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Abstract
Abstract In this study, we have chosen the computer network with the shape of a king’s graph. The king’s graph G is defined as a set of edges, that is $$E=\{((i,j),(p,q))|i,p \in [0,M], j,q \in [0,N], M,N \in \textbf{Z},((i,j),(p,q))~{is\, an\, edge}\,\iff i = p \quad {and} \quad j = q\pm 1 \quad {or} \quad i = p\pm 1 \quad {and} \quad j = q \quad {or} \quad i = p\pm 1 \quad {and} \quad j = q\pm 1\}$$ E = { ( ( i , j ) , ( p , q ) ) | i , p ∈ [ 0 , M ] , j , q ∈ [ 0 , N ] , M , N ∈ Z , ( ( i , j ) , ( p , q ) ) i s a n e d g e ⟺ i = p and j = q ± 1 or i = p ± 1 and j = q or i = p ± 1 and j = q ± 1 } . We also set a delivery rule, in which the shortest paths in the graph are used for the message deliveries, to restrict the source consumption. Then, the paths are encoded in a way that we discover using binary arrays based on other well-known encoding methods. We prove that the path-coding method we present prevents errors denoted by false positives from the graph. Data transfer issues from computer science served as the motivation for this study.
Highlights
In this paper, we consider a graph denoted by king’s graph G = (V, E) that models a computer network [5]
We show that the Bloom filter that we improve in this research for the shortest paths in a king’s graph does not generate false positives
The motivation for this study came from data transfer problems between computers in computer networks
Summary
The path is known before the message is sent, and once a message is forwarded through the path, it is not directed backward This routing scenario in grid models was proposed by [6, 10, 15]. We have invented path-labeling methods for the shortest paths in some graphs such as rectangular grids [10], hexagonal grids [12] and triangular grids [13] We consider another edge-labeling model in a king’s graph [5]. A path-labeling method has been considered in [11], unlike edge-labeling, vertex-labeling has been studied using Bloom filters in [11]. The path encoding method presented in this study is based on a conventional approach, denoted by the Bloom filter, which is an approach of the encoding methods previously explored under a data transmission scenario between computers in a computer network. The structure of this paper is that we introduce both standard Bloom filters and our labeling method, we show how our labeling method does not produce any error, and we show why the method introduced in this paper is better than some other methods
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