Broadcasting in grid graphs

Wojciechowska, Iwona; Scoy, Frances L. Van

doi:10.33915/etd.3172

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…In some special situations, for instance, when

|{V}_{0}|=1

and the graph is a tree (Koh and Tcha, 1991; Su et al., 2010) or a complete grid (Wojciechowska and Scoy, 1999), the MBT can be optimality solved in polynomial time. For arbitrary graphs, the exact approaches include a dynamic programming algorithm (Scheuermann and Wu, 1984) and the ILP models presented by de Sousa et al.…”

Section: Related Workmentioning

confidence: 99%

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

Lima

Aquino

Nogueira

et al. 2022

Int Trans Operational Res

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The Minimum Broadcast Time (MBT) is a well‐known data dissemination problem whose goal is to find a broadcast scheme that minimizes the number of steps needed to execute the broadcast operation. The problem has many applications in distributed systems and, in particular, the Industry 4.0 domain. Because Industry 4.0 applications rely primarily on the use of large‐scale machine to machine communications, they need data dissemination techniques that combine high reliability with low communication latency. This work proposes a Biased Random‐Key Genetic Algorithm and a matheuristic for the MBT. We carry out experiments with our algorithms on instances commonly used in the literature (hypercube, shuffle exchange, cube‐connected cycles, de Bruijn, Harary graphs), and also on massive synthetic instances (up to 1000 vertices), allowing to cover many possibilities of real industry topologies. Our proposal is also compared with state‐of‐the‐art exact methods and heuristics. Experimental results show that our algorithm is able to outperform the best‐known heuristics for the MBT, and also that it is a very good alternative for large instances that cannot be solved by current exact methods.

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“…In some special situations, for instance, when

|{V}_{0}|=1

Section: Related Workmentioning

confidence: 99%

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

Lima

Aquino

Nogueira

et al. 2022

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…Thus, multiple message broadcasting has been studied. Some examples in which multiple message broadcast schemes have been investigated include grids [W99,WV96,VB94], paths [S99], hypercubes [QA97,S99] and complete graphs [KC95].…”

Section: Related Workmentioning

confidence: 99%

Broadcasting in cycles with chords

Scoy

Kovalchick

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Broadcasting is the process of information dissemination in which one node, the originator, knows a single piece of information and using a series of calls must inform every other node in the network of this information. We assume that at any given time, a node can communicate the message to another node, with which it shares an edge, by acting as either a sender or receiver, but not both. Multiple message broadcasting considers the case when the originator has m messages, where m > 1, to disseminate. Whereas broadcasting limits the communication of a message from one node to another node via a single edge, line broadcasting allows one node to send a message to any other node in the network as long as a simple path exists between the sending node and the receiving node and every edge along the path is not in use. In this dissertation, we consider the problem of broadcasting in a cycle with chords and we develop broadcast schemes for this type of network. We begin by investigating the problem of broadcasting in a cycle with one and two chords, respectively. Then, we consider the problem of multiple message broadcasting in cycles with one and two chords. Finally, we consider the problem of line broadcasting in cycles with chords. Through our investigations, we develop two algorithms for the problem of broadcasting in a cycle with one and two chords, respectively and we analyze the correctness and complexity of these algorithms. Then, we discuss problems associated with multiple message broadcasting in cycles with one and two chords. Finally, we use techniques developed for line broadcasting in cycles to create minimum time broadcast schemes for cycles through the addition of chords. Using techniques developed in this dissertation, we are able to broadcast in minimum time in cycles with chords. In cycles whose size is a power of 2, we have proved that the number of chords that we add to the cycle is the minimum number of chords required to broadcast in minimum time in such a cycle. Committee. Finally, I wish to thank my parents, James and Dorothy Kovalchick and my sister, Amanda Kovalchick for their support and encouragement.

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A generalized broadcasting schema for the mesh structures

Shen

2007

Applied Mathematics and Computation

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Broadcasting in grid graphs

Cited by 5 publications

References 13 publications

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

Broadcasting in cycles with chords

A generalized broadcasting schema for the mesh structures

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