scholarly journals A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm

Information ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 418
Author(s):  
Jörg Schäfer
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Greedy Algorithms ◽  
Reconstruction Algorithm ◽  
Minimum Spanning Trees ◽  
Ultrametric Spaces ◽  
Correctness Proof ◽  
Topological Distance ◽  
Join Algorithm

We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications. Although (greedy) algorithms for constructing minimum spanning trees such as Prim’s or Kruskal’s algorithm have been known for a long time, they require the complete graph to be specified and the weights of all edges to be known upfront in order to construct a minimum spanning tree. However, if the weights of the underlying graph stem from an ultrametric, the minimum spanning tree can be constructed incrementally and it is not necessary to know the full graph in advance. This is possible, because the join algorithm responsible for joining new nodes on behalf of the topological distance algorithm is independent of the order in which the nodes are added due to the property of an ultrametric. Apart from the mathematical elegance which some readers might find interesting in itself, this provides not only proofs (and clearer ones in the opinion of the author) for optimality theorems (i.e., proof of the minimum spanning tree construction) but a simple proof for the optimality of the reconstruction algorithm omitted in previous publications too. Furthermore, we define a new algorithm by extending the join algorithm to minimize the topological distance and (network) latency together and provide a correctness proof.

scholarly journals A Minimum-Spanning-Tree-Inspired Algorithm for Channel Assignment in 802.11 Networks

2016 ◽  
Vol 62 (4) ◽  
pp. 379-388 ◽  
Author(s):  
Iwona Dolińska ◽  
Mariusz Jakubowski ◽  
Antoni Masiukiewicz ◽  
Grzegorz Rządkowski ◽  
Kamil Piórczyński
Keyword(s):  
Greedy Algorithm ◽  
Channel Assignment ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Minimum Spanning Trees ◽  
Undirected Graphs ◽  
Interference Level ◽  
802.11 Networks ◽  
Crowded Environment

Abstract Channel assignment in 2.4 GHz band of 802.11 standard is still important issue as a lot of 2.4 GHz devices are in use. This band offers only three non-overlapping channels, so in crowded environment users can suffer from high interference level. In this paper, a greedy algorithm inspired by the Prim’s algorithm for finding minimum spanning trees (MSTs) in undirected graphs is considered for channel assignment in this type of networks. The proposed solution tested for example network distributions achieves results close to the exhaustive approach and is, in many cases, several orders of magnitude faster.

scholarly journals Meminimalisir Biaya Pembuatan Saluran Air PDAM Di Wilayah KLU Menggunakan Algoritma Kruskal

2019 ◽  
Vol 1 (1) ◽  
pp. 27
Author(s):  
Devi Lastri ◽  
Masriani ◽  
Nadia W ◽  
Parizal Hidayatullah ◽  
Wahyu Ulfayandhie Misuki ◽  
...  
Keyword(s):  
Spanning Tree ◽  
Water Distribution ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Clean Water ◽  
Minimum Spanning Trees ◽  
Tree Algorithm ◽  
Shortest Route ◽  
Minimize Costs

The kruskal algorithm is an algorithm to search for minimum spanning trees directly based on the general MST (Minimum Spanning Tree) algorithm. In the kruskal algorithm, the sides in the graph are sorted first based on their weight from small to large. The kruskal algorithm in the search for a minimum spanning tree can be applied to the distribution of clean water of PDAM in North Lombok district. This problem is intended to get the shortest route for PDAM water distribution in North Lombok district in order to minimize costs.

EVOLUTIONARY TOPOLOGY OF A CURRENCY NETWORK IN ASIA

2010 ◽  
Vol 21 (04) ◽  
pp. 471-480 ◽  
Author(s):  
XIAOBING FENG ◽  
XIAOFAN WANG
Keyword(s):  
Exchange Rate ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Structural Evolution ◽  
Growth Cycle ◽  
Minimum Spanning Trees ◽  
Trade Volume ◽  
National Wealth ◽  
Us Dollar

Although recently there are extensive research on currency network using minimum spanning trees approach, the knowledge about the actual evolution of a currency web in Asia is still limited. In the paper, we study the structural evolution of an Asian network using daily exchange rate data. It was found that the correlation between Asian currencies and US Dollar, the previous regional key currency has become weaker and the intra-Asia interactions have increased. This becomes more salient after the exchange rate reform of China. Different from the previous studies, we further reveal that it is the trade volume, national wealth gap and countries growth cycle that has contributed to the evolutionary topology of the minimum spanning tree. These findings provide a valuable platform for theoretical modeling and further analysis.

scholarly journals Parallel Oblivious Array Access for Secure Multiparty Computation and Privacy-Preserving Minimum Spanning Trees

2015 ◽  
Vol 2015 (2) ◽  
pp. 188-205 ◽  
Author(s):  
Peeter Laud
Keyword(s):  
Large Class ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Black Box ◽  
Secure Multiparty Computation ◽  
Multiparty Computation ◽  
Minimum Spanning Trees ◽  
Asymptotic Performance ◽  
Underlying Graph

AbstractIn this paper, we describe efficient protocols to perform in parallel many reads and writes in private arrays according to private indices. The protocol is implemented on top of the Arithmetic Black Box (ABB) and can be freely composed to build larger privacypreserving applications. For a large class of secure multiparty computation (SMC) protocols, our technique has better practical and asymptotic performance than any previous ORAM technique that has been adapted for use in SMC.Our ORAM technique opens up a large class of parallel algorithms for adoption to run on SMC platforms. In this paper, we demonstrate how the minimum spanning tree (MST) finding algorithm by Awerbuch and Shiloach can be executed without revealing any details about the underlying graph (beside its size). The data accesses of this algorithm heavily depend on the location and weight of edges (which are private) and our ORAM technique is instrumental in their execution. Our implementation is the first-ever realization of a privacypreserving MST algorithm with sublinear round complexity.

scholarly journals Investigating the Disparities of China’s Insurance Market Based on Minimum Spanning Tree from the Viewpoint of Geography and Enterprise

2017 ◽  
Vol 5 (3) ◽  
pp. 216-228
Author(s):  
Chi Xie ◽  
Yingying Zhou ◽  
Gangjin Wang ◽  
Xinguo Yan
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Insurance Market ◽  
Minimum Spanning Trees ◽  
Monthly Data ◽  
Property Insurance ◽  
Personal Insurance

Abstract In this paper, we investigate the disparities of China’s insurance market from the viewpoint of geography and enterprise by using the monthly data from January 2006 to December 2015. We divide the whole insurance market into two parts, namely property insurance and personal insurance. By constructing and analyzing minimum spanning trees of insurance market, we obtain the results as follows: (i) The connections between provinces are much closer than those of firms, and there are regional links between neighboring provinces in the minimum spanning tree (MST); and (ii) the domestic funded firms and foreign funded firms form two explicit clusters in the MSTs of property and personal insurance market.

AN EREW PARM ALGORITHM FOR UPDATING MINIMUM SPANNING TREES

1999 ◽  
Vol 09 (01) ◽  
pp. 111-122 ◽  
Author(s):  
SAJAL K. DAS ◽  
PAOLO FERRAGINA
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Substantial Improvement ◽  
Minimum Spanning Trees ◽  
Single Edge ◽  
Sequential Approach ◽  
Work Complexity

We propose a parallel algorithm for the EREW PRAW model that maintains a minimum spanning tree (MST) of an undirected graph under single edge insertions and deletions. For a graph of n nodes and m edges, each update requires O( log n) time and O(m 2/3 log n) work. This is a substantial improvement over the known bounds on the work complexity. Our algorithm uses a partition of the MST, similar to the sequential approach due to Frederickson [6], and also employs a novel data structure for efficiently managing edge insertions in parallel.

scholarly journals IMPLEMENTASI ALGORITMA KRUSKAL DAN ALGORITMA PRIM SUATU GRAPH DENGAN APLIKASI BERBASIS DESKTOP

2020 ◽  
Vol 3 (2) ◽  
pp. 89-93
Author(s):  
Siti Alvi Sholikhatin ◽  
Adi Budi Prasetyo ◽  
Ade Nurhopipah
Keyword(s):  
Spanning Tree ◽  
Research Study ◽  
Minimum Spanning Tree ◽  
Greedy Algorithms ◽  
Relevant Literature ◽  
Weighted Graph ◽  
Self Assessment ◽  
Technological Readiness ◽  
Actual Environment ◽  
Application Design

A graph has several algorithms in its solution, including the Kruskal algorithm and Prim algorithm, both of which are greedy algorithms for determining the minimum spanning tree. Completion of graphs is useful in various fields of life, so an accurate graph calculation is important. Making an application to solve a graph, especially the Kruskal algorithm and Prim algorithm aims to facilitate the work of the graph so as to produce an accurate final result. The flow of research carried out are: a background review of research, study of literature and relevant literature, application design, building desktop-based applications, as well as implementation and application tests. The level of technological readiness or TKT in this research is based on self-assessment which is at level 7, meaning the prototype demonstration system in the actual environment, with details of the TKT indicators as follows: TKT indicator 1 is met, TKT indicator 2 is met, TKT indicator 3 is not met, TKT indicator 4, TKT indicator 5 are met, TKT indicator 6 are met, TKT indicator 7 is met, TKT indicator 8 and 9 are not met. The application that has been built is useful for completing a graph with the Kruskal algorithm and Prim algorithm. This research was conducted to answer the crucial needs of a weighted graph settlement application.

scholarly journals Development of Gis Tool for the Solution of Minimum Spanning Tree Problem using Prim's Algorithm

2014 ◽  
Vol XL-8 ◽  
pp. 1105-1114 ◽  
Author(s):  
S. Dutta ◽  
D. Patra ◽  
H. Shankar ◽  
P. Alok Verma
Keyword(s):  
Spanning Tree ◽  
Road Network ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Transportation Network ◽  
Travelling Salesman Problem ◽  
Optimal Path ◽  
Road Transportation ◽  
Gis Technology ◽  
Weighted Network

minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it’s minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.

scholarly journals Zastosowanie metody minimalnego drzewa rozpinającego (najkrótszego dendrytu) w ocenie efektywności i spójności sieci osadniczej województwa mazowieckiego = Application of the minimum spanning tree method in assessing the effectiveness and cohesion of the settlement network of Mazowieckie voivodeship

2019 ◽  
Vol 91 (2) ◽  
pp. 61-80 ◽  
Author(s):  
Przemysław Śleszyński ◽  
Paweł Sudra
Keyword(s):  
Urban Areas ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Research Area ◽  
Rural Settlements ◽  
Single Family ◽  
Network Effectiveness ◽  
Spatial Cohesion ◽  
The 19Th Century

Contemporary settlement systems observed in Poland bear numerous traces of historical transformations of rural settlements which took place in the 19th century, at the time of foreign partitioning of Polish territory, in different ways in particular regions. The result of processes occurring from the second half of the 20th century is the extensive development of urban areas, and – after 1990 – chaotic, spontaneous processes of transformation in suburban zones. Research methods using graph theory have been applied for years in investigating settlement networks on various scales. One of the more useful graphs is the minimum spanning tree (MST), which connects all vertices in such a way that the sum of the distances between them is the shortest. This article presents the application of the minimum spanning tree (or shortest dendrite) method with a view to its suitability for determining the degree of dispersion and spatial cohesion of urbanised structures being assessed. Two indicators have been proposed thanks to alignment of the shortest dendrite length to other variables. The settlement network effectiveness indicator is the ratio of MST length to the population in an area. The settlement network cohesion indicator is in turn the ratio of the MST length to population density. Mazowieckie voivodeship has been chosen as the research area, while address points obtained from the central official database collecting data from municipal records have been chosen as the source dataset. Over 1 million address points were considered, in line with their status as at the end of 2016. Minimum spanning trees were plotted for each of the 314 gminas (local-authority areas) aking up the voivodeship, using ArcGIS software. Subsequently, the proposed indicators were calculated by reference to the MSTs. The results were then mapped. The proposed indicators may be helpful in studies on the origin of settlements, allowing areas with varying degrees of uniformity or isolation of building locations to be indicated. They can be made use of in comparative studies, especially concerning rural settlements, in which single-family housing predominates, and hamlets and uildings standing in isolation are present. The effectiveness indicator can be used in the assessment of infrastructural coverage, i.a. in the ontext of the costs of spatial chaos and demographic capacity.

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