scholarly journals The Use of Weighted Adjacency Matrix for Searching Optimal Transportation Routes

2018 ◽  
Author(s):  
Karel Antoš
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Optimal Transportation ◽  
New Approach ◽  
New Variant ◽  
Transportation Routes ◽  
Weighted Adjacency Matrix

This article provides a new approach to searching solutions of the ship transport optimalization problems. It brings a new variant of one algorithm of searching for the Minimum Spanning Tree. The new element in the algorithm is that it uses the Weighted Adjacency Matrix. This Weighted Adjacency Matrix is suitable for searching for the Minimum Spanning Tree (MST) of the graph. It shows how it could be used in cases where weighted edges of the graph are given. This creates a new procedure of searching for the MST of the graph and completes previously known algorithms of searching for the MST. In the field of transportation it could be succesfully used for solutions of optimizing transportation routes where smallest costs are wanted. Proposed Weighted Adjacency Matrix could be used in similar issues in the field of the graph theory, where graphs with weighted edges are given. The procedure is shown on the attached example.

An Algorithm for Determining the Position and Orientation of 3-D Objects from Images Using Spectral Graph Theory

2015 ◽  
Vol 770 ◽  
pp. 585-591
Author(s):  
Alexey Barinov ◽  
Aleksey Zakharov
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Spectral Decomposition ◽  
Spectral Graph Theory ◽  
Feature Points ◽  
Image Comparison ◽  
Spectral Graph ◽  
Position And Orientation ◽  
Weighted Adjacency Matrix

This paper describes an algorithm for computing the position and orientation of 3-D objects by comparing graphs. The graphs are based on feature points of the image. Comparison is performed by a spectral decomposition with obtaining eigenvectors of weighted adjacency matrix of the graph.

scholarly journals A graph theory approach of the study of macroeconomics networks

2017 ◽  
Author(s):  
Γεώργιος-Αντώνιος Σαραντίτης
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dominating Set ◽  
Theory Approach ◽  
Minimum Dominating Set

Πολλά σύγχρονα οικονομικά συστήματα χαρακτηρίζονται από αυξημένο βαθμό πολυπλοκότητας. Οι οντότητες αυτών των συστημάτων αναπτύσσουν διακριτές, αναδυόμενες και μη γραμμικές συμπεριφορές που δεν μπορούν να περιγραφούν πλήρως με οικονομετρικές τεχνικές. Τα τελευταία χρόνια, λόγω της γρήγορης αύξησης της υπολογιστικής ισχύος και της εξέλιξης των αλγορίθμων, η επιστήμη της Ανάλυσης Δικτύων ενσωματώθηκε στην ανάλυση τέτοιων πολύπλοκων οικονομικών συστημάτων, συμπληρώνοντας τη χρήση της οικονομετρίας.Μια κοινώς χρησιμοποιούμενη τεχνική στο πλαίσιο της Ανάλυσης Δικτύων είναι το Minimum Spanning Tree (MST). Το MST παράγει ένα υπο-δίκτυο του αρχικού δικτύου στο οποίο είναι συνδεδεμένοι όλοι οι κόμβοι έτσι ώστε να μην υπάρχουν βρόχοι. Ωστόσο, το MST φέρει κάποια εγγενή μειονεκτήματα που προέρχονται άμεσα από τη διαδικασία αλγοριθμικού προσδιορισμού του και μπορεί να το καταστήσουν ακατάλληλο για τη μελέτη οικονομικών δικτύων. Αυτή η διατριβή αποσκοπεί στο να αναδείξει τα μειονεκτήματα του MST όταν χρησιμοποιείται στα οικονομικά δίκτυα και να επισημάνει τα πλεονεκτήματα μιας νέας τεχνικής βελτιστοποίησης, που ονομάζεται Threshold-Minimum Dominating Set (T-MDS) ως μια καταλληλότερη λύση. Επιπλέον, εισάγεται το Threshold Weighted - Minimum Dominating Set (TW-MDS), το οποίο διατηρεί όλα τα πλεονεκτήματα του T-MDS και, ανάλογα με το δεδομένο σύνολο, μπορεί να είναι πιο κατάλληλο για διαχρονικές αναλύσεις που εκτελούνται στην πάροδο του χρόνου.Η ανωτερότητα των T-MDS και TW-MDS σε σχέση με το κλασικό MST αρχικά επισημαίνεται σε αυτή τη διατριβή με κατάλληλα θεωρητικά παραδείγματα. Στη συνέχεια συνεχίζουμε παρέχοντας ένα ευρύ φάσμα μακροοικονομικών εφαρμογών: τον συγχρονισμό των οικονομικών κύκλων, την εξέλιξη της ανισότητας εισοδήματος και τη μέτρηση του πληθωρισμού πυρήνα. Με αυτόν τον τρόπο τονίζουμε την καταλληλότητα των προτεινόμενων μεθοδολογιών στη μακροοικονομική ανάλυση. Έτσι, αυτή η διατριβή έχει διπλή συμβολή στην ανάλυση των σύνθετων οικονομικών δικτύων: από τη θεωρητική πλευρά επεκτείνει τη σχετική βιβλιογραφία παρέχοντας ένα πιο κατάλληλο εργαλείο από αυτό που χρησιμοποιείται προς το παρόν, ενώ από την εμπειρική πλευρά παρέχει νέα αποτελέσματα από τις διαφορετικές οικονομικές Εφαρμογές του T-MDS.

Mathematical Modelling for Transportation With Application to Airline Transportation Network

2021 ◽  
pp. 28-51
Author(s):  
Sadiqah Almarzooq ◽  
Njwd Albishi
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Transportation Networks ◽  
Transportation Network ◽  
Weighted Graph ◽  
Search Method ◽  
Nearest Neighbour ◽  
Water Pipelines ◽  
Regional Airports

Graph theory is a basic tool to solve real-world problems such as communication between people, water pipelines, and transportation networks. A transportation network can be modeled as connected weighted graph. This chapter starts by introducing some fundamental concepts of graph theory to be applied to three main problems: the minimum spanning tree, the shortest path, and the travel salesperson. The authors discuss some appropriated algorithms such as depth first algorithm, Prim's algorithm, Kruskal's algorithm, Dijkstra's algorithm, the nearest neighbour algorithm, the minimum spanning tree depth first search method (MST-DFS) algorithm, and the Christofides' algorithm to solve these problems and apply them the airlines network between international and regional airports in Saudi Arabia.

Interrelationships Among the Liliatae: a Graph Theory Approach

1980 ◽  
Vol 28 (2) ◽  
pp. 261 ◽  
Author(s):  
HT Clifford ◽  
WT Williams
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Theory Approach ◽  
Nearest Neighbours ◽  
Shared Ancestry ◽  
Evolutionary Convergence

The interrelationships of the families of Liliatae were investigated by using a network generating program (NETS) which, unlike minimum spanning tree programs, considers both first and second nearest neighbours. Within the resultant network the distribution of families reflects many traditionally accepted assemblages, including the Zingiberales and Alismatales. The affinities of the Arecaceae in particular suggests that the observed similarities between some families may be due to evolutionary convergence rather than to a shared ancestry. This fact, plus the tendency of the network to branch rather than to form loops, helps to account for the difficulty in classifying the class.

New Approach to Portfolio Creation Using the Minimum Spanning Tree Theory and Its Robust Evaluation

2020 ◽  
Vol 24 (2) ◽  
pp. 22
Author(s):  
Jakub Danko ◽  
Vincent Šoltés ◽  
Tomáš Bindzár
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Investment Strategy ◽  
Point Of View ◽  
Equal Weight ◽  
Individual Investor ◽  
New Approach ◽  
Active Approach ◽  
Risky Investment ◽  
One Year

<p><strong>Purpose:</strong> The aim of this paper is to describe another possibility of portfolio creation using the minimum spanning tree method. The research contributes to the existing body of knowledge with using and subsequently developing a new approach based on graph theory, which is suitable for an individual investor who wants to create an investment portfolio.</p><p><strong>Methodology/Approach:</strong> The analyzed data is divided into two (disjoint) sets – a training and a testing set. Portfolio comparisons were carried out during the test period, which always followed immediately after the training period and had a length of one year. For the sake of objectivity of the comparison, all proposed portfolios always consist of ten shares of equal weight.</p><p><strong>Findings:</strong> Based on the results from the analysis, we can see that our proposed method offers (on average) the best appreciation of the invested resources and also the least risky investment in terms of relative variability, what could be considered as very attractive from an individual investor’s point of view.</p><p><strong>Research Limitation/implication:</strong> In our paper, we did not consider any fees related to the purchase and holding of financial instruments in the portfolio. For periods with extreme market returns (sharp increase or decrease), the use of Pearson’s correlation coefficient is not appropriate.</p><strong>Originality/Value of paper:</strong> The main practical benefit of the research is that it presents and offers an interesting and practical investment strategy for an individual investor who wants to take an active approach to investment.

scholarly journals ALGORITMA “HANCURKAN SEMUA SIKEL” UNTUK MENENTUKAN POHON PERENTANG MINIMUM DARI SUATU GRAF BERBOBOT

2019 ◽  
Vol 21 (2) ◽  
pp. 91-98
Author(s):  
Ricky Aditya
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Alternative Algorithm

The minimum spanning tree is one of the applications of graph theory in various fields. There are several algorithms for determining the minimum spanning tree of a weighted graph, such as Kruskal's algorithm and Prim's algorithm. These two algorithms are not really easy to teach to students in general. Therefore in this paper presented an alternative algorithm called the algorithm "Destroy All Sikel", which is more intuitive and easier to understand. Furthermore, there are also examples of implementation and comparison with two other algorithms.

scholarly journals The Generalized STAR Modelling with Minimum Spanning Tree Approach of Weight Matrix for COVID-19 Case in Java Island

2021 ◽  
Vol 2084 (1) ◽  
pp. 012003
Author(s):  
Utriweni Mukhaiyar ◽  
Bayu Imadul Bilad ◽  
Udjianna Sekteria Pasaribu
Keyword(s):  
Spanning Tree ◽  
Large Scale ◽  
Minimum Spanning Tree ◽  
Weight Matrix ◽  
Average Score ◽  
New Approach ◽  
Central Java ◽  
Good Ability ◽  
The Relationship ◽  
Inverse Distance

Abstract The ongoing global Coronavirus 2019 (COVID-19) pandemic poses a major threat. The spread of the COVID-19 virus is likely to occur from one location to another location due to the mobility of people. Many efforts and policies have been made by each country to reduce the spread of the COVID-19 outbreak. The imposition of lockdown and large-scale social restrictions or social distancing has been widely applied to limit the transmission of this virus among the community and provincial levels. Both policies have proven effective in reducing the spread of the COVID-19 virus. To obtain the overview of this case, many researchers were conducted. Here, the Generalized STAR (GSTAR) model was applied to model the increasing number of COVID-19 positive cases per day in six provinces in Java Island. The data was recorded simultaneously in six locations, namely in the Provinces of Banten, Jakarta, West Java, Central Java, Yogyakarta Special Region, and East Java. This paper proposes a new approach in constructing the weight matrix required to build the GSTAR model, namely Minimum Spanning Tree (MST). The weight matrix represents the relationship among observed locations. By using the MST, a topological (undirected graph) network model could be created to show the correlation, centrality, and relationship on the increase of COVID-19 positive cases among the provinces in Java Island. The GSTAR(1;1) with the inverse distance weight matrix using MST presents a good ability to predict the COVID-19 increasing cases of Java island. This is indicated by the final MAPE average score of 19.55.

scholarly journals Penentuan Rute Terpendek Jalur Distribusi Air Artesis Menggunakan Kruskal

2018 ◽  
Vol 2 (2) ◽  
pp. 121
Author(s):  
Diah Ayu Retnani Wulandari ◽  
Fajrin Nurman Arifin
Keyword(s):  
Graph Theory ◽  
Water Supply ◽  
Water Flow ◽  
Shortest Path ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Flow Distribution ◽  
Path Optimization ◽  
Network Method ◽  
Artesian Water

Water flow distribution to home residents from the artesian well is affected by infrastructure. The more houses that distributed makes decreased amount supply of artesian water in every house. the longer of pipe leight and many branches traversed makes decrease of water supply because there will be many possible pipeline leaks. The more pipes used make the more expensive infrastructure cost. This problem occurs in Jubung area. These problems is one variation of the minimum Spanning Tree problems. This problem can be solved by the shortest path optimization route. It uses network method by implementing graph theory through kruskal algorithm. The first step is determined the nodes and sides. Nodes represent house and the sides represents the connecting pipes between houses. Kruskal is chosen because the kruskal focuses on the side and the graph is incomplete. focus of this study is the length optimation of the connecting pipe that is represented by side. In the pipe infrastructure figure map is representing of an incomplete graph because there are several nodes that are not connected to all nodes because it is adapted to the contour of the land that is not possible traversed the pipe. The results is there are several paths that are changed, especially the side to connect between node 1-4, 4-12, 19-20, 21-6 dispensed because forming cycles. The result of this research is kruskal can make decreasing infrastrukture cost Rp.7.535.500 with length of 201,5 meter so can save Rp.4.401.000 from Rp Rp.11.936.500.

scholarly journals Proposal of creation of a portfolio with minimal risk

2017 ◽  
Vol 14 (2) ◽  
pp. 107-115 ◽  
Author(s):  
Vincent Šoltés ◽  
Jakub Danko
Keyword(s):  
Graph Theory ◽  
Standard Deviation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Stock Index ◽  
Discrete Mathematics ◽  
Second Step ◽  
Minimal Risk ◽  
Investment Strategies ◽  
Individual Investor

The aim of this work is to propose a method for creating portfolios with a minimal expected risk. The proposed method consists of two steps. In the first step, the authors use a method for finding a minimum spanning tree. It is a graph theory tool, which is the field of discrete mathematics. Graph is defined as a set of vertices and edges. By this method the authors distribute assets, for example a stock index, into several subgroups. From each group it is then chosen an asset, from which most of the edges come out. These selected assets will be used to create a portfolio. In the second step, the authors will use a method of minimizing the standard deviation of the portfolio to calculate the weight of its assets. By this method, first it is found the weight of each asset so that the resulting portfolio would have the lowest possible expected risk. Then the authors find the portfolio with the lowest possible expected risk at required yield and create investment strategies. These strategies are compared during the time and between each other based on the variation coefficient. The article can be a practical guide for an individual investor during the minimal risk portfolio creation and shows him, which assets (and which asset weights) of the selected index to purchase.

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