwick (TZ) compact routing scheme is the first generic stretch3 routing scheme delivering a nearly optimal pernode memory upper bound. Using both direct analysis and simulation, we derive the stretch distribution of this routing scheme on Internetlike interdomain topologies. ..."
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Cited by 54 (7 self)
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Abstract — The ThorupZwick (TZ) compact routing scheme is the first generic stretch3 routing scheme delivering a nearly optimal pernode memory upper bound. Using both direct analysis and simulation, we derive the stretch distribution of this routing scheme on Internetlike interdomain topologies. By investigating the TZ scheme on random graphs with powerlaw node degree distributions, Pk � k −γ, we find that the average TZ stretch is quite low and virtually independent of γ. In particular, for the Internet interdomain graph with γ � 2.1, the average TZ stretch is around 1.1, with up to 70 % of all pairwise paths being stretch1 (shortest possible). As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for 10 4node networks. Furthermore, we find that both the average shortest path length (i.e. distance) d and width of the distance distribution σ observed in the real Internet interAS graph have values that are very close to the minimums of the average stretch in the d and σdirections. This leads us to the discovery of a unique critical point of the average TZ stretch as a function of d and σ. The Internet distance distribution is located in a close neighborhood of this point. This is remarkable given the fact that the Internet interdomain topology has evolved without any direct attention paid to properties of the stretch distribution. It suggests the average stretch function may be an indirect indicator of the optimization criteria influencing the Internet’s interdomain topology evolution.
Routing in Distributed Networks: Overview and Open Problems
 ACM SIGACT News  Distributed Computing Column
, 2001
"... This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems. ..."
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Cited by 49 (12 self)
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This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems.
Persistent personal names for globally connected mobile devices
 In Proc. of OSDI 2006
, 2006
"... The Unmanaged Internet Architecture (UIA) provides zeroconfiguration connectivity among mobile devices through personal names. Users assign personal names through an ad hoc device introduction process requiring no central allocation. Once assigned, names bind securely to the global identities of th ..."
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Cited by 39 (3 self)
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The Unmanaged Internet Architecture (UIA) provides zeroconfiguration connectivity among mobile devices through personal names. Users assign personal names through an ad hoc device introduction process requiring no central allocation. Once assigned, names bind securely to the global identities of their target devices independent of network location. Each user manages one namespace, shared among all the user’s devices and always available on each device. Users can also name other users to share resources with trusted acquaintances. Devices with naming relationships automatically arrange connectivity when possible, both in ad hoc networks and using global infrastructure when available. A UIA prototype demonstrates these capabilities using optimistic replication for name resolution and group management and a routing algorithm exploiting the user’s social network for connectivity. 1
Object Location Using Path Separators
, 2006
"... We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpat ..."
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Cited by 35 (11 self)
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We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpath separable graphs can be used to solve several object location problems: (1) a smallworldization with an average polylogarithmic number of hops; (2) an (1 + ε)approximate distance labeling scheme with O(log n) space labels; (3) a stretch(1 + ε) compact routing scheme with tables of polylogarithmic space; (4) an (1+ε)approximate distance oracle with O(n log n) space and O(log n) query time. Our results generalizes to much wider classes of weighted graphs, namely to boundeddimension isometric sparable graphs.
Compact routing with name independence
 IN PROCEEDINGS OF THE FIFTEENTH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 2003
"... This paper is concerned with compact routing schemes for arbitrary undirected networks in the nameindependent model first introduced by Awerbuch, BarNoy, Linial and Peleg. A compact routing scheme that uses local routing tables of size Õ(n1/2), 1 O(log 2 n)sized packet headers, and stretch bounde ..."
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Cited by 27 (3 self)
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This paper is concerned with compact routing schemes for arbitrary undirected networks in the nameindependent model first introduced by Awerbuch, BarNoy, Linial and Peleg. A compact routing scheme that uses local routing tables of size Õ(n1/2), 1 O(log 2 n)sized packet headers, and stretch bounded by 5 is obtained, where n is the number of nodes in the network. Alternative schemes reduce the packet header size to O(log n) at the cost of either increasing the stretch to 7 or increasing the table size to Õ(n2/3). For smaller tablesize requirements, the ideas in these schemes are generalized to a scheme that uses O(log 2 n)sized headers, Õ(k2 n 2/k)sized tables, and achieves a stretch of min{1 + (k − 1)(2 k/2 − 2), 16k 2 − 8k}, improving the best previouslyknown nameindependent scheme due to Awerbuch and Peleg.