Efficient line broadcasting in a d-dimensional grid

Averbuch, Amir; Roditty, Yehuda; Shoham, Barack

doi:10.1016/s0166-218x(00)00277-8

Cited by 3 publications

(3 citation statements)

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“…We shall prove that in any minimum-time linebroadcasting algorithm 1. The cumulative cost after 1, .…”

Section: Proof Of the Lower Boundmentioning

confidence: 96%

“…In their paper, they suggested examining classes of graphs other than paths or cycles, for example, binary and binomial trees. Averbuch et al [1] obtained efficient line-broadcasting algorithms in a d-dimensional grid, which produce a linear cost as a function of n. Motivated by Fujita and Farley's [5] suggestion, we present minimum-time line-broadcasting schemes for the complete binary trees. We use the same model used by the mentioned researchers, in which line broadcasting must be completed in log 2 n time units and the optimization measure is the cumulative cost.…”

Section: Introductionmentioning

confidence: 99%

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Low‐cost minimum‐time line‐broadcasting schemes in complete binary trees

2001

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Broadcasting is the process of transmitting a message from a member in a network (originator) to all other members. A line-broadcasting scheme allows two members to communicate during one time unit as long as there is a path of lines between them and no link is used in more than one call between two members. Farley [3] showed an algorithm that accomplishes line broadcasting in any tree on n vertices in minimum time, which is log 2 n n n time units. Since the structure of the tree is unknown in advance, the total number of communication link uses (cost) of his scheme is Θ(n n n − − − 1) log 2 n n n . In this paper, we present line-broadcasting schemes for complete binary trees. The cost of the algorithms is linear in the number of vertices. This answers a question raised by Fujita and Farley [5].

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“…We shall prove that in any minimum-time linebroadcasting algorithm 1. The cumulative cost after 1, .…”

Section: Proof Of the Lower Boundmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Low‐cost minimum‐time line‐broadcasting schemes in complete binary trees

2001

Self Cite

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“…Averbuch et al developed efficient line‐broadcasting algorithms in a d ‐dimensional grid. These algorithms produce a linear cumulative cost as a function of the number of vertices in the graph, with any vertex as the originator.…”

Section: Introductionmentioning

confidence: 99%

Line-broadcasting in complete k -ary trees

Shabtai

Roditty

2015

NETWORKS

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A line‐broadcasting model in a connected graph G = ( V , E ) , | V | = n , is a model in which one vertex, called the originator of the broadcast, holds a message that has to be transmitted to all vertices of the graph through placement of a series of calls over the graph. In this model, an informed vertex can transmit a message through a path of any length in a single time unit, as long as two transmissions do not use the same edge at the same time. Farley [6] has shown that the process can be completed within at most ⌈ log 2 n ⌉ time units from any originator in a tree (and thus in any connected undirected graph) and that the cumulative cost of broadcasting one message from any vertex, that is, the total number of edges used, is at most ( n − 1 ) ⌈ log 2 n ⌉ . In this article, we present lower and upper bounds for the cumulative cost to broadcast one message in a complete k‐ary tree, k ≥ 2 , from any vertex using the line‐broadcasting model. We prove that if B(u) is the minimum cumulative cost of line‐broadcast in a graph G = ( V , E ) from an originator u ∈ V using the line‐broadcasting model, then ( 2 − o ( 1 ) ) n ≤ B ( u ) ≤ ( 2 + o ( 1 ) ) n , where u is any vertex in a complete k‐ary tree. Furthermore, for certain conditions, B(u) is about ( 2 − o ( 1 ) ) n . © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(2), 139–147 2016

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Minimal-Time k-Line Broadcasting

Gaber¹

2005

SIAM J. Discrete Math.

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Efficient line broadcasting in a d-dimensional grid

Abstract: The results of Fujita and Farley (Discrete Appl. Math. 75 (1997) 255-268) and Kane and Peters (Discrete Appl. Math. 83 (1998) 207-228) on line broadcasting in paths and cycles are extended into a d-dimensional grid, obtaining optimal algorithms in most cases.

Cited by 3 publications

References 9 publications

Low‐cost minimum‐time line‐broadcasting schemes in complete binary trees

Low‐cost minimum‐time line‐broadcasting schemes in complete binary trees

Line-broadcasting in complete k -ary trees

Minimal-Time k-Line Broadcasting

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