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47
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
Report from the IAB workshop on routing and addressing
 In InternetDraft
, 2007
"... This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. This document reports the outcome of the Routing and Addressing Workshop that was held by the Internet Architecture Board (IAB) on October 1819, 2 ..."
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Cited by 38 (1 self)
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This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. This document reports the outcome of the Routing and Addressing Workshop that was held by the Internet Architecture Board (IAB) on October 1819, 2006, in Amsterdam, Netherlands. The primary goal of the workshop was to develop a shared understanding of the problems that the large backbone operators are facing regarding the scalability of today’s Internet routing system. The key workshop findings include an analysis of the major factors that are driving routing table growth, constraints in router technology, and the limitations of today’s Internet addressing architecture. It is hoped that these findings will serve as input to the IETF community and help identify next steps towards effective solutions.
Routing with Improved CommunicationSpace TradeOff
 IN 18 TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2004
"... Given a weighted undirected network with arbitrary node names, we present a family of routing schemes characterized by an integral parameter κ ≥ 1. The scheme uses log D) space routing table at each node, and routes along paths of linear stretch O(κ), where D is the normalized diamete ..."
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Cited by 27 (10 self)
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Given a weighted undirected network with arbitrary node names, we present a family of routing schemes characterized by an integral parameter κ ≥ 1. The scheme uses log D) space routing table at each node, and routes along paths of linear stretch O(κ), where D is the normalized diameter of the network. When D is polynomial in n, the scheme has asymptotically optimal stretch factor. With the same memory bound, the best previous results obtained stretch O(κ²). Of independent interest, ...
Compact Routing for Graphs Excluding a Fixed Minor (Extended Abstract)
, 2005
"... This paper concerns compact routing schemes with arbitrary node names. We present a compact nameindependent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routin ..."
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Cited by 19 (10 self)
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This paper concerns compact routing schemes with arbitrary node names. We present a compact nameindependent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routing tables with polylogarithmic number of bits at each node. For shortestpath labeled routing scheme in planar graphs, we prove an Ω(n ɛ) space lower bound for some constant ɛ>0. This lower bound holds even for bounded degree triangulations, and is optimal for polynomially weighted planar graphs (ɛ =1/2).
Towards small world emergence
 In Proceedings of 18th ACM Symposium on Parallelism in Algorithms and Architectures
, 2006
"... We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using ..."
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Cited by 18 (3 self)
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We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using the distance in the original network, computes paths of polylogarithmic length between any pair of nodes with probability 1 − O(1/n). Previously known small world augmentation processes require the global knowledge of the network and centralized computations, which is unrealistic for large decentralized networks. Our algorithm, based on a careful multilayer sampling of the nodes and the construction of a light overlay network, bypasses these limitations. For bounded growth graphs, i.e., graphs where, for any node u and any radius r the number of nodes within distance 2r from u is at most a constant times the number of nodes within distance r, our augmentation process proceeds with high probability in O(log n log D) communication rounds, with O(log n log D) messages of size O(log n) bits sent per node and requiring only O(log n log D) bit space in each node, where n is the number of nodes, and D the diameter. In particular, with the only knowledge of original distances, greedy routing computes,
On spacestretch tradeoffs: upper bounds
 In SPAA
, 2006
"... One of the fundamental tradeoffs in compact routing schemes is between the space used to store the routing table on each node and the stretch factor of the routing scheme – the maximum ratio over all pairs between the cost of the route induced by the scheme and the cost of a minimum cost path betwe ..."
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Cited by 18 (8 self)
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One of the fundamental tradeoffs in compact routing schemes is between the space used to store the routing table on each node and the stretch factor of the routing scheme – the maximum ratio over all pairs between the cost of the route induced by the scheme and the cost of a minimum cost path between the same pair. All previous routing schemes required storage that is dependent on the diameter of the network. We present a new scalefree routing scheme, whose storage and header sizes are independent of the aspect ratio of the network. Our scheme is based on a decomposition into sparse and dense neighborhoods. Given an undirected network with arbitrary weights and n arbitrary node names, for any integer k ≥ 1 we present the first scalefree routing scheme with asymptotically optimal spacestretch tradeoff that does not require edge weights to be polynomially bounded. The scheme uses e O(n 1/k) space routing table at each node, and routes along paths of asymptotically optimal linear stretch O(k).
Practical localityawareness for large scale information sharing
 In Proc. IPTPS
, 2005
"... Tulip is an overlay for routing, searching and publishlookup information sharing. It offers a unique combination of the advantages of both structured and unstructured overlays, that does not coexist in any previous solution. Tulip features locality awareness (stretch 2) and fault tolerance (nodes c ..."
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Cited by 18 (1 self)
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Tulip is an overlay for routing, searching and publishlookup information sharing. It offers a unique combination of the advantages of both structured and unstructured overlays, that does not coexist in any previous solution. Tulip features locality awareness (stretch 2) and fault tolerance (nodes can route around failures). It supports under the same roof exact keyedlookup, nearest copy location, and global information search. Tulip has been deployed and its locality and fault tolerance properties verified over a real widearea network. 1
Expanders via random spanning trees
 In SODA
, 2009
"... Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any boundeddegree nvertex graph, the union of two random spanning trees approximates the expansion of every cut of the graph to with ..."
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Cited by 14 (0 self)
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Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any boundeddegree nvertex graph, the union of two random spanning trees approximates the expansion of every cut of the graph to within a factor of O(log n). For the random graph Gn,p, for p = Ω(log n/n), we give a randomized algorithm for constructing two spanning trees whose union is an expander. This is suggested by the case of the complete graph, where we prove that two random spanning trees give an expander. The construction of the splicer is elementary; each spanning tree can be produced independently using an algorithm by Aldous and Broder: A random walk in the graph with edges leading to previously unvisited vertices included in the tree. Splicers also turn out to have applications to graph cutsparsification where the goal is to approximate every cut using only a small subgraph of the original graph. For random graphs, splicers provide simple algorithms for sparsifiers of size O(n) that approximate every cut to within a factor of O(log n). 1
Compact Routing in PowerLaw Graphs
"... Abstract. We adapt the compact routing scheme by Thorup and Zwick to optimize it for powerlaw graphs. We analyze our adapted routing scheme based on the theory of unweighted random powerlaw graphs with fixed expected degree sequence by Aiello, Chung, and Lu. Our result is the first theoretical bou ..."
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Cited by 14 (3 self)
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Abstract. We adapt the compact routing scheme by Thorup and Zwick to optimize it for powerlaw graphs. We analyze our adapted routing scheme based on the theory of unweighted random powerlaw graphs with fixed expected degree sequence by Aiello, Chung, and Lu. Our result is the first theoretical bound coupled to the parameter of the powerlaw graph model for a compact routing scheme. In particular, we prove that, for stretch 3, instead of routing tables with Õ(n 1/2) bits as in the general scheme by Thorup and Zwick, expected sizes of O(n γ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n 1+γ log n), with γ = τ−2 + ε, where τ ∈ (2, 3) 2τ−3 is the powerlaw exponent and ε> 0. Both bounds also hold with probability at least 1 − 1/n (independent of ε). The routing scheme is a labeled scheme, requiring a stretch5 handshaking step and using addresses and message headers with O(log n log log n) bits, with probability at least 1−o(1). We further demonstrate the effectiveness of our scheme by simulations on realworld graphs as well as synthetic powerlaw graphs. With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick for stretch 3 and obtain a new upper bound of expected Õ(n1+γ) for space and preprocessing. 1
Compact Routing on Power Law Graphs with Additive Stretch
"... We present a universal routing scheme for unweighted, undirected networks that always routes a packet along a path whose length is at most an additive factor of d more than opt (where opt is the length of an optimal path), using O(e log² n)bit local routing tables and packet addresses, with d and e ..."
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Cited by 13 (0 self)
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We present a universal routing scheme for unweighted, undirected networks that always routes a packet along a path whose length is at most an additive factor of d more than opt (where opt is the length of an optimal path), using O(e log² n)bit local routing tables and packet addresses, with d and e parameters of the network topology. For powerlaw random graphs, we demonstrate experimentally that d and e take on small values. The ThorupZwick universal multiplicative stretch 3 scheme has recently been suggested for routing on the Internet interAS graph; we argue, based on the results in this paper, that it is possible to improve worstcase performance on this graph by directly exploiting its powerlaw topology.