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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 ..."
Abstract

Cited by 223 (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.
Deterministic Broadcasting in Unknown Radio Networks
, 2000
"... We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and nod ..."
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Cited by 76 (26 self)
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We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes are completely ignorant of the network: they know neither its topology, nor size, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. We study the time of deterministic broadcasting under this total ignorance scenario. Previous research has concentrated on distributed randomized broadcasting algorithms working for unknown networks, and on deterministic offline broadcasting algorithms assuming full knowledge of the radio network. Ours are the first broadcasting algorithms si...
Deterministic Broadcasting in Ad Hoc Radio Networks
, 2002
"... We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and ..."
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Cited by 31 (2 self)
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We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multihop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a lineartime broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary nnode graphs, working in time O(n 11=6 ). Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop ecient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Key words: broadcasting, distributed, deterministic, radio network. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02097 Warszawa, Poland. Email: fchlebus,rytterg@mimuw.edu.pl y Department of Computer Science, The University of Liverpool, Liverpool L69 7ZF, United Kingdom. Email: fleszek,A.M.Gibbons,rytterg@csc.liv.ac.uk z Departement d'Informatique, Universite du Quebec a Hull, Hull, Quebec J8X 3X7, Canada. Email: Andrzej Pelc@uqah.uquebec.ca Research supported in part by NSERC grant OGP 0008136. This research was done during this author's stay at The Un...
Sense of Direction in Distributed Computing
 In 12th International Symposium on Distributed Computing (DISC
, 1998
"... Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this pr ..."
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Cited by 29 (10 self)
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Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this property are still not known; in fact, the ongoing investigations continue to bring new (often surprising) results, to establish unsuspected links with other research and/or application areas, and to pose more questions than they answer. The aim of this paper is to provide a view of the current status of research, describing some of the relevant results, and providing pointers to future research directions. 1 Introduction In its more general formulation, a distributed system is a collection of computational entities communicating by exchanging finite amounts of information, which we shall call messages. The exact nature of the entities (i.e., processors, processes, network nodes, agents,...
Interval Routing Schemes allow Broadcasting with Linear MessageComplexity
, 2000
"... The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we an ..."
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Cited by 11 (4 self)
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The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we answer a longstanding conjecture by showing that compact routing can also help to perform distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows to broadcast with an O(n) messagecomplexity, where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suce to solve leaderelection for any graph labeled by a shortest path interval routing scheme, improving therefore the O(m + n) previous known bound.
Interval Routing Schemes allow Broadcasting with Linear MessageComplexity (Extended Abstract)
, 2000
"... ] Pierre Fraigniaud y Cyril Gavoille z Bernard Mans x ABSTRACT The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required ..."
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] Pierre Fraigniaud y Cyril Gavoille z Bernard Mans x ABSTRACT The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we answer a longstanding conjecture by showing that compact routing can also help to perform distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows to broadcast with an O(n) messagecomplexity, where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suce to solve leaderelection for any graph labeled by a shortest path interval routing scheme, improving therefore the O(m + n) previous known bound. Keywords: Compact routing, Interval routing, Broadcasting, Distributed computing. 1. INTRODUCTION This paper addresses a prob...
DISCRETE APPLIED
, 1991
"... This paper is a survey of existing methods of communication in usual networks. We particularly study the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the star graph, the shuffleexchange graph, and the butterfly graph. Two ..."
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This paper is a survey of existing methods of communication in usual networks. We particularly study the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the star graph, the shuffleexchange graph, and the butterfly graph. Two different models of communication time are analysed, namely the constant model and the linear model. Other constraints like fullduplex or halfduplex links, processorbound, DMAbound or linkbound possibilities are separately studied. For each case we give references, upper bound (algorithms) and lower bounds. We have also proposed improvements or new results when possible. Hopefully, optimal results are not always known and we present a list of open problems. 1.