Deterministic broadcasting time with partial knowledge of the network

We consider the time of deterministic broadcasting in networks whose nodes have limited knowledge of network topology. Each node u knows only the part of the network within knowledge radius r from it, i.e., it knows the graph induced by all nodes at distance at most r from u. Apart from that, each node knows the maximum degree Delta of the network. One node of the network, called the source, has a message which has to reach all other nodes. We adopt the widely studied communication model called the one-way model in which, in every round, each node can communicate with at most one neighbor, and in each pair of nodes communicating in a given round, one can only send a message while the other can only receive it. This is the weakest of all store-and-forward models for point-to-point networks, and hence our algorithms work for other models as well, in at most the same time.We show trade-offs between knowledge radius and time of deterministic broadcasting, when the knowledge radius is small, i.e., when nodes are only aware of their close vicinity. While for knowledge radius 0, minimum broadcasting time is theta(e), where e is the number of edges in the network, broadcasting can be usually completed faster for positive knowledge radius. Our main results concern knowledge radius 1. We develop fast broadcasting algorithms and analyze their execution time. We also prove lower bounds on broadcasting time, showing that our algorithms are close to optimal

Lower bounds on systolic gossip

AbstractGossiping is an extensively investigated information dissemination process in which each processor has a distinct item of information and has to collect all the items possessed by the other processors. In this paper we provide an innovative and general lower bound technique relying on the novel notion of delay digraph of a gossiping protocol and on the use of matrix norm methods. Such a technique is very powerful and allows the determination of new and significantly improved lower bounds in many cases. In fact, we derive the first general lower bound on the gossiping time of systolic protocols, i.e., constituted by a periodic repetition of simple communication steps. In particular, given any network of n processors and any systolic period s, in the directed and the undirected half-duplex cases every s-systolic gossip protocol takes at least log(n)/log(1/λ)−O(loglog(n)) time steps, where λ is the unique solution between 0 and 1 of λ·p⌊s/2⌋(λ)·p⌈s/2⌉(λ)=1, with pi(λ)=1+λ2+⋯+λ2i−2 for any integer i>0. We then provide improved lower bounds in the directed and half-duplex cases for many well-known network topologies, such as Butterfly, de Bruijn, and Kautz graphs. All the results are extended also to the full-duplex case. Our technique is very general, as for s→∞ it allows the determination of improved results even for non-systolic protocols. In fact, for general networks, as a simple corollary it yields a lower bound only an O(loglog(n)) additive factor far from the general one independently proved in [Proc. 1st ACM Symposium on Parallel Algorithms and Architectures (SPAA), 1989, p. 318; Topics in Combinatorics and Graph Theory (1990) 451; SIAM Journal on Computing 21(1) (1992) 111; Discrete Applied Mathematics 42 (1993) 75] for all graphs and any (non-systolic) gossip protocol. Moreover, for specific networks, it significantly improves with respect to the previously known results, even in the full-duplex case. Correspondingly, better lower bounds on the gossiping time of non-systolic protocols are determined in the directed, half-duplex and full-duplex cases for Butterfly, de Bruijn, and Kautz graphs. Even if in this paper we give only a limited number of examples, our technique has wide applicability and gives a general framework that often allows to get improved lower bounds on the gossiping time of systolic and non-systolic protocols in the directed, half-duplex and full-duplex cases

Neighbourhood Broadcasting in Hypercubes

International audienceIn the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least $\lceil \log_2 N \rceil$ rounds in a network of $N$ nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with $N$ nodes, each node has $\log_2 N$ neighbors, so neighborhood broadcasting takes at least $\lceil \log_2 \log_2 (N+1) \rceil$ rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes

Optimal Sequential Gossiping by Short Messages

International audienceGossiping is the process of information di ffusion 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

Neighbourhood Broadcasting in Hypercubes

International audienceIn the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least $\lceil \log_2 N \rceil$ rounds in a network of $N$ nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with $N$ nodes, each node has $\log_2 N$ neighbors, so neighborhood broadcasting takes at least $\lceil \log_2 \log_2 (N+1) \rceil$ rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes

Multiple message broadcasting and gossiping in the dynamically orientable graphs

This research investigates the problems of gossiping and multiple message broadcasting in dynamically orientable graphs of different network topologies. These are new problems never attempted before. Dynamically orientable graphs and six different network topologies are considered: paths, cycles, stars, binary trees, complete trees and two-dimensional grids. Information dissemination in graphs that are dynamically orientable requires that number of messages sent in each direction along an edge be balanced and therefore necessitates a different approach in gossiping and multiple message broadcasting.;The obvious upper bound for gossiping and multiple message broadcasting in dynamically orientable graphs is twice the best known time for gossiping and multiple message broadcasting in classical graphs. This is obtained by inserting an additional time step t\u27 after each time step t in the classical graph algorithm in which all calls of time step t are repeated with messages moving along the same edges but in the opposite direction to reset the bias of these edges. Finding better bounds for gossiping and multiple message broadcasting in dynamically orientable graphs is the goal of this research.;For each network topology an algorithm is proposed to perform gossiping and multiple message broadcasting. For some network topologies proposed algorithms for dynamically orientable graphs achieved the same upper bound as it is known for classical graphs, for example, gossiping in dynamically orientable grid graphs. In some cases the best time is the twice the best known time for gossiping and multiple message broadcasting in classical graphs, for example, gossiping in dynamically orientable star graphs. In other cases, good time bounds are achieved that are very close to the upper bounds in classical graphs, for example, multiple message broadcasting in dynamically orientable grid graphs. Multiple message broadcasting in dynamically orientable cycle graphs is also a good example of close upper bounds. As number of messages increases bounds become very close to each other

Deep Heuristic: A Heuristic for Message Broadcasting in Arbitrary Networks

With the increasing popularity of interconnection networks, efficient information dissemination has become a popular research area. Broadcasting is one of the information dissemination primitives. Finding the optimal broadcasting scheme for any originator in an arbitrary network has been proved to be an NP-Hard problem. In this thesis, a new heuristic that generates broadcast schemes in arbitrary networks is presented, which has O(|E| + |V | log |V |) time complexity. Based on computer simulations of this heuristic in some commonly used topologies and network models, and comparing the results with the best existing heuristics, we conclude that the new heuristic show comparable performances while having lower complexity

Algorithms for Data Dissemination and Collection

Broadcasting and gossiping are classical problems that have been widely studied for decades. In broadcasting, one source node wishes to send a message to every other node, while in gossiping, each node has a message that they wish to send to everyone else. Both are some of the most basic problems arising in communication networks. In this dissertation we study problems that generalize gossiping and broadcasting. For example, the source node may have several messages to broadcast or multicast. Many of the works on broadcasting in the literature are focused on homogeneous networks. The algorithms developed are more applicable to managing data on local-area networks. However, large-scale storage systems often consist of storage devices clustered over a wide-area network. Finding a suitable model and developing algorithms for broadcast that recognize the heterogeneous nature of the communication network is a significant part of this dissertation. We also address the problem of data collection in a wide-area network, which has largely been neglected, and is likely to become more significant as the Internet becomes more embedded in everyday life. We consider a situation where large amounts of data have to be moved from several different locations to a destination. In this work, we focus on two key properties: the available bandwidth can fluctuate, and the network may not choose the best route to transfer the data between two hosts. We focus on improving the task completion time by re-routing the data through intermediate hosts and show that under certain network conditions we can reduce the total completion time by a factor of two. This is done by developing an approach for computing coordinated data collection schedules using network flows