Linear Algorithm for Broadcasting in Unicyclic Graphs

Harutyunyan, Hovhannes A.; Maraachlian, Edward

doi:10.1007/978-3-540-73545-8_37

Cited by 17 publications

(2 citation statements)

References 14 publications

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“…Slater et al [30] also gave an algorithm to determine b 1 (u, T ) for an arbitrary vertex in an arbitrary tree T . Their algorithm runs in time linear in the size of T. Harutyunyan and Maraachlian [14] gave a linear time algorithm to find b 1 (u, G) for an arbitrary vertex u in an arbitrary unicyclic graph G. Dessmark et al [4] gave efficient algorithms for 1-broadcasting in almost trees and in partial k-trees. These are the only algorithms for finding the exact 1-broadcast time of a vertex in a graph of a certain type.…”

Section: Introductionmentioning

confidence: 98%

A linear algorithm for finding the k‐broadcast center of a tree

2009

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The term k -broadcast indicates the process of disseminating a message from one vertex to all vertices of a graph in such a way that in each time unit, an informed vertex can send the message to up to k of its neighbors. The k -broadcast center of a graph is the set of vertices that can initiate a minimum time k -broadcast within the graph. We present a linear algorithm to determine the kbroadcast center of a given tree. From this, we obtain a linear time algorithm for finding the k -broadcast time of any vertex of the tree and, thus, the k -broadcast time of the tree itself.

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Section: Introductionmentioning

confidence: 98%

A linear algorithm for finding the k‐broadcast center of a tree

2009

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“…The heuristics in [1] and [12] are the best existing heuristics for broadcasting in practice with O(|V | 2 · |E|) and O(|E|) respectively. The broadcast problem has been solved with a linear algorithm only for trees [20], unicyclic graphs [10], [11] and tree of cycles [9]. Also there is an O(n 4k+5 ) broadcast algorithm for partial k-trees [2].…”

Section: Introductionmentioning

confidence: 99%

Broadcasting in Fully Connected Trees

Harutyunyan

Maraachlian

2009

2009 15th International Conference on Parallel and Distributed Systems

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Abstract-Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Once informed, the nodes aid the originator in distributing the message. Finding the minimum broadcast time of a vertex in an arbitrary graph is NP-complete. The problem is solved polynomially only for trees, unicyclic graphs, and tree of cycles. In this paper we will consider broadcasting in a new class called the Fully Connected Trees (FCT). We will present a O(n log n) algorithm to find the broadcast time of any originator in an arbitrary FCT.

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