Improved Networks Routing Using an Arrow-Based Description
- Section 2 introduces the basic notations used in the paper;
- Section 3 describes an arrow-description of the graph;
- Section 4 describes the use of the arrow algebra;
- Section 5 describes the routing algorithm using arrows;
- Section 6 is dedicated to a more detailed description of the algorithm;
- Section 7 is dedicated to conclusions and future work.
2. Basic Definitions and Notations
2.2. Adjacency and Cycles Merger
3. An Arrow-Based Description and Its Algebra
3.1. Graph Arrows
- ; if and ;
3.2. Basic Graph Operations with Arrows
4. Using Graph Arrows
5. Routing Algorithm Using Arrows
5.1. Serial Addition
5.2. Parallel Composition of Graph Arrows
5.3. Series-Parallel Composition of Graph Arrows
|Algorithm 1: The path finding using graph arrows.|
|Input: the starting node nsand the end node ne;|
Determine the cycles containing nsand ne;
Determine the cycles paths comprising both nsand ne
using cycles mergers;
If there is no path, then STOP and print “No path found”;
Once a path is found, translate the list of graph arrows
to sets T and H as discussed.
By successive applications of the KMP algorithm as
described above, find a direct and a return path
between the nodes;
Output: the path discovered.
- Each time, the number of cycles limits the iterations to less than C.
- The end criteria of the program can be flexible such that it can be stopped whenever a first path is found or alternatively it can be run until a path with a specific length is obtained.
6. The Algorithm in More Detail
7. Conclusions and Further Work
Conflicts of Interest
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Onete, C.E.; Onete, M.-C.C. Improved Networks Routing Using an Arrow-Based Description. Telecom 2020, 1, 150-160. https://doi.org/10.3390/telecom1030011
Onete CE, Onete M-CC. Improved Networks Routing Using an Arrow-Based Description. Telecom. 2020; 1(3):150-160. https://doi.org/10.3390/telecom1030011Chicago/Turabian Style
Onete, Cristian E., and Maria-Cristina C. Onete. 2020. "Improved Networks Routing Using an Arrow-Based Description" Telecom 1, no. 3: 150-160. https://doi.org/10.3390/telecom1030011