Broadcasting multiple messages in a grid

Scoy, Frances L. Van; Brooks, Jeffrey A.

doi:10.1016/0166-218x(94)90194-5

Cited by 9 publications

(7 citation statements)

References 4 publications

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“…Recently a generalization of broadcasting in trees was obtained [2], where positive weights were assigned to the edges or the vertices of the tree. Other results concerning broadcasting in various topologies are available for complete graphs [4,6,7,12], planar graphs [19], grids in several dimensions and multiple messages [10,11,22,24,26,29], trees [15,25,28], minimal broadcast graphs [1,8,16,17], weighted trees [2,13], and various problems [20,21].…”

Section: Introductionmentioning

confidence: 99%

New upper bound on m‐time‐relaxed k‐broadcast graphs

2017

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Broadcasting is a process in which an individual has an item of information which needs to be transmitted to all of the members in a network (which is viewed as a connected graph). k‐broadcasting is a variant of broadcasting in which each processor can transmit the message to up to k of its neighbors. Another variant of broadcasting is the concept of m‐time‐relaxed broadcasting, where we allow m additional time units, enabling one to decrease the number of edges in the communication network. The combination of m‐time‐relaxed and k‐broadcasting is studied in this article. The results shown here are an improvement on the upper bound obtained by Harutyunyan and Liestman, Discrete Math 262 (2003), 149–157, by constructing a connected graph, which admits m‐time‐relaxed k‐broadcasting for all n, n > ( k + 1 ) m + 2 , m > 1 and has fewer edges than the graph presented in Harutyunyan and Liestman, Discrete Math 262 (2003), 149–157. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 72–78 2017

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Section: Introductionmentioning

confidence: 99%

New upper bound on m‐time‐relaxed k‐broadcast graphs

2017

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“…The source has k messages which have to reach all nodes of the network. The problem of minimizing the time of k-message broadcasting has been investigated in [15] for grids in the whispering model and in [2,12,13] for complete graphs and trees in the simultaneous sendÂreceive model and its generalization, the LogP model.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Algorithm for Broadcasting Multiple Messages in Trees

Diks¹,

Lingas²,

Pełc³

1999

Journal of Parallel and Distributed Computing

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“…Van Scoy [26] found an algorithm for broadcasting a small number of messages from a corner vertex of a square n × n grid in the time predicted by Farley's lower bound. Her algorithm divides the messages into two sets of (approximately) equal size: black (odd numbered) messages and gray (even numbered) messages.…”

Section: Broadcasting a Few Messagesmentioning

confidence: 99%

“…Van Scoy and Brooks [27] published another time 2n+ 5 2 M −constant broadcasting algorithm. This algorithm required time 2n + 5 2 M − 4.…”

Section: Broadcasting Many Messages In Non Optimal Timementioning

confidence: 99%

“…Van Scoy and Brooks [27] constructed an algorithm for broadcasting M messages in an n × n × n grid (all messages originate in vertex (1, 1, 1)) in time 3n + 10 3 M + 2. They also conjectured that there exists an algorithm for broadcasting M messages from a corner vertex of an equilateral d-dimensional grid with n points per edge in time dn Figure 3.2: Broadcasting many messages in time 2n + 5 2 M + constant (Brooks, 1989)…”

Section: Broadcasting Many Messages In Higher Dimension Gridsmentioning

confidence: 99%

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Broadcasting in grid graphs

Wojciechowska¹,

Scoy²

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Broadcasting in Grid Graphs Iwona WojciechowskaThis work consists of two separate parts. The first part deals with the problem of multiple message broadcasting, and the topic of the second part is line broadcasting. Broadcasting is a process in which one vertex in a graph knows one or more messages. The goal is to inform all remaining vertices as fast as possible. In this work we consider a special kind of graphs, grids.In 1980 A. M. Farley showed that the minimum time required to broadcast a set of M messages in any connected graph with diameter d is d + 2(M − 1). This work presents an approach to broadcasting multiple messages from the corner vertex of a 2-dimensional grid. This approach gives us a broadcasting scheme that differs only by 2 (and in the case of an even × even grid by only 1) from the above lower bound.Line broadcasting describes a different variant of the broadcasting process. A. M. Farley showed that line broadcasting can always be completed in log n time units in any connected graph on n vertices. He defined three different cost measures for line broadcasting. This work presents strategies for minimizing those costs for various grid sizes.

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Broadcasting multiple messages in a grid

Cited by 9 publications

References 4 publications

New upper bound on m‐time‐relaxed k‐broadcast graphs

New upper bound on m‐time‐relaxed k‐broadcast graphs

An Optimal Algorithm for Broadcasting Multiple Messages in Trees

Broadcasting in grid graphs

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