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101
Randomized rumor spreading
 In IEEE Symposium on Foundations of Computer Science
, 2000
"... We investigate the class of socalled epidemic algorithms that are commonly used for the lazy transmission of updates to distributed copies of a database. These algorithms use a simple randomized communication mechanism to ensure robustness. Suppose players communicate in parallel rounds in each of ..."
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Cited by 201 (1 self)
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We investigate the class of socalled epidemic algorithms that are commonly used for the lazy transmission of updates to distributed copies of a database. These algorithms use a simple randomized communication mechanism to ensure robustness. Suppose players communicate in parallel rounds in each of which every player calls a randomly selected communication partner. In every round, players can generate rumors (updates) that are to be distributed among all players. Whenever communication is established between two players, each one must decide which of the rumors to transmit. The major problem (arising due to the randomization) is that players might not know which rumors their partners have already received. For example, a standard algorithm forwarding each rumor from the calling to the called players for rounds needs to transmit the rumor times in order to ensure that every player finally receives the rumor with high probability. We investigate whether such a large communication overhead is inherent to epidemic algorithms. On the positive side, we show that the communication overhead can be reduced significantly. We give an algorithm using only transmissions and rounds. In addition, we prove the robustness of this algorithm, e.g., against adversarial failures. On the negative side, we show that any addressoblivious algorithm (i.e., an algorithm that does not use the addresses of communication partners) needs to send messages for each rumor regardless of the number of rounds. Furthermore, we give a general lower bound showing that time and communicationoptimality cannot be achieved simultaneously using random phone calls, that is, every algorithm that distributes a rumor
Methods and problems of communication in usual networks
, 1994
"... 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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Cited by 110 (11 self)
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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.
Efficient Collective Communication in Optical Networks
 In Proc. of ICALP 96
"... This paper studies the problems of broadcasting and gossiping in optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wav ..."
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Cited by 51 (9 self)
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This paper studies the problems of broadcasting and gossiping in optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. In this paper we consider both singlehop and multihop optical networks. In singlehop networks the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high speed communication. In multi hop networks a packet may have to be routed through a few intermediate nodes before reaching its final destination. In both models, we give efficient broadcasting and gossiping algorithms, in terms of time and number of wavelengths. We consider both networks with arbitrary topologies and particular networks of practical interest. Several of our algorithms exhibit optimal performances. 1 Introduction Motivations. Op...
Algorithms for Data Migration with Cloning
, 2003
"... Our work is motivated by the problem of managing data on storage devices, typically a set of disks. Such high demand storage servers are used as web servers, or multimedia servers for handling high demand for data. As the system is running, it needs to dynamically respond to changes in demand for di ..."
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Cited by 33 (4 self)
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Our work is motivated by the problem of managing data on storage devices, typically a set of disks. Such high demand storage servers are used as web servers, or multimedia servers for handling high demand for data. As the system is running, it needs to dynamically respond to changes in demand for di#erent data items. In this work we study the data migration problem, which arises when we need to quickly change one storage configuration into another. We show that this problem is NPhard. In addition, we develop polynomialtime approximation algorithms for this problem and prove a worst case bound of 9.5 on the approximation factor achieved by our algorithm. We also compare the algorithm to several heuristics for this problem.
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 31 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
Distributed Computation in Dynamic Networks
, 2009
"... In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worstcase 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 rou ..."
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Cited by 31 (8 self)
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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 worstcase 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 allows the study of the fundamental computation power of dynamic networks. In particular, it 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
Fast Gossiping by Short Messages
, 1995
"... Gossiping is the process of information diffusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed numbe ..."
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Cited by 26 (10 self)
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Gossiping is the process of information diffusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed number p of packets at each round. In the first part of the paper we study the extremal case p = 1 and we exactly determine the optimal number of communication rounds to perform gossiping for several classes of graphs, including Hamiltonian graphs and complete kary trees. For arbitrary graphs we give asymptotically matching upper and lower bounds. We also study the case of arbitrary p and we exactly determine the optimal number of communication rounds to perform gossiping under this hypothesis for complete graphs, hypercubes, rings, and paths. Finally, we investigate the problem of determining sparse networks in which gossiping can be performed in the minimum possible number of rounds.
Parsimonious flooding in dynamic graphs
 In Proc. of 28th Symp. on Principles of Distributed Computing (PODC
, 2009
"... An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi e ..."
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Cited by 15 (1 self)
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An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi et al. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time — flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t ′> t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Clementi et al. Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we al! so show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is kactive if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the kactive flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show A part of this work was done during the stay of the second
Optimal Sequential Gossiping by Short Messages
 DAMATH: DISCRETE APPLIED MATHEMATICS AND COMBINATORIAL OPERATIONS RESEARCH AND COMPUTER SCIENCE, VOL 86
, 1998
"... Gossiping is the process of information diffusion in which each node of a network holds a block that must be communicated to all the other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed nu ..."
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Cited by 12 (3 self)
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Gossiping is the process of information diffusion in which each node of a network holds a block that must be communicated to all the other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed number p of blocks during each call. We study the minimum numbers of call necessary to perform gossiping among n processor for any arbitrary fixed upper bound on the message size p.
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
, 1997
"... . Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T , so that no two paths of the same colour use the same arc of T , is equal to the maximum number ..."
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Cited by 12 (1 self)
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. Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T , so that no two paths of the same colour use the same arc of T , is equal to the maximum number of paths passing through an arc of T . This result is applied to solve the alltoall communication problem in wavelength divisionmultiplexing (WDM) routing in alloptical networks, that is, we give an efficient algorithm to optimally assign wavelengths to the all the paths of a tree network. It is known that the problem of colouring a general subset of all possible paths in a symmetric directed tree is an NPhard problem. We study conditions for a given set S of paths be coloured efficiently with the minimum possible number of colours/wavelengths. 1 Introduction Let T be a tree and x; y two vertices of T . The dipath P (x; y) in T is the undirected path joining x to y, in which each ed...