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.

In this paper, we address the problem of gathering information in a specific node (or sink) of a radio network, where interference constraints are present. We take into account the fact that, when a node transmits, it produces interference in an area bigger than the area in which its message can actually be received. The network is modeled by a graph; a node is able to transmit one unit of information to the set of vertices at distance at most dT in the graph, but when doing so it generates interference that does not allow nodes at distance up to dI (dI ≥ dT) to listen to other transmissions. Time is synchronous and divided into time-steps in each of which a round (set of non-interfering radio transmissions) is performed. We give general lower bounds on the number of rounds required to gather into a sink of a general graph, and present an algorithm working on any graph, with an approximation factor of 4. We also show that the problem of finding an optimal strategy for gathering is NP-hard, for any values of dI and dT. If dI> dT, we show that the problem remains hard when restricted to the uniform case where each vertex in the network has exactly one piece of information to communicate to the sink. 1

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...

We study the problem of gathering information from the nodes of a radio network into a central destination node. A transmission can be received by a node if it is sent from a distance of at most dT and there is no interference from other transmissions. One transmission interferes with the reception of another transmission if the sender of the first transmission is at distance dI or less from the receiver of the second transmission. In this paper we study the case dT = 1 and dI> 1 for two-dimensional grid networks with unit time transmissions. We prove lower bounds on the number of rounds required for any two-dimensional grid and we describe protocols for n × n grids with n odd that are optimal for odd dI and near-optimal for even dI.

The problems of gossiping and broadcasting have been widely studied. The basic gossip problem is defined as follows: there are n individuals, with each individual having an item of gossip. The goal is to communicate each item of gossip to every other individual.

We give a polynomial-time O( log n log OPT)-approximation algorithm for minimum-time broadcast and minimum-time multicast in n-node networks under the single-port vertex-disjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n) lower bound for the approximation ratio of the minimum-time multicast problem in directed networks. This lower bound holds unless NP Dtime(n log log n). An important consequence of this latter result is that the Steiner version of the Minimum Degree Spanning Tree (MDST) problem in digraphs cannot be approximated within a constant ratio, as opposed to the undirected version. Finally, we give a polynomial-time O(1)-approximation algorithm for minimumtime gossip (i.e., all-to-all broadcast).

In the gossiping problem, each node in a network possesses a token initially; after gossiping, every node has a copy of every other node's token. The nodes exchange their tokens by packets. A solution to the problem is judged by how many rounds of packet sending it requires. In this paper, we consider the version of the problem in which a packet is of limited size (a packet can hold up to p tokens), the links (edges) of the network are half-duplex (only one packet can flow through a link at a time), and the nodes are all-port (a node's incident edges can all be active at the same time). This is also known as the H* model. We study the path and the cycle which are essential building blocks for more complex structures. We present tight lower bounds and matching algorithms. The results also lead to the conclusion that p = 2 is the optimal packet size. 1 Introduction In parallel and distributed computing, communication among the processors is an important issue. Gossiping, also known a...

This paper considers the problem of gossiping with packets of limited size in a network with cost function. We show that the problem of determining the minimum cost necessary to perform gossiping among a given set of participants with packets of limited size is NP-hard. We also give an approximate (with respect to the cost) gossiping algorithm. The ratio between the cost of an optimal algorithm and the approximate one is less than 1+2(k \Gamma 1)=n, were n is the number of nodes participating to the gossiping process and k n \Gamma 1 is the upper bound on the number of individual blocks of information that a packet can carry. We also analyze the communication time and communication complexity, i.e., the product of the communication cost and time, of gossiping algorithms.

This paper considers problems of fault--tolerant information diffusion in a network with cost function. We show that the problem of determining the minimum cost necessary to perform fault-- tolerant gossiping among a given set of participants is NP-hard and give approximate (with respect to the cost) fault-tolerant gossiping algorithms. We also analyze the communication time and communication complexity of fault-tolerant gossiping algorithms. Finally, we give an optimal cost fault tolerant broadcasting algorithm and apply our results to the atomic commitment problem. Key Words: Communication Networks, Gossiping, Atomic Commitment, Fault--Tolerance. Research partially supported by the Italian Ministry of University and of Scientific Research in the framework of the "Algoritmi, Modelli di Calcolo e Strutture Informative" project. 1 Introduction In this paper we study the problems of fault--tolerant broadcasting, gossiping, and atomic commitment in a weighted network. Gossiping in ...