Graph’s theory approach for searching the shortest routing path in RIP protocol: a case study

Routing is a problem domain with an infinite number of final-solutions. One of the possible approaches to solving such problems is using graph theory. This paper presents mathematical analysis methodologies based on circular graphs for solving a shortest path routing problem. The problem is focused on searching for the shortest path within a circular graph. Such a search coincides with the network routing problem domain. In this paper, we introduce in the detail all necessary parts needed to understand such an approach. This includes: definition of the routing problem domain, introduction to circular graphs and their usage, circular graph’s properties, definition of walks through a circular graph, searching and determining the shortest path within a circular graph, etc. The state of the art routing methods, implemented in contemporary highly sophisticated routers, includes well-known weight-based algorithms and distance-vectors-based algorithms. The proposed solution can be placed between the two abovementioned methods. Each of these known methods strives for optimal results, but each of them also has its own deficiencies, which should be rectified with the proposed new method. This theoretically presented method is argued by a practical example and compared with the RIP (Routing Information Protocol) technique, where we look for the shortest path and possible walks through a specified circular graph. Streszczenie. W artykule zaprezentowano matematyczną analizę bazująca na teorii grafów do rozwiązania problemu poszukiwania najkrótszej ścieżki routingu. Przedstawiono problem routingu oraz grafy kołowe i ich użycie. (Wykorzystanie teorii grafów do poszukiwania najkrótszej ścieżki routingu w protokole RIP)