Review of Methods and Algorithms for Modelling Transportation Networks Based on Graph Theory

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Przegląd metod i algorytmów modelowania sieci transportowych opartych na teorii grafów

Sambor Guze    https://orcid.org/0000-0003-1635-1924     

1

Gdynia Maritime University, 81-87 Morska, 81-225 Gdynia, Faculty of Navigation, Department of Mathematics, e-mail: s.guze@wn.umg.edu.pl

Abstract: 

One of the best ways of modelling a transport network is to use a graph with vertices and edges. They represent nodes and arcs of such network respectively. Graph theory gives dozens of parameters or characteristics, including a connectivity, spanning trees or the different types of domination number and problems related to it. The main aim of the paper is to show graph theory methods and algorithms helpful in modelling and optimization of a transportation network. Firstly, the descriptions of basic notations in graph theory are introduced. Next, the concepts of domination, bondage number, edge-subdivision and their implementations to the transportation network description and modeling are proposed. Moreover, the algorithms for finding spanning tree or maximal flow in networks are presented. Finally, the possible usage of distinguishing concepts to exemplary transportation network is shown. The conclusions and future directions of work are presented at the end of the paper.

Streszczenie: 

Jednym z najlepszych sposobów modelowania sieci transportowej jest użycie grafu z wierzchołkami i krawędziami. Reprezentują one odpowiednio węzły i łuki takiej sieci. Teoria grafów daje możliwość użycia dziesiątek parametrów lub charakterystyk, w tym spójności, drzew spinających lub różnych typów liczb dominowania i związanych z tym problemów. Głównym celem artykułu jest przedstawienie metod i algorytmów teorii grafów pomocnych w modelowaniu i optymalizacji sieci transportowej. Po pierwsze, wprowadzono opisy podstawowych pojęć w teorii grafów. Następnie zaprezentowano koncepcje domino­wania, liczby zniewolenia czy podziału krawędzi grafu oraz ich implementacji do opisu i modelowania sieci transportowej. Ponadto przedstawiono algorytmy do wyszukiwa­nia drzewa opinającego i maksymalnego przepływu w sieciach. Wreszcie pokazano możliwe sposoby wykorzystania wyróżnionych koncepcji do przykładu sieci transportowej. Na zakoń­czenia przedstawiono wnioski i przyszłe kierunki prac.

Keywords: 
knapsack problem, domination number, bondage-connected number, MST, maximal flow, transportation network, vulnerability
Słowa kluczowe: 
problem plecakowy, liczba dominowania, liczba zniewolenia spójnego, MST, maksymalny przepływ, sieć transportowa, wrażliwość sieci
Pages: 
25
39
Doi: 
10.26408/107.02
Submitted: 
01.11.2018
Accepted: 
12.11.2018
Published: 
28.12.2018
Download full text in pdf: 
PDF icon 107_02.pdf

This article is an open access article distributed under a Creative Commoms Attribution (CCBY 4.0) licence

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Citation pattern: Guze S., Review of Methods and Algorithms for Modelling Transportation Networks Based on Graph Theory, Scientific Journal of Gdynia Maritime University, No. , pp. 25-39,

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