Showing papers on "Prim's algorithm published in 2015"

SimplePPT: A simple principal tree algorithm

Abstract: Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are not self-intersected, which is quite restrictive for real applications. To address this issue, we develop a new model, which captures the local information of the underlying graph structure based on reversed graph embedding. A generalization bound is derived that show that the model is consistent if the number of data points is sufficiently large. As a special case, a principal tree model is proposed and a new algorithm is developed that learns a tree structure automatically from data. The new algorithm is simple and parameter-free with guaranteed convergence. Experimental results on synthetic and breast cancer datasets show that the proposed method compares favorably with baselines and can discover a breast cancer progression path with multiple branches.

A 2k-vertex Kernel for Maximum Internal Spanning Tree

Abstract: We consider the parameterized version of the maximum internal spanning tree problem: given an n-vertex graph and a parameter k, does the graph have a spanning tree with at least k internal vertices? Fomin et al. [J. Comput. System Sci., 79:1–6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3k-vertex kernel for this problem. Here we propose a novel way to use the same reduction rule, resulting in an improved 2k-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a \(4^k \cdot n^{O(1)}\)-time deterministic algorithm, improving all previous algorithms for the problem.

An exact algorithm for maximum lifetime data gathering tree without aggregation in wireless sensor networks

Abstract: In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NP-complete. In this paper, we prove that, unless P = NP, no polynomial-time algorithm can approximate the problem with a factor strictly greater than 2/3. The result even holds in the special case where all sensors have the same initial energy. Existing works for the problem focus on approximation algorithms, but these algorithms only find sub-optimal spanning trees and none of them can guarantee to find an optimal tree. We propose the first non-trivial exact algorithm to find an optimal spanning tree. Due to the NP-hardness nature of the problem, this proposed algorithm runs in exponential time in the worst case, but the consumed time is much less than enumerating all spanning trees. This is done by several techniques for speeding up the search. Featured techniques include how to grow the initial spanning tree and how to divide the problem into subproblems. The algorithm can handle small networks and be used as a benchmark for evaluating approximation algorithms.

An artificial immune approach for service restoration in smart distribution systems

Abstract: The power system reconfiguration is a challenging task. As smart grids concepts develop, different approaches try to take advantage of the grid intelligent features and infrastructure to evolve a fast and robust self-healing scheme. At the distribution level, the self-healing schemes are responsible for performing automatic corrective and self-restorative actions. This task includes managing the service restoration by locating and isolating the fault, and reconfiguring the network topology to decrease the harm. This paper presents a self-healing scheme using Artificial Immune System as an optimization tool to solve the service restoration problem in power systems considering faults within the internal switch breakers. To make this approach suitable for bigger systems, the Prim Algorithm is used due to its capacity to generate minimum spanning trees from a graph. The proposed scheme is tested on benchmark systems to investigate the capacity of proposing feasible solutions for faulted systems.

Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Abstract: Degree constrained minimum spanning tree (DCMST) refers to constructing a spanning tree of minimum weight in a complete graph with weights on edges while the degree of each node in the spanning tree is no more than d (d ≥ 2). The paper proposes an improved multicolony ant algorithm for degree constrained minimum spanning tree searching which enables independent search for optimal solutions among various colonies and achieving information exchanges between different colonies by information entropy. Local optimal algorithm is introduced to improve constructed spanning tree. Meanwhile, algorithm strategies in dynamic ant, random perturbations ant colony, and max-min ant system are adapted in this paper to optimize the proposed algorithm. Finally, multiple groups of experimental data show the superiority of the improved algorithm in solving the problems of degree constrained minimum spanning tree.

A Survey on: Enhancement of Minimum Spanning Tree

Abstract: Minimum spanning tree can be obtained for connected weighted edges with no negative weight using classical algorithms such as Boruvka’s, Prim’s and Kruskal. This paper presents a survey on the classical and the more recent algorithms with different techniques. This survey paper also contains comparisons of MST algorithm and their advantages and disadvantages.

The hybrid of depth first search technique and Kruskal's algorithm for solving the multiperiod degree constrained minimum spanning tree problem

Abstract: Given edge weighted graph G(V, E) (all weights are nonnegative) where vertices can represent terminals, cities, etc., and edges can represent cables, road, etc., the Multi Period Degree Constrained Minimum Spanning Tree Problem (MPDCMST) is a problem of finding the total minimum installation cost whilst also maintaining the maximum number of edges incidence to every vertex. The restriction of the links on every vertex occurs to keep the reliability of the network. Moreover, the installation process also divided into some periods due to fund limitation. In this research we will discuss the hybrid between the depth first search technique and Kruskal's Algorithm applying to solve the MPDCMST problem.

The shortest route for transportation in supply chain by minimum spanning tree

Abstract: The aim of this article is to propose a solution for finding the shortest route for transportation between supply and demand. The problem of supplying car battery from Tehran to the centres of provinces of Iran has been investigated and a graph has been developed. Then, by using the heuristic prim algorithm, the minimum spanning tree of this graph has been obtained, and this tree has shown the shortest route for transportation. The problem has also been solved by meta-heuristic genetic algorithm, and the response has been compared with prim algorithm, and it has been shown that for big problems, the genetic algorithm can be used. In order to reduce the density of freight cars in roads, a scenario has been proposed by which, roads traffic and accidents, fuel consumption and customer delivery time can be reduced.

Distribution uniformity assessment method based on watershed algorithm and minimum spanning tree

Abstract: The invention provides a distribution uniformity assessment method based on a watershed algorithm and a minimum spanning tree. The method comprises the steps that an image is subjected to gray processing and median filtering; binarization processing is conducted through an OTSU method; morphological operation is conducted to obtain a feature tag image; segmentation is conducted through the watershed algorithm; an adjoining matrix composed of centroids of segmented regions in the segmented image and distances between the centroids is calculated; the minimum spanning tree is calculated through a Prim algorithm; the distribution uniformity of particles or spots in the image is analyzed based on the minimum spanning tree. According to the method, interference, noise and other ineffective information of the image are filtered out, a tag source is provided for the watershed algorithm, and mistaken segmentation caused by inconsistency of sizes of the particles or the spots and over segmentation caused by the noise are avoided; segmentation based on the watershed algorithm better represents the relation among the particles or the spots and the relation between the particles or the spots and overall distribution; since the Prim algorithm is used for obtaining the minimum spanning tree, the time complexity is low, the efficiency is high, and the assessment of distribution uniformity is more accurate.

Determining minimum spanning tree in an undirected weighted graph

Abstract: This paper proposed a new algorithm to find a minimum spanning tree of an undirected weighted graph graph This new algorithm provides a fresh approach to produce a minimum spanning tree A minimum spanning tree is a sub graph of any undirected weighted graph that gives the minimal cost valued edges to reach every node of any graph The proposed algorithm is named as RAY algorithm for determining the minimum spanning tree We named this new algorithm as RAY, as it gives a new ray of hope in the field of graphs that can be used as a better option for finding the minimum spanning tree of any undirected weighted graph with less duration of time as well as with an easy approach RAY has less complexity with respect to time for finding the minimum spanning tree of any graph in comparison to other algorithms like prim's algorithm and Kruskal's algorithm which are mostly used to find a minimum spanning tree of the graph RAY algorithm select any one node of the given graph as a root node and then it joins every edge connected to that node, which do not form any cycle in the graph This process is repeated until we traverse each node of the graph and the edges those forms cycle during this process are stored separately Now only these separately stored edges are traversed and we check in the graph for maximum weighted edge from the edges that are coming in the cycle which is formed due that particular separately stored edge If there is any edge in the cycle which is greater in weigh than that of separately stored edge then we discarded maximum weighted edge and the new edge which we stored separately is taken into the minimum spanning tree This same procedure is repeated for each edge that we stored separately At the end of this procedure we get a tree which is the minimum spanning tree of the given graph by using RAY algorithm

The Application of Minimum Spanning Tree Algorithm in the Water Supply Network

Abstract: The system of urban water supply network is the important lifeline project of the city. With the continuous development of social economy, people are no longer satisfied with water supply requirements, but to put forward higher requirements for the safety, reliability and economy of the water supply. Based on actual demands to solve the economic problems of water supply network to ensure the lowest costs in the laying the pipelines. First, establishing a mathematical model of water supply network, so we can use the knowledge of graph theory to solve this problem; from the above that, the minimum spanning tree was needed to establish to ensure that costs are the lowest in the case of pipeline connectivity. Then using the Kruskal algorithm to generate minimum spanning tree; finally, an example was analyzed to verify its practicality, and the algorithm solved the problem of water supply network in laying pipelines successfully. Introduction Water is the source of life, and is closely related to human survival. Water supply network is a water distribution system created by people, which is a vital part of water supply system. Water supply system in the order usually consists of water intake structures, water treatment structures, water supply pumping stations, adjustment structures, drainage pipes and water supply pipe network. The water supply network mainly refers to the urban water supply pipe network system, which is an important material base to protect the city people's life and develop production and construction [1]. Urban water supply pipe network system can be regarded as an important lifeline of urban engineering. The traditional view is that the water supply network's mission is to provide sufficient amount of water, the residents have enough water to use. However, with the continuous development of social economy, people put forward higher requirements for the safety, reliability and economy of the water supply. Specifically, in the process of water supply, the quality of supplied water is healthy or not, such as water pipe corrosion or other factors lead to water quality problems; after an earthquake or major disaster, the water supply network is reliable or not, urban water supply network can be normal without the occurrence of secondary disasters; pipe network not only to have above two characteristics, economic issues is the focus. In the case of the entire water supply network connectivity, we must to ensure the lowest costs that aim to produce hedge-fund-like returns at lower cost. So in recent years, research on the economic aspect of water supply network is increasingly attracted people's attention. Water supply system is an important infrastructure of the city, and it also is an important part of urban lifeline project, which plays an irreplaceable role in protecting economic development, ensuring social production and meeting human life [2]. The Establishment of the Mathematical Model for Water Supply Network In laying city network, the street interchanges must be considered because the pipelines must along the street to lay. In case of that water supply network can connect all users to make it with the lowest costs. To achieve this goal, you must consider how to select and handle these interchanges. This problem is a serious problem. The solution of this problem can provide a standard for the International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 52 laying of water supply network to ensure best design effect. According to graph theory, the water supply network can be viewed as a graph. So the contents of the water supply network need to be translated into the language of graph theory to help solve the problem of water supply network costs. The language from pipelines to graph is described as follows [3]: a) The water supply center and users in the planning area are referred to as nodes, the intersection of the street known as the intersections. The nodes and intersections are regarded as the vertices of graph. So the issue can be converted to the shortest path between each vertex, and each vertex must be connected indirectly or not indirectly. b) The routes that may be laying between nodes and intersections can be considered as edges of the graph. c) The sum of construction costs and operating costs of each line is regarded as the weights of edges. The sum of weights is the minimum that is the lowest costs, that is the purpose of the design you want to achieve. Through the above three steps, the water supply network can form a graph, this graph includes the vertices, edges and weights. Using G (V, E, W) to represent, V represents the set of vertices in the graph; E represents the set of edges in the graph; W represents the set of weights of each edge in the graph. Setting T is a spanning tree of diagram of G, then: W(T)=∑ Wuv euv∈T (1) Among them, W(T) is the sum of weights in the tree of T; euv is the any edge in the tree of T; Wuv is the weights of euv. The purpose of design is to require the minimum values of W(T). Only this way can ensure the lowest costs of laying pipelines. In summary, the problem of the minimum costs of the water supply network may be as a problem of seeking minimum spanning tree in the graph. The minimum spanning tree must exist. According to the actual situation, each node will certainly connected when laying water supply network, so there will be a minimum spanning tree certainly. There are a variety of algorithms to generate minimum spanning tree, such as Prim algorithm, Kruskal algorithm and simple algorithm and so on [4]. The Basic Concept of Algorithm Kruskal algorithm chooses the right edge according to the ascending order of weights to construct a minimum spanning tree. Kruskal algorithm, also known as avoidance circle method, starting from the shortest side, the edge attached to the tree does not form a loop, then the edge can be added to the tree, otherwise examine the next edge [5]. Specific steps are as follows: (1) Firstly, all vertices in connectivity network need to be added to minimum spanning tree to Start Arranging according to the ascending order of weights Setting d(vj)=min{d(u), d(v)}

A Deterministic and a Randomized Algorithm for Approximating Minimum Spanning Tree under the SINR Model

Abstract: We describe a deterministic and a randomized distributed algorithm for computing a spanning tree over a wireless network whose weight approximates the weight of a Minimum Spanning Tree (MST). The network is composed of n static nodes embedded in a 2-dimensional Euclidean space which communicate according to the Signal-to-Interference- and-Noise Ratio (SINR) model. Under the assumption that each node knows its position and the granularity g of the network, the deterministic algorithm computes a tree within O(D log g) rounds, where D is the diameter of the graph. When nodes additionally know the local density of the network, the randomized algorithm computes a tree within O(D+log n+log g) rounds. The computed trees have weight that is within an O(log n) factor of the weight of MST. To the best of our knowledge we describe the first deterministic algorithm for this problem under the SINR model.

A distributed algorithm to construct multicast trees in wireless multi-hop networks

Abstract: The minimum-length multicast tree can achieve efficient multicast transmissions and can be formulated as a Steiner Tree. Its construction is non-trivial and has been proven to be NP-hard. In this paper, we combine the design wisdoms in the minimum spanning tree and the shortest path, and propose a new distributed algorithm for constructing an approximate Steiner Tree, particularly applicable to dynamic wireless networks without centralized control. We rigorously prove the performance bounds of our algorithm in terms of tree length, running time and energy consumption. Let m be the multicast group size and n be the network size. We theoretically show that the ratio of our tree length to the minimum value is upper bounded by equation (where δ can be any positive value). Simulation results show that this ratio is in fact very close to 1. We also prove that the running time is equation. The energy consumption is evaluated in terms of message complexity, and is upper bounded by O(n logm). In all, our algorithm achieves the near-optimal tree length, as well as the shortest running time and the lowest message complexity among all solutions we are aware of. We believe our algorithm provides a significant improvement in designing practical routing policies in wireless networks.

Pavement Crack Connection Algorithm Based on Prim Minimum Spanning Tree

Abstract: When the digital image processing technology is used to detect the cracks on the pavement,it is very hard to detect an intact structure for the cracks because parts of the cracks are very narrow,or shadowed by other objects,or filled with dust. These seriously affects the accuracy of the crack parameter measurement and damage index evaluation. Aiming at the problems above,a pavement crack connection algorithm using Prim minimum spanning tree is proposed. The ridge detection method is used to mark out all the suspicious cracks targets,with the shape features of cracks to remove the noises like spots or blocks. So all the long or obvious cracks are remained. Using the morphology method,the endpoints of the remained crack segments are extracted,and the Prim algorithm is used to construct a minimum spanning tree and makes all the discontinuous cracks connected. All the forced pseudo connections are deleted through the orientation and contrast characteristics of the cracks. On the basis of connection,the cracks are enhanced by filling operation and an intact crack structure is acquired.200 pavement images with cracks are tested,and the Hausdorff distance is used to evaluate the performance of various algorithms. Experimental results show that the proposed algorithm significantly improves the continuity of the detected crack targets,the detection accuracy rate of which is higher than other algorithms with by 6 ~13 percentage.

Mathematical Modeling on Network Fractional Routing Through Minimum Spanning Tree

Abstract: A minimum Spanning Tree is one of the most important optimization techniques to help Decision Making in Network. A Minimum spanning Tree problem calls for optimizing linear functions of variables called objective function. The objective function minimizes the total outflow from source node to sink node. I will prove fractional routing capacity for some solvable networks using minimum spanning tree.

Generating spanning tree of non-regular graphic sequences through a variant of Prim's algorithm

Abstract: Determining graphic degree sequences and finding the spanning tree of a graph are two popular problems of combinatorial optimization. A simple graph that realizes such a degree sequence is often termed as a realization of the given sequence. In this paper we have proposed a method for generating a spanning tree from a degree sequence, provided the degree sequence is graphic and non-regular. The proposed method first constructs the adjacency matrix corresponding to the degree sequence and then applies a modified version of Prim's algorithm to generate the spanning tree from it.

Unveiling the tree: A convex framework for sparse problems

Abstract: This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown topology. For every pre-walk of the tree an initial set of generally dense feasible solutions is processed in such a way that the sparsity of each solution increases with each generation unveiled. The specific computation performed at any particular child node is shown to correspond to an embedding of a polytope into the polytope received from that nodes parent. Several issues related to pre-walk order selection, computational complexity and tractability, and the use of heuristic and/or side information is discussed. An example of a single-path, depth-first algorithm on a tree with randomized vertex reduction and a run-time path selection algorithm is presented in the context of sparse lowpass filter design.

An Algorithm for the Minimum Spanning Tree Problem with Uncertain Structures

Abstract: The minimum spanning tree problem consists to find the smallest weight among all possible trees in a network. It is one of the main problems of graphs theory, since it has a wide range of applications in Engineering and Computation areas, such as: electricity distribution networks, information storage, transportation, etc. In this paper is proposed an exact algorithm to the minimum spanning tree problem with uncertain structures. It is based on the mainly papers of the literature and presents a solution ordered set of minimum spanning trees. The uncertainties of the structures are resolved using the fuzzy sets theory. The algorithm was tested on literature instances having the same results. Its complexity is O((v-a)(v^2)), where v is the node sets and a is the arcs sets.

A Novel Cluster Head Selection Method based on HAC Algorithm for Energy Efficient Wireless Sensor Network

Abstract: Improving the lifetime of wireless sensor networks (WSNs) remains an open and active research area. One of the challenging problems in this field is the partitioning of a WSN into disjoint clusters so that the network lifetime is maximized. In particular, the selection of a head for each cluster should consider various parameters related to transmission costs. In this paper, we propose a novel clustering scheme based on hierarchical agglomerative clustering algorithm. The selection of the cluster heads is based on the proximity with a virtual node representing the optimal head location with respect to energy consumption. The proposed algorithm is re-executed at each packet delivering round to maintain energy efficiency during the whole network lifetime. In the transmission of packets to BS, we consider two cases: - Single Hop transmission between CHs and BS that, each CH directly send packets to BS. and - Multi-Hop transmission between the BS and CHs that, each CH transmits to another CH or to a base station according to the results obtained by the algorithm of the spanning tree Experimental results show that our clustering scheme is less energy-consuming than LEACH, HEED and clustering protocol using k-means algorithm.

Narrow passage identification using cell decompositionapproximation and minimum spanning tree

Abstract: Narrow passage problem is a problematic issue facing the sampling-based motion planner. In this paper, a new approach for narrow areas identification is proposed. The quad-tree cell-decomposition approximation is used to divide the free workspace into smaller cells, and build a graph of adjacency for these. The proposed method follows the graph edges and finds a sequence of cells, which have the same size, preceded and followed by a bigger cell size. The sequence, which has the pattern bigger-smaller-bigger cells size, is more likely to be located in a narrow area. The minimum spanning tree algorithm is used, to linearize adjacency graph. Many methods have been proposed to manipulate the edges cost in the graph, in order to make the generated spanning tree traverse through narrow passages in detectable ways. Five methods have been proposed, some of them give bad results, and the others give better on in simulations

A new algorithm for the minimum spanning tree verification problem

Abstract: This paper proposes a new algorithm for the minimum spanning tree verification (MSTV) problem in undirected graphs. The MSTV problem is distinct from the minimum spanning tree construction problem. The above problems have been studied extensively, and there exist several papers in the literature devoted to them. Our algorithm for the MSTV problem combines the insights of Bor?vka's algorithm for constructing a minimum spanning tree with a bucketing scheme. The principal idea underlying this combination is the efficient identification of edges that cannot be part of any minimum spanning tree. Although the proposed algorithm imposes no restrictions on the input graph, it was designed to exploit the case in which the number of distinct edge weights is small. On a graph with $$n$$n vertices, $$m$$m edges, and $$K$$K distinct edge weights, our algorithm runs in $$O(m+n\cdot K)$$O(m+n·K) time. It follows that our algorithm runs in linear time if $$K$$K is a fixed constant. Although there exist several linear time MSTV algorithms in the literature, our algorithm improves on the state of the art in two ways, viz., it is conceptually simpler, and it is easy to implement. We contrast the performance of our algorithm vis-a-vis Hagerup's linear time MSTV algorithm, which is one of the more practical linear-time MSTV algorithms. Our experiments indicate that the proposed algorithm is superior to Hagerup's algorithm when $$K \le 24$$K≤24. One surprising observation is that our algorithm is substantially faster than Hagerup's algorithm on "No" instances, i.e., on instances in which the input spanning tree is not the minimum spanning tree.

Load Balancing Technique to Release Multiple Overloading of Distribution Feeders using Minimum Spanning Tree

Abstract: Power supplying capacity of the distribution feeder should be maintained within thermal capacity of the wire. This paper presents the minimum spanning tree based load balancing technique to release multiple overloading of distribution feeders. In order to minimize number of involved backup feeders, Dijkstra and Prim algorithm are adopted to construct minimum spanning tree. Simulation testing result based on part of KEPCO's commercial distribution systems shows effectiveness of proposed scheme.

An improved minimum spanning tree stereo matching algorithm

Abstract: The minimum spanning tree stereo matching algorithm only takes one channel of R, G, B channels into account, ignoring the effect of the other two channels on the final edge weight in color image. This paper proposes an improved minimum spanning tree stereo matching algorithm, which calculates the weighted euclidean distance using a three-channel approach, and combines three-channel edge weight. This algorithm has been tested on Tsukuba, Venus, Teddy, Cones image. Simulation results show that the improved algorithm enhances the robustness of edge weight function and the connectivity of minimum spanning tree. It not only improves stereo matching accuracy, but also increases computational speed.

Matlab program for minimum weighted spanning tree using dominating set

Abstract: Finding a minimum weighted spanning tree is an important problem as it has many applications. Finding minimum weighted spanning tree using graph properties is not in much use. In this paper we provide a MATLAB Programme, for generating a minimum weighted spanning tree using adjacency matrix.

최소신장트리를 이용한 배전선로 다중 과부하 해소 방법

Abstract: Power supplying capacity of the distribution feeder should be maintained within thermal capacity of the wire. This paper presents the minimum spanning tree based load balancing technique to release multiple overloading of distribution feeders. In order to minimize number of involved backup feeders, Dijkstra and Prim algorithm are adopted to construct minimum spanning tree. Simulation testing result based on part of KEPCO’s commercial distribution systems shows effectiveness of proposed scheme.

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Abstract: Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.