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22
Hardness and approximation of gathering in static radio networks
 Parallel Processing Letters
, 2006
"... 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 act ..."
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Cited by 35 (7 self)
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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 timesteps in each of which a round (set of noninterfering 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 NPhard, 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
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.
Efficient gathering in radio grids with interference
 In Septièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel’05
, 2005
"... 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 ..."
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Cited by 14 (5 self)
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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 twodimensional grid networks with unit time transmissions. We prove lower bounds on the number of rounds required for any twodimensional grid and we describe protocols for n × n grids with n odd that are optimal for odd dI and nearoptimal for even dI.
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 14 (4 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.
Gossiping in Cayley Graphs by Packets
 In Conf. CCS95 (8 th FrancoJapanese and 4 th FrancoChinese Conf. Combin. Comput. Sci
, 1995
"... . Gossiping (also called total exchange or alltoall 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 storeandforward, fullduplex and \Deltaport (o ..."
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Cited by 12 (5 self)
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. Gossiping (also called total exchange or alltoall 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 storeandforward, fullduplex and \Deltaport (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...
On Generalized Gossiping and Broadcasting
 in Proceedings of the 11th Annual European Symposium on Algorithms (ESA), Lecture Notes in Comput. Sci. 2832
, 2003
"... 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. ..."
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Cited by 5 (1 self)
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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.
Approximation algorithms for minimumtime broadcast under the vertexdisjoint paths mode
 In 9th Annual European Symposium on Algorithms (ESA '01), volume 2161 of LNCS
, 2001
"... We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n) lower ..."
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Cited by 4 (1 self)
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We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint 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 minimumtime 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 polynomialtime O(1)approximation algorithm for minimumtime gossip (i.e., alltoall broadcast).
Implementing atomic data through indirect learning in dynamic networks
, 2006
"... Developing middleware services for dynamic distributed systems, e.g., adhoc networks, is a challenging task given that such services deal with dynamically changing membership and asynchronous communication. Algorithms developed for static settings are often not usable in such settings because they ..."
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Cited by 4 (2 self)
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Developing middleware services for dynamic distributed systems, e.g., adhoc networks, is a challenging task given that such services deal with dynamically changing membership and asynchronous communication. Algorithms developed for static settings are often not usable in such settings because they rely on (logical) alltoall node connectivity through routing protocols, which may be unfeasible or prohibitively expensive to implement in highly dynamic settings. This paper explores the indirect learning, via periodic gossip, approach to information dissemination within a dynamic, distributed data service implementing atomic read/write memory service. The indirect learning scheme is used to improve the liveness of the service in the settings with uncertain connectivity. The service is formally proved to guarantee atomicity in all executions. Conditional performance analysis of the new service is presented, where this analysis has the potential of being generalized to other similar dynamic algorithms. Under the assumption that the network is connected, and assuming reasonable timing conditions, the bounds on the duration of read/write operations of the new service are calculated. Finally, the paper proposes a deployment strategy where indirect learning leads to an improvement in communication costs relative to a previous solution that assumes alltoall connectivity. 1
Lower Bounds on the Broadcasting and Gossiping Time of Restricted Protocols
 SIAM JOURNAL ON DISCRETE MATHEMATICS
, 1999
"... In this paper we extend the technique provided in [6] to allow the determination of lower bounds on the broadcasting and gossiping time required by the socalled "restricted" protocols. Informally, a protocol is (i, o)restricted at a given processor if every outgoing activation of an arc depends on ..."
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Cited by 3 (1 self)
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In this paper we extend the technique provided in [6] to allow the determination of lower bounds on the broadcasting and gossiping time required by the socalled "restricted" protocols. Informally, a protocol is (i, o)restricted at a given processor if every outgoing activation of an arc depends on at most i previous incoming activations and any incoming activation influences at most o successive outgoing activations. Examples of restricted protocols are those running on bounded degree networks or systolic. We thus derive improved lower bounds on the broadcasting time in several wellknown networks, such as Butterfly, de Bruijn and Kautz graphs. Moreover, we derive the first general lower bound on the gossiping time of dbounded degree networks in the directed and halfduplex cases. Improved lower bounds on gossiping are also obtained for Butterfly, de Bruijn and Kautz graphs. Finally, as a corollary we obtain the same lower bounds on ssystolic protocols obtained in [6]. All the ...
Optimal Gossiping in Paths and Cycles
, 1997
"... 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 consid ..."
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Cited by 2 (2 self)
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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 halfduplex (only one packet can flow through a link at a time), and the nodes are allport (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...