We investigate the class of so-called 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 address-oblivious 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

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 single--hop and multihop optical networks. In single--hop 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...

We survey routing problems on fixed-connection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, k-relation 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.

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 NP-hard. In addition, we develop polynomial-time 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.

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 k-ary 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.

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 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

. 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 all-to-all communication problem in wavelength-- division--multiplexing (WDM) routing in all--optical 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...

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. Partially supported by the French-Italian project GALILEO and by the european HCM project MAP. y Work partially supported by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative, and by the French-Italian project GALILEO. 1 Introduction Gossiping (also called total exchange or all--to--all communication) in interconnection networks is the process in which initially each processor has an item of information that must be distributed to e...

. Gossiping (also called total exchange or all-to-all communication) 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 here gossiping in the store-and-forward, fullduplex and \Delta-port (or shouting) model. In such a model, the protocol consists of a sequence of rounds and during each round, each node can send (and receive) messages from all its neighbors. The great majority of the previous works on gossiping problems allows the messages to be freely concatenated and so messages of arbitrary length can be transmitted during a round. Here we restrict the problem to the case where at each round communicating nodes can exchange exactly one packet. We give a lower bound of N \Gamma1 ffi , where ffi is the minimum degree, and show that it is attained in Cayley symmetric digraphs with some additional properties. That implies the existence of an optimal gossiping protocol for clas...

This paper continues with the study of the communication modes introduced in [J. Hromkovic, R. Klasing, E.A. St¨ohr, "Dissemination of Information in Vertex-Disjoint Paths Mode, Part 1: General Bounds and Gossiping in Hypercube-Like Networks", submitted to Information and Computation. (Extended abstract presented at WG'93.)] as a generalization of the standard one-way and two-way modes allowing to send messages between processors of interconnection networks via vertex-disjoint paths in one communication step. The complexity of communication algorithms is measured by the number of communication steps (rounds). Here, the complexity of gossiping in grids and in planar graphs is investigated. The main results are the following: 1. Effective one-way and two-way gossip algorithms for d-dimensional grids, d 2, are designed. 2. The lower bound 2 log 2 n \Gamma log 2 k \Gamma log 2 log 2 n \Gamma 2 is established on the number of rounds of every two-way gossip algorithm working on any graph...