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117
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 256 (13 self)
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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 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 such distance information to build a virtual distance map of the Internet and estimate the distance between any pair of IP addresses. We present our solutions to the measurement server placement and distance map construction problems in IDMaps. We show that IDMaps can indeed provide useful distance estimations to applications such as closestmirror selection. 1 Keywords: network service, distributed algorithms, scalability, modeling. 1
A quantitative comparison of graphbased models for internet topology
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly ..."
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Cited by 222 (3 self)
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Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly generated topologies. While many researchers rely upon graphs for analytic and simulation studies, there has been little analysis of the implications of using a particular model, or how the graph generation method may a ect the results of such studies. Further, the selection of one generation method over another is often arbitrary, since the differences and similarities between methods are not well understood. This paper considers the problem of generating and selecting graph models that reflect the properties of real internetworks. We review generation methods in common use, and also propose several new methods. We consider a set of metrics that characterize the graphs produced by a method, and we quantify similarities and differences amongst several generation methods with respect to these metrics. We also consider the effect of the graph model in the context of a speciffic problem, namely multicast routing.
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
Approximating a Finite Metric by a Small Number of Tree Metrics
 In Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science
, 1998
"... Bartal [4, 5] gave a randomized polynomial time algorithm that given any n point metric G, constructs a tree T such that the expected stretch (distortion) of any edge is at most O(log n log log n). His result has found several applications and in particular has resulted in approximation algorithms f ..."
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Cited by 82 (10 self)
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Bartal [4, 5] gave a randomized polynomial time algorithm that given any n point metric G, constructs a tree T such that the expected stretch (distortion) of any edge is at most O(log n log log n). His result has found several applications and in particular has resulted in approximation algorithms for many graph optimization problems. However approximation algorithms based on his
New Sparseness Results on Graph Spanners
, 1992
"... Let G = (V, E) be an nvertex connected graph with positive edge weights. A subgraph G ’ = (V, E’) is a tspanner of G if for all u, v E V, the weighted distance between u and v in G ’ is at most t times the weighted distance between u and v in G. We consider the problem of constructing sparse span ..."
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Cited by 79 (8 self)
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Let G = (V, E) be an nvertex connected graph with positive edge weights. A subgraph G ’ = (V, E’) is a tspanner of G if for all u, v E V, the weighted distance between u and v in G ’ is at most t times the weighted distance between u and v in G. We consider the problem of constructing sparse spanners. Sparseness of spanners is measured by two criteria, the size, defined as the number of edges in the spanner, and the weight, defined as the sum of the edge weights in the spanner. In this paper, we concentrate on constructing spanners of small weight. For an arbitrary positive edgeweighted graph G, for any t> 1, and any c>0, we show that a tspanner of G with weight O(n * ). wt(MST) can be constructed in polynomial time. We also show that (logz n)spanners of weight O(1). wt(MST) can be constructed. We then consider spanners for complete graphs induced by a set of points in ddimensional real normed space. The weight of an edge Zy is the norm of the ~y vector. We show that for these graphs, tspanners with total weight O(log n). wt(MST) can be constructed in polynomial time.
Implicit Representation of Graphs
 SIAM Journal On Discrete Mathematics
, 1992
"... How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place h ..."
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Cited by 71 (0 self)
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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place holders to allow data on the edges to encode the structure of the graph. In our scenario, there is no such waste. By assigning O(log n) bit labels to the vertices, we completely encode the structure of the graph, so that given the labels of two vertices we can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the vertices, we can find structure coding labels (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex induced universal graphs of polynomial size. For example, we can label planar graphs with structure coding labels of size ! 4 log n, which implies the existence of a graph with n 4 vertices that contains all nvertex planar graphs as vertex induced subgraphs.
On the Fundamental Tradeoffs between Routing Table Size and Network Diameter in PeertoPeer Networks
, 2003
"... In this work, we study a fundamental tradeoff issue in designing distributed hash table (DHT) in peertopeer networks: the size of the routing table v.s. the network diameter. It was observed by Ratnasamy et al. that existing DHT schemes either (a) have a routing table of size O(log2n) and network ..."
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Cited by 65 (2 self)
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In this work, we study a fundamental tradeoff issue in designing distributed hash table (DHT) in peertopeer networks: the size of the routing table v.s. the network diameter. It was observed by Ratnasamy et al. that existing DHT schemes either (a) have a routing table of size O(log2n) and network diameter of #(log2n), or (b) have a routing table of size d and network diameter of #(n ). They asked whether this represents the best asymptotic "stateefficiency" tradeoffs. Our first major result is to show that there are straightforward routing algorithms which achieve better asymptotic tradeoffs. However, such algorithms all cause severe congestion on certain network nodes, which is undesirable in a P2P network. We then rigorously define the notion of "congestion" and conjecture that the above tradeoffs are asymptotically optimal for a congestionfree network. In studying this conjecture, we have thoroughly clarified the role that "congestionfree " plays in this "stateefficiency" tradeoff. Our second major result is to prove that the aforementioned tradeoffs are asymptotically optimal for uniform algorithms. Furthermore, for uniform algorithms, we find that the routing table size of #(log2n) is a magic threshold point that separates two different "stateefficiency" regions. Our third and final result is to study the exact (instead of asymptotic) optimal tradeoffs for uniform algorithms. We propose a new routing algorithm that reduces the routing table size and the network diameter of Chord both by 21.4% without introducing any other protocol overhead, based on a novel numbertheoretical technique.
Bypassing the embedding: Algorithms for lowdimensional metrics
 In Proceedings of the 36th ACM Symposium on the Theory of Computing (STOC
, 2004
"... The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into l ..."
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Cited by 64 (4 self)
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The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into low dimensional Euclidean spaces, they would inherit several algorithmic and structural properties of the Euclidean spaces. Unfortunately however, such a restriction on dimension does not suffice to guarantee embeddibility in a normed space. In this paper we explore the option of bypassing the embedding. In particular we show the following for low dimensional metrics: • Quasipolynomial time (1+ɛ)approximation algorithm for various optimization problems such as TSP, kmedian and facility location. • (1 + ɛ)approximate distance labeling scheme with optimal label length. • (1+ɛ)stretch polylogarithmic storage routing scheme.
SpaceEfficiency for Routing Schemes of Stretch Factor Three
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1997
"... We deal with routing algorithms on arbitrary nnode networks. A routing algorithm is a deterministic distributed algorithm which routes messages from any source to any destination. It includes not only the classical routing tables, but also the routing algorithm that generates paths with loops. Our ..."
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Cited by 63 (6 self)
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We deal with routing algorithms on arbitrary nnode networks. A routing algorithm is a deterministic distributed algorithm which routes messages from any source to any destination. It includes not only the classical routing tables, but also the routing algorithm that generates paths with loops. Our goal is to design routing algorithms which minimize, for each router of the network, the amount of routing information that needs to be stored by the router in order to implement its own local routing algorithm. So as to simplify the implementation of a routing algorithm, names of the routers can be chosen in advance. We take also into account the efficiency of the routing, i.e., the length of the routing paths. The stretch factor is the maximum ratio, taken over all sourcedestination pairs, between the length of the paths computed by the routing algorithm and the distance between the source and the destination. We show that there exists an nnode network on which every routing algorithm o...
Tree spanners
 SIAM J. Discrete Math
, 1995
"... A tree tspanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most t times their distance in G. This notion is motivated by applications in communication networks, distributed systems, and network design. This paper studies graph theoretic, algorithmic ..."
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Cited by 58 (1 self)
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A tree tspanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most t times their distance in G. This notion is motivated by applications in communication networks, distributed systems, and network design. This paper studies graph theoretic, algorithmic and complexity issues about tree spanners. It is shown that a tree 1spanner, if it exists, in a weighted graph with m edges and n vertices is a minimum spanning tree and can be found in O(m log β(m, n)) time, where β(m, n) = min{i  log (i) n ≤ m/n}. On the other hand, for any fixed t> 1, the problem of determining the existence of a tree tspanner in a weighted graph is proven to be NPcomplete. For unweighted graphs, it is shown that constructing a tree 2spanner takes linear time, whereas determining the existence of a tree tspanner is NPcomplete for any fixed t ≥ 4. A theorem which captures the structure of tree 2spanners is presented for unweighted graphs. For digraphs, an O((m+n)α(m, n)) algorithm is provided for