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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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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
Scalable routing easy as pie: A practical isometric embedding protocol
 in Network Protocols (ICNP), 2011 19th IEEE International Conference on, 2011
"... We present PIE, a scalable routing scheme that achieves 100 % packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which ena ..."
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We present PIE, a scalable routing scheme that achieves 100 % packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internetlike graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable stateoftheart algorithms: PIE always finds short paths and often enough finds the shortest paths. Abstract — 1 I.
The workshop on Internet topology (WIT) report
 Computer Communication Review
"... Internet topology analysis has recently experienced a surge of interest in computer science, physics, and the mathematical sciences. However, researchers from these different disciplines tend to approach the same problem from different angles. As a result, the field of Internet topology analysis and ..."
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Internet topology analysis has recently experienced a surge of interest in computer science, physics, and the mathematical sciences. However, researchers from these different disciplines tend to approach the same problem from different angles. As a result, the field of Internet topology analysis and modeling must untangle sets of inconsistent findings, conflicting claims, and contradicting statements. On May 1012, 2006, CAIDA hosted the Workshop on Internet topology (WIT). By bringing together a group of researchers spanning the areas of computer science, physics, and the mathematical sciences, the workshop aimed to improve communication across these scientific disciplines, enable interdisciplinary crossfertilization, identify commonalities in the different approaches, promote synergy where it exists, and utilize the richness that results from exploring similar problems from multiple perspectives. This report describes the findings of the workshop, outlines a set of relevant open research problems identified by participants, and concludes with recommendations that can benefit all scientific communities interested in Internet topology research.
A compact routing scheme and approximate distance oracle for powerlaw graphs
, 2009
"... Abstract. Compact routing addresses the tradeoff between table sizes and stretch, which is the worstcase ratio between the length of the path a packet is routed through by the scheme and the length of a shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwic ..."
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Abstract. Compact routing addresses the tradeoff between table sizes and stretch, which is the worstcase ratio between the length of the path a packet is routed through by the scheme and the length of a shortest path from source to destination. 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(n1/2) 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 2τ−3 + ε, where τ ∈ (2, 3) is the powerlaw exponent and ε> 0 (which implies ε < γ < 1/3 + ε). 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 for random powerlaw graphs. 1
Sparse spanners vs. compact routing
 IN: SPAA
, 2011
"... Routing with multiplicative stretch 3 (which means that the path used by the routing scheme can be up to three times longer than a shortest path) can be done with routing tables of ˜ Θ (√n) bits 1 per node. The space lower bound is due to the existence of dense graphs with large girth. Dense graphs ..."
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Cited by 5 (2 self)
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Routing with multiplicative stretch 3 (which means that the path used by the routing scheme can be up to three times longer than a shortest path) can be done with routing tables of ˜ Θ (√n) bits 1 per node. The space lower bound is due to the existence of dense graphs with large girth. Dense graphs can be sparsified to subgraphs, called spanners, with various stretch guarantees. There are spanners with additive stretch guarantees (some even have constant additive stretch) but only very few additive routing schemes are known. In this paper, we give reasons why routing in unweighted graphs with additive stretch is difficult in the form of space lower bounds for general graphs and for planar graphs. We prove that any routing scheme using routing tables of size µ bits per node and addresses of polylogarithmic length has additive stretch ˜ Ω ( p n/µ) for general graphs, and ˜ Ω ( √ n/µ) for planar graphs, respectively. Routing with tables of size Õ(n1/3) thus requires a polynomial additive stretch of ˜Ω(n 1/3), whereas spanners with average degree O(n 1/3) and constant additive stretch exist for all graphs. Spanners, however sparse they are, do not tell us how to route. These bounds provide the first separation of sparse spanner problems and compact routing problems. On the positive side, we give an almost tight upper bound: we present the first nontrivial compact routing scheme with o(lg 2 n)bit addresses, additive stretch Õ(n1/3), and table size Õ(n1/3) bits for all graphs with linear local treewidth such as planar, boundedgenus, and apexminorfree graphs.
ShortestPath Queries for Complex Networks: Exploiting Low Treewidth Outside the Core
"... We present new and improved methods for efficient shortestpath query processing. Our methods are tailored to work for two specific classes of graphs: graphs with small treewidth and complex networks. Seemingly unrelated at first glance, these two classes of graphs have some commonalities: complex ne ..."
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We present new and improved methods for efficient shortestpath query processing. Our methods are tailored to work for two specific classes of graphs: graphs with small treewidth and complex networks. Seemingly unrelated at first glance, these two classes of graphs have some commonalities: complex networks are known to have a core–fringe structure with a dense core and a treelike fringe. Our main contributions are efficient algorithms and data structures on three different levels. First, we provide two new methods for graphs with small but not necessarily constant treewidth. Our methods achieve new tradeoffs between space and query time. Second, we present an improved treedecompositionbased method for complex networks, utilizing the methods for graphs with small treewidth. Third, we extend our method to handle the highly interconnected core with existing exact and approximate methods. We evaluate our algorithms both analytically and experimentally. We prove that our algorithms for lowtreewidth graphs achieve improved tradeoffs between space and query time. Our experiments on several realworld complex networks further confirm the efficiency of our methods: Both the exact and the hybrid method have faster preprocessing and query times than existing methods. The hybrid method in particular provides an improved tradeoff between space and accuracy.
Evaluating Compact Routing Algorithms on RealWorld Networks
, 2010
"... Compact routing has shown promise for reducing the forwarding state in Internetlike graphs, without badly impacting traffic flows. This dissertation compares two such compact routing algorithms on real Internet snapshots from router data across 12 years. The results indicate that these algorithms be ..."
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Cited by 4 (1 self)
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Compact routing has shown promise for reducing the forwarding state in Internetlike graphs, without badly impacting traffic flows. This dissertation compares two such compact routing algorithms on real Internet snapshots from router data across 12 years. The results indicate that these algorithms behave consistently over time, and exhibit extremely small forwarding tables with very low path inflation. Acknowledgements Colin Perkins and Stephen Strowes for their support, feedback, discussions, helpful pointers, field trips, anecdotes, and, of course, the initial idea for this project. The departmental support staff for their help through out the year with machine upkeep, and allowing access to copious amounts of server space, hard drives, and docks; their assistance was invaluable. The Embedded, Networked and Distributed Systems group for their help and support through out. The Algorithms group for sanity checking any graph theory and algorithms I produced. My fellow MSci and MRes students for their company, help, and generally making this year bearable. Finally, the Level 4 and 3 students for their patience while I stole their CPU cycles, RAM modules, and hard drive space. ii 5.2.3 Routing............................. 29 5.3 Summary................................ 29 6 BradyCowen (BC) compact routing 30
Memoryassisted universal compression of network flows
 in IEEE INFOCOM
, 2012
"... Abstract—Recently, the existence of considerable amount of redundancy in the Internet traffic has stimulated the deployment of several redundancy elimination techniques within the network. These techniques are often based on either packetlevel Redundancy Elimination (RE) or ContentCentric Network ..."
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Abstract—Recently, the existence of considerable amount of redundancy in the Internet traffic has stimulated the deployment of several redundancy elimination techniques within the network. These techniques are often based on either packetlevel Redundancy Elimination (RE) or ContentCentric Networking (CCN). However, these techniques cannot exploit subpacket redundancies. Further, other alternative techniques such as the endtoend universal compression solutions would not perform well either over the Internet traffic, as such techniques require infinite length traffic to effectively remove redundancy. This paper proposes a memoryassisted universal compression technique that holds a significant promise for reducing the amount of traffic in the networks. The proposed work is based on the observation that if a source is to be compressed and sent over a network, the associated universal code entails a substantial overhead in transmission
Harnessing Internet topological stability in ThorupZwick compact routing
 In Proc. IEEE Infocom
, 2012
"... Abstract—ThorupZwick (TZ) compact routing guarantees sublinear state growth with the size of the network by routing via landmarks and incurring some path stretch. It uses a pseudorandom landmark selection designed for static graphs, and unsuitable for Internet routing. We propose a landmark select ..."
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Abstract—ThorupZwick (TZ) compact routing guarantees sublinear state growth with the size of the network by routing via landmarks and incurring some path stretch. It uses a pseudorandom landmark selection designed for static graphs, and unsuitable for Internet routing. We propose a landmark selection algorithm for the Internet AS graph that uses kshells decomposition to choose landmarks. Using snapshots of the AS graph from 1997–2010, we demonstrate that the ASes in the kmaxshell are highlystable over time, and form a sufficient landmark set for TZ routing in the overwhelming majority of cases (in the remainder, adding the next kshell suffices). We evaluate path stretch and forwarding table sizes, and show that these landmark sets retain low average path stretch with tiny forwarding tables, but are better suited to the dynamic nature of the AS graph than the original TZ landmark selection algorithm. I.