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51
Distributed Data Location in a Dynamic Network
 IN PROC. OF ACM SPAA
, 2002
"... Modern networking applications replicate data and services widely, leading to a need for locationindependent routing  the ability to route queries directly to objects using names that are independent of the objects' physical locations. Two important properties of a routing infrastructure are ..."
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Cited by 20 (4 self)
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Modern networking applications replicate data and services widely, leading to a need for locationindependent routing  the ability to route queries directly to objects using names that are independent of the objects' physical locations. Two important properties of a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be achieved with an efficient solution to the nearestneighbor problem. We present a new distributed algorithm that can solve the nearestneighbor problem for a restricted metric space. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton, Rajaraman, and Richa [16].
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 (8 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).
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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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).
Treedecompositions with bags of small diameter
, 2007
"... This paper deals with the length of a Robertson–Seymour’s treedecomposition. The treelength of a graph is the largest distance between two vertices of a bag of a treedecomposition, minimized over all treedecompositions of the graph. The study of this invariant may be interesting in its own right ..."
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Cited by 19 (1 self)
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This paper deals with the length of a Robertson–Seymour’s treedecomposition. The treelength of a graph is the largest distance between two vertices of a bag of a treedecomposition, minimized over all treedecompositions of the graph. The study of this invariant may be interesting in its own right because the class of bounded treelength graphs includes (but is not reduced to) bounded chordality graphs (like interval graphs, permutation graphs, ATfree graphs, etc.). For instance, we show that the treelength of any outerplanar graph is ⌈k/3⌉, where k is the chordality of the graph, and we compute the treelength of meshes. More fundamentally we show that any algorithm computing a treedecomposition approximating the treewidth (or the treelength) of an nvertex graph by a factor α or less does not give an αapproximation of the treelength (resp. the treewidth) unless if α = Ω(n 1/5). We complete these results presenting several polynomial time constant approximate algorithms for the treelength. The introduction of this parameter is motivated by the design of compact distance labeling, compact routing tables with nearoptimal route length, and by the construction of sparse additive spanners.
Abouzeid, “Routing in adhoc networks: A theoretical framework with practical implications
 in Proceedings IEEE Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM
, 2005
"... Abstract — In this paper, information theoretic techniques are used to derive analytic expressions for the minimum expected length of control messages exchanged by proactive routing in a twolevel hierarchical ad hoc network. Several entropy measures are introduced and used to bound the memory size ..."
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Cited by 17 (3 self)
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Abstract — In this paper, information theoretic techniques are used to derive analytic expressions for the minimum expected length of control messages exchanged by proactive routing in a twolevel hierarchical ad hoc network. Several entropy measures are introduced and used to bound the memory size necessary for the storage of the routing tables. The entropy rates of the topology sequences are used to bound the communication routing overhead both the interior routing overhead within a cluster and the exterior routing overhead across clusters. A scalability analysis of the routing overheads with regard to the number of nodes and number of clusters is provided under three different network scaling modes. Finally, practical design issues are studied by providing the optimal numbers of clusters that asymptotically minimize (i) the memory requirement for each cluster head; (ii) the total control message routing overhead. I.
Optimal scalefree compact routing schemes in doubling networks
 In ACMSIAM symposium on Discrete algorithms
, 2007
"... We consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value α such that any ball in the network can be covered by at most 2 α balls of half radius. There are two variants of routing scheme design: (i) labeled (namedependent) routing, wh ..."
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Cited by 10 (2 self)
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We consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value α such that any ball in the network can be covered by at most 2 α balls of half radius. There are two variants of routing scheme design: (i) labeled (namedependent) routing, where the designer is allowed to rename the nodes so that the names (labels) can contain additional routing information, e.g. topological information; and (ii) nameindependent routing, which works on top of the arbitrary original node names in the network, i.e. the node names are independent of the routing scheme. In this paper, given any constant ǫ ∈ (0, 1), and an nnode weighted network of low doubling dimension α ∈ O(loglog n), we present • A (1+ǫ)stretch labeled compact routing scheme with ⌈log n⌉bit routing labels, O(log 2 � n/log log n)bit packet headers, andbit routing information at each node; ( 1 ǫ)O(α) log 3 n • A (9 + ǫ)stretch nameindependent compact routing scheme with O(log 2 � n/log log n)bit packet headers, andbit routing information at each node. ( 1 ǫ)O(α) log 3 n In addition, we also prove a lower bound: any nameindependent routing scheme with o(n (ǫ/60)2) bits of storage at each node has stretch no less than 9 −ǫ, for any ǫ ∈ (0, 8). Therefore our nameindependent routing scheme achieves asymptotically optimal stretch with polylogarithmic storage at each node and packet headers. Note that both schemes are scalefree in the sense that their space requirements do not depend on the normalized diameter ∆ of the network. We also present a simpler nonscalefree (9 + ǫ)stretch nameindependent compact routing scheme with improved space requirements if ∆ is polynomial in n. 1
Improved Sparse Covers for Graphs Excluding a Fixed Minor
, 2007
"... We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the γneighborhood of each node. For planar graphs, the cover has radius no more than 24γ − 8 and degree (maximum cluster overlap) no more than ..."
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Cited by 8 (1 self)
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We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the γneighborhood of each node. For planar graphs, the cover has radius no more than 24γ − 8 and degree (maximum cluster overlap) no more than 30. The radius and degree are optimal up to constant factors. For every n node graph that excludes a fixed minor, we present an algorithm that yields a cover with radius no more than 4γ and degree O(log n). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius of O(γ), it was required to have degree polynomial in n. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories and synchronizers, our improved cover construction results in improved algorithms for all these problems, for the class of minorfree graphs.
Geometric routing without geometry
 in 12th Colloquium on Structural Information and Communication Complexity. MontStMichel
, 2005
"... In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On the ..."
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Cited by 6 (2 self)
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In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On theses pseudo coordinates we employ greedy geometric routing. Almost as a side effect, pseudogeometric routing is not restricted to planar unit disk graph networks anymore, but succeeds on general networks. 1
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 polynomiallysized edges, both in the topologyindependent nodename model. 1 These are the first topologyindependent results that apply to routing in directed networks.