Compact Routing Schemes for Dynamic Ring Networks

Kriz̧anc, Danny; Luccio, Flaminia L.; Raman, Rajeev

doi:10.1007/s00224-004-1080-z

Cited by 5 publications

(4 citation statements)

References 23 publications

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“…We refer to [15] for a comprehensive treatment of this topic. Another assumption, studied for example in [26,28,35], requires topology changes to be infrequent and spread out over time, so that the system has enough time to recover from a change before the next one occurs. Some of these algorithms use link-reversal [18], an algorithm for maintaining routes in a dynamic topology, as a building block.…”

Section: Related Workmentioning

confidence: 99%

Distributed computation in dynamic networks

Kühn

Lynch

Oshman

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

325

571

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In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages. The model captures mobile networks and wireless networks, in which mobility and interference render communication unpredictable. In contrast to much of the existing work on dynamic networks, we do not assume that the network eventually stops changing; we require correctness and termination even in networks that change continually. We introduce a stability property called T -interval connectivity (for T ≥ 1), which stipulates that for every T consecutive rounds there exists a stable connected spanning subgraph. For T = 1 this means that the graph is connected in every round, but changes arbitrarily between rounds.We show that in 1-interval connected graphs it is possible for nodes to determine the size of the network and compute any computable function of their initial inputs in O(n 2 ) rounds using messages of size O(log n + d), where d is the size of the input to a single node. Further, if the graph is T -interval connected for T > 1, the computation can be sped up by a factor of T , and any function can be computed in O(n + n 2 /T ) rounds using messages of size O(log n + d). We also give two lower bounds on the token dissemination problem, which requires the nodes to disseminate k pieces of information to all the nodes in the network.The T-interval connected dynamic graph model is a novel model, which we believe opens new avenues for research in the theory of distributed computing in wireless, mobile and dynamic networks.

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Section: Related Workmentioning

confidence: 99%

Distributed computation in dynamic networks

Kühn

Lynch

Oshman

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

325

571

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“…In a recent work by Krizanc, Luccio, and Raman, [58], three schemes for dynamic routing on rings with different stretch-space-adaptation trade-offs are constructed. All of the three schemes are dynamic versions of interval routing schemes.…”

Section: Previous Workmentioning

confidence: 99%

Compact routing on internet-like graphs

Krioukov¹,

Fall

Yang

Ieee Infocom 2004

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The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, P k ∼ k −γ . We find that the average stretch is very low and virtually independent of γ. In particular, for the Internet interdomain graph, γ ∼ 2.1, the average stretch is around 1.1, with up to 70% of paths being shortest. 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 4 -node 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 inter-AS graph have values that are very close to the minimums of the average stretch in the d-and σ-directions. This leads us to the discovery of a unique critical quasi-stationary 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 observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution. * dima@krioukov.net † kfall@intel-research.net ‡ yxw@mit.edu RoutingSince the pioneering work by Kleinrock and Kamoun,[55], the trade-off between stretch 1 and the amount of routing information (i.e. memory space) required by a routing scheme has been understood, analyzed, and improved. Many relatively recent "Internet routing architecture" proposals, [16,54], are based on the ideas of [55]. Since [55] was the first work of its type, it is not surprising that naïve routing based on it would generate stretch that is far from optimal. Indeed, the simple calculations presented in Appendix A show that the stretch produced by [55] on the present Internet interdomain graph would be of the order of 10.However, the high value of stretch was not the central problem with [55]. This work along with the works that closely followed it, [56,77], concentrated on optimal hierarchical network clustering (splitting into areas) satisfying a set of assumptions, but no proof of existence of such clustering for generic graphs and no algorithm to find it when it exists were obtained. While several subsequent works tried to overcome these problems, all known hierarchical routing schemes eventually turned out to be inferior with respect to more recent direct routing schemes. 2 In the work by Peleg and Upfal, [76], the trade-off between memory space and stretch for generic 3 networks was rigourously analyzed for the first time. The work contained several issues that were addressed in many publications that followed [76]. One of the issues was that only the total (per network) space was bounded, the local (per node) space was unbounded. Another issue was that the ...

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“…First, it is assumed that the network remains static in each recovery stage. This assumption is often used (e.g., [Kor08,HST12,KLR04,MWV00]) and helps to emphasize the running time aspect of dynamic networks. Also note that we assume that the network is synchronous, but our algorithms will also work in an asynchronous model under the same asymptotic time bounds, using a synchronizer [Pel00,Awe85].…”

Section: Introductionmentioning

confidence: 99%

Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks

Henzinger

Krinninger

Nanongkai

2017

ACM Trans. Algorithms

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We study the problem of maintaining a breadth-rst spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1 + ε)-approximation algorithms whose amortized time (over some number of link changes) is sublinear in D, the maximum diameter of the network.Our technique also leads to a deterministic (1 + ε)-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach [ES81] that is optimal under some assumptions [RZ11, Hen + 15]. Our result is the rst to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed.Complex networks are among the most ubiquitous models of interconnections between a multiplicity of individual entities, such as computers in a data center, human beings in society, and neurons in the human brain. The connections between these entities are constantly changing; new computers are gradually added to data centers, or humans regularly make new friends. These changes are usually local as they are known only to the entities involved. Despite their locality, they could a ect the network globally; a single link failure could result in several routing path losses or destroy the network connectivity. To maintain its robustness, the network has to quickly respond to changes and repair its infrastructure. The study of such tasks has been the subject of several active areas of research, including dynamic, self-healing, and self-stabilizing networks.One important infrastructure in distributed networks is the breadth-rst spanning (BFS) tree [Lyn96, Pel00]. It can be used, for instance, to approximate the network diameter and to provide a communication backbone for broadcast, routing, and control. In this paper, we study the problem of maintaining a BFS tree from a root node on dynamic distributed networks. Our main interest is repairing a BFS tree as fast as possible after each topology change.Model. We model the communication network by the CONGEST model [Pel00], one of the major models of (locality-sensitive) distributed computation. Consider a synchronous network of processors modeled by an undirected unweighted graph G = (V , E), where nodes model the processors and edges model the bounded-bandwidth links between the processors. We let V and E denote the set of nodes and edges of G, respectively, and let s be a speci ed root node. For any node u and , we denote by d G (u, ) the distance between u and in G. The processors (henceforth, nodes) are assumed to have unique IDs of O(log n) bits and in nite computational power. Each node has limited topological knowledge; in particular, it only knows the IDs of its neighbors and knows no other topological information (such as whether its neighbors are linked by an edge or not). The communication is synchronous and occurs in discrete pulses, calle...

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Compact Routing Schemes for Dynamic Ring Networks

Cited by 5 publications

References 23 publications

Distributed computation in dynamic networks

Distributed computation in dynamic networks

Compact routing on internet-like graphs

Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks

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