Showing papers on "Prim's algorithm published in 2016"
TL;DR: The proposed integrated optimization strategy based on the extended network has better performance compared with a two-step restoration strategy; also, the proposed loop-breaking technique has faster calculation speed compared with prim algorithm and DFS based on adjacent matrix.
Abstract: A novel extended network for service restoration optimization problem under distributed generation scenarios is presented in which the main network restoration and DG island restoration problems are integrated into a unified spanning-tree problem. The proposed technique is aimed to realize synchronous optimization of both main network and island restorations, and thus ensure the algorithms that are used find the global optimization solution. A fast loop-breaking technique is also proposed in this paper. Based on the circuit-branch correlation matrix, the proposed technique can break the loops in the distribution systems through matrix operations that significantly improve calculation speeds. Simulation results verify the correctness and advantage of the proposed algorithms: the proposed integrated optimization strategy based on the extended network has better performance compared with a two-step restoration strategy; also, the proposed loop-breaking technique has faster calculation speed compared with prim algorithm and DFS based on adjacent matrix.
28 citations
TL;DR: The proposed multi-operator genetic algorithm for the generalized MST problem suggests that for many other combinatorial optimization problems, which have been addressed with a genetic algorithm, better results could possibly be obtained simply by using a greater number of variation operators.
Abstract: We propose a multi-operator genetic algorithm for the generalized MST problem.Two operators are used for the crossover and five for the mutation.A synergic effect emerges from the multi-operator approach.An average error of 0.01% was achieved for the 101 most challenging instances. The generalized minimum spanning tree problem, with applications in the field of communication networks, is a computational challenge due essentially to its NP-hardness. The problem consists of finding a minimum cost spanning tree in an undirected graph whose vertices are grouped in clusters, such that the spanning tree contains only one vertex of each cluster. The algorithms that have provided the best results still do not optimally solve all instances in the literature. One of the most widely studied approaches to the problem is the use of genetic algorithms that, in all cases, use only single operators for crossover and mutation, disregarding the potential synergy of multi-operators. We present a multi-operator genetic algorithm of the genotype-phenotype class, in which the genotype is a chain of integers that represents a cluster's selected vertex. Therefore, the phenotype is a minimum cost spanning tree that is generated by means of Kruskal's algorithm and joins the vertices selected from each cluster. Two operators are used for crossover and five for mutation, three of which are local search operators. The performance of the resultant algorithm is evaluated using the most challenging instances in the literature, the results of which are compared with those of other mono-operator genetic algorithms and with the best existing results. With the 101 instances that are considered, an average error of 0.0142% is achieved, and in 83 instances, the best solution cost is obtained. Such performance is due both to the synergistic effect produced among the operators and the mutation operators working as local searches. Additionally, the results suggest that for many other combinatorial optimization problems, which have been addressed with a genetic algorithm, better results could possibly be obtained simply by using a greater number of variation operators.
23 citations
Proceedings Article•
09 Jul 2016TL;DR: This paper proposes a novel centrality notion of a vertex, called aggregated spanning tree centrality, which also considers the number of connected components obtained by removing the vertex, and gives an efficient algorithm for estimating aggregated spans tree centralities.
Abstract: In a connected graph, spanning tree centralities of a vertex and an edge measure how crucial they are for the graph to be connected. In this paper, we propose efficient algorithms for estimating spanning tree centralities with theoretical guarantees on their accuracy. We experimentally demonstrate that our methods are orders of magnitude faster than previous methods. Then, we propose a novel centrality notion of a vertex, called aggregated spanning tree centrality, which also considers the number of connected components obtained by removing the vertex. We also give an efficient algorithm for estimating aggregated spanning tree centrality. Finally, we experimentally show that those spanning tree centralities are useful to identify vulnerable edges and vertices in infrastructure networks.
19 citations
24 Oct 2016
TL;DR: The correctness of Prim’s algorithm for computing minimum spanning trees is formally proved, and new generalisations of relation algebras and Kleene algeBRas are introduced, in which most of the proof can be carried out.
Abstract: We formally prove the correctness of Prim’s algorithm for computing minimum spanning trees. We introduce new generalisations of relation algebras and Kleene algebras, in which most of the proof can be carried out. Only a small part needs additional operations, for which we introduce a new algebraic structure. We instantiate these algebras by matrices over extended reals, which model the weighted graphs used in the algorithm. Many existing results from relation algebras and Kleene algebras generalise from the relation model to the weighted-graph model with no or small changes. The overall structure of the proof uses Hoare logic. All results are formally verified in Isabelle/HOL heavily using its integrated automated theorem provers.
15 citations
01 Jan 2016
TL;DR: In this paper, an evolutionary algorithm with guided mutation (EA/G) was proposed to solve the dominating tree problem in wireless sensor networks. But, the proposed EA/G algorithm is not suitable for wireless sensor network.
Abstract: Given an undirected, connected, edge-weighted graph, the dominating tree problem (DTP) seeks on this graph a tree of minimum weight such that each node of the graph either belongs to the tree or is adjacent to a node in the tree. This problem is $${\fancyscript{NP}}$$NP-hard. In this paper, we present an evolutionary algorithm with guided mutation (EA/G) to solve the DTP. This problem has several practical applications in the field of wireless sensor networks. EA/G is a recently proposed evolutionary algorithm that tries to overcome the shortcomings of genetic algorithms (GAs) and estimation of distribution algorithms both, and has the characteristics of both. We have compared the performance of our proposed approach with the state-of-the-art approaches presented in the literature. Computational results show the superiority of our approach in terms of solution quality as well as execution time.
12 citations
27 Jun 2016
TL;DR: This paper presents an efficient algorithm, namely Edge Pruned Minimum Spanning Tree (EPMST) algorithm, which combines ideas from randomized selection, Kruskal's algorithm and Prim's algorithm, and has a superior performance relative to the best-known algorithms.
Abstract: Finding minimum spanning trees (MST) in various types of networks is a well-studied problem in theory and practical applications. A number of efficient algorithms have been already developed for this problem. In this paper we present an efficient algorithm, namely Edge Pruned Minimum Spanning Tree (EPMST) algorithm, which combines ideas from randomized selection, Kruskal's algorithm and Prim's algorithm. The algorithm has a superior performance relative to the best-known algorithms especially when the graph is not very sparse. Specifically, EPMST outperforms a recently devised efficient algorithm on a wide range of input graphs.
9 citations
TL;DR: Two linearly parallelizable metaheuristics are described which significantly improve the performance of MOD_PRIM and are capable of finding near-optimal solutions of very large GCTPs in quadratic time in |V|.
Abstract: Vasko et al., Comput Oper Res 29 2002, 441-458 defined the cable-trench problem CTP as a combination of the Shortest Path and Minimum Spanning Tree Problems. Specifically, let G=V,i¾źE be a connected weighted graph with specified vertex v1∈V referred to as the root, length lei¾ź0 for each e∈E, and positive parameters i¾ź and γ. The CTP is the problem of finding a spanning tree T of G such that i¾źli¾źT+γlγT is minimized, where li¾źT is the total length of the spanning tree T and lγT is the total path length in T from v1 to all other vertices of V. Recently, Jiang et al., Proceedings of MICCAI 6893 2011, 528-536 modeled the vascular network connectivity problem in medical image analysis as an extraordinarily large-scale application of the generalized cable-trench problem GCTP. They proposed an efficient solution based on a modification of Prim's algorithm MOD_PRIM, but did not elaborate on it. In this article, we formally define the GCTP, describe MOD_PRIM in detail, and describe two linearly parallelizable metaheuristics which significantly improve the performance of MOD_PRIM. These metaheuristics are capable of finding near-optimal solutions of very large GCTPs in quadratic time in |V|. We also give empirical results for graphs with up to 25,001 vertices. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 673, 199-208 2016
8 citations
TL;DR: A technique based on a genotype-phenotype genetic algorithm to automatically construct new algorithms for the generalized minimum spanning tree problem, which contain combinations of heuristics, which are competitive in terms of the quality of the solution obtained.
Abstract: The generalized minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph for which the vertices are divided into clusters. Such spanning tree includes only one vertex from each cluster. Despite the diverse practical applications for this problem, the NP-hardness continues to be a computational challenge. Good quality solutions for some instances of the problem have been found by combining specific heuristics or by including them within a metaheuristic. However studied combinations correspond to a subset of all possible combinations. In this study a technique based on a genotype-phenotype genetic algorithm to automatically construct new algorithms for the problem, which contain combinations of heuristics, is presented. The produced algorithms are competitive in terms of the quality of the solution obtained. This emerges from the comparison of the performance with problem-specific heuristics and with metaheuristic approaches.
7 citations
26 Jun 2016
TL;DR: Experimenal results show that the proposed fast heuristic is based on a simple algorithm called “list-heuristic,” which calculates better solutions in shorter time than approximation algorithms for MWVCP.
Abstract: Given a vertex-weighted undirected graph, to find the vertex cover of minimum weight is called minimum weight vertex cover problem (MWVCP). It is known as an NP-hard problem. In this paper, a fast heuristic for MWVCP is proposed. Our algorithm is based on a simple algorithm called “list-heuristic.” Experimenal results show that our algorithm calculates better solutions in shorter time than approximation algorithms for MWVCP.
7 citations
TL;DR: In the paper, based on Dijkstra algorithm, an approximation algorithm is obtained for the minimum vertex cover problem and an example is given to illustrate the process and the validity of the Algorithm.
7 citations
TL;DR: This paper presents a cycle detection based greedy algorithm, to obtain a minimal spanning tree of a given input weighted undirected graph, which operates on the idea that every connected graph without any cycle is a tree.
01 May 2016
TL;DR: The generalized minimum spanning tree game is introduced, a constraint generation algorithm to calculate a stable payoff distribution is described and computational results obtained using the proposed algorithm are presented.
Abstract: The minimum-cost spanning tree game is a special class of cooperative games defined on a graph with a set of vertices and a set of edges, where each player owns a vertex. Solutions of the game represent ways to distribute the total cost of a minimum-cost spanning tree among all the players. When the graph is partitioned into clusters, the generalized minimum spanning tree problem is to determine a minimum-cost tree including exactly one vertex from each cluster. This paper introduces the generalized minimum spanning tree game and studies some properties of this game. The paper also describes a constraint generation algorithm to calculate a stable payoff distribution and presents computational results obtained using the proposed algorithm.
TL;DR: This work proposes a solution to the problem of creating minimum spanning tree (MST) in cognitive radio network, a message passing based distributed algorithm that is useful for data dissemination in Cognitive Radio Networks.
Patent•
08 Jun 2016
TL;DR: In this paper, a Dijkstra algorithm was used to acquire a shortest path graph and calculate an influence coefficient of each branch according to the shortest-path graph of two end points of a branch.
Abstract: The invention relates to an offshore wind plant submarine cable wiring acquisition method. The method comprises the following steps of according to an electrical connection graph of an offshore wind plant, acquiring an adjacent matrix among nodes of the offshore wind plant and using the adjacent matrix to express a topology mode in the electrical connection graph and a branch weight among the modes; according to a Dijkstra algorithm, acquiring a shortest path graph and calculating an influence coefficient of each branch according to the shortest path graph of two end points of each branch; multiplying the branch weight in the adjacent matrix by the corresponding influence coefficient so as to acquire the weight of the branch and form a new adjacent matrix; for the acquired new adjacent matrix, using a Prim algorithm and taking a summit of a tree as a lead so as to acquire a minimum spanning tree W; according to a direct current trend equation, calculating a current value of each cable, selecting a submarine cable model so that a current-carrying capacity parameter of the submarine cable is greater than a calculated current value, determining a parameter value of each segment of the submarine cable and calculating submarine cable investment cost of the minimum spanning tree.
01 Dec 2016
TL;DR: A simple and efficient near optimal algorithm, named Maximum Adjacent Minimum degree Algorithm (MAMA) for optimization of minimum vertex cover problem which outperforms the other well-known algorithm and returns near optimal result in quick time.
Abstract: This paper presents a simple and efficient near optimal algorithm, named Maximum Adjacent Minimum degree Algorithm (MAMA) for optimization of minimum vertex cover problem. The proposed algorithm at each step add that maximum degree vertex which is adjacent to minimum degree vertex. The computational complexity and optimality comparison are carried with other state of the art algorithms on small benchmark instances as well as on large benchmark instances to check the efficiency of the proposed algorithm. The proposed algorithm outperforms the other well-known algorithm and returns near optimal result in quick time.
10 Nov 2016
TL;DR: This work has used a heuristic approach, namely hybrid modified genetic algorithm (HMGA), with motivated criteria of encoded data structures of graph, to represent the problem as a graph and finding a spanning tree with specific design criteria.
Abstract: In real life, we always want to reach our goal in minimum effort, it should have a minimum constrained path. The path may be shortest route in practical, either physical or electronic medium, or the minimum costing path in term of resources. The idea is to represent the problem as a graph and finding a spanning tree with specific design criteria. Here, we have chosen a minimum degree spanning tree, which can be generated in real time with minimum turnaround time [11]. The solution approach, in general, is approximate. We have used a heuristic approach, namely hybrid modified genetic algorithm (HMGA), with motivated criteria of encoded data structures of graph. We compare the experimental result with the existing approximate algorithms and the results are very promising.
02 Aug 2016
TL;DR: A novel clustering method based on spectral clustering theory and spectral cut standard is proposed via analyzing the characteristics of short text and the defects of the existing clustering algorithms, which demonstrates the effectiveness of the new clustering algorithm.
Abstract: A novel clustering method based on spectral clustering theory and spectral cut standard is proposed via analyzing the characteristics of short text and the defects of the existing clustering algorithms. First of all, a weighted undirected graph is created according to spectral clustering theory, similarity between node and node is calculated on graph, and a symmetrical documents similarity matrix is constructed, which provides all information for the clustering algorithm. Inspired by Greedy strategy, we utilize prim to develop PrimMAE algorithm for the purpose of partitioning graph into two parts, in which RMcut is termination condition of partitioning process, and then it is fed into CASC algorithm to cut the documents set iteratively. Ultimately, high quality clustering results demonstrate the effectiveness of the new clustering algorithm.
TL;DR: It is shown that if G is a cograph then finding a spanning tree with a non-terminal set VNT of G is linearly solvable when each edge has the weight of one, and that this problem is NP-hard.
Abstract: Given a graph G = (V, E) where V and E are a vertex and an edge set, respectively, specified with a subset VNT of vertices called a non-terminal set, the spanning tree with non-terminal set VNT is a connected and acyclic spanning subgraph of G that contains all the vertices of V where each vertex in a non-terminal set is not a leaf. In the case where each edge has the weight of a nonnegative integer, the problem of finding a minimum spanning tree with a non-terminal set VNT of G was known to be NP-hard. However, the complexity of finding a spanning tree on general graphs where each edge has the weight of one was unknown. In this paper, we consider this problem and first show that it is NP-hard even if each edge has the weight of one on general graphs. We also show that if G is a cograph then finding a spanning tree with a non-terminal set VNT of G is linearly solvable when each edge has the weight of one. key words: spanning tree, cograph, algorithm
31 Mar 2016
TL;DR: A rapid spanning tree detection algorithm based on the independent discrimination of weakly connected edge is proposed to independently discriminate social network community with the weak connected edge in order to improve the accuracy of community recommendation and reduce the complexity of algorithm.
Abstract: Aiming at the problem of low accuracy and high computational complexity of the traditional social network community recommendation algorithm, a rapid spanning tree detection algorithm is proposed to independently discriminate social network community with the weak connected edge, in order to improve the accuracy of community recommendation and reduce the complexity of algorithm. Firstly, according to the characteristics of social network community recommendation, the maximum spanning tree algorithm is proposed, which is based on the edge weight distribution node similarity, to realize the effective detection of social network community. Secondly, for the proposed algorithm having the problems of repeated adding and deleting of weakly connected edges and the waste of computing resources, a rapid spanning tree detection algorithm based on the independent discrimination of weakly connected edge is proposed so as to further improve the calculation efficiency of the algorithm. Lastly, the effectiveness of the proposed algorithm is verified by comparing the experimental results in the standard test database.
01 Oct 2016
TL;DR: This study investigates the performance of a tabu search algorithm with ejection chain for the bi-objective version of the minimum quadratic spanning tree problem.
Abstract: Given an edge-weighted simple graph G, the minimum quadratic spanning tree problem consists in finding a spanning tree of G such that the sum of the weights of its edges plus the sum of the product of the weights of pairs of edges is minimum over all spanning trees of G. When the product of the weights of pairs of edges is calculated only for adjacent edges, the problem is called adjacent-only minimum quadratic spanning tree. This problem belongs to NP-hard. In this study we investigate the performance of a tabu search algorithm with ejection chain for the bi-objective version of this problem. An experiment with 168 instances is reported.
Patent•
07 Dec 2016
Abstract: The invention discloses a network connectivity correction method for intelligent optimization of a recovery path of a power failure system. The method comprises the following steps of A) establishing an initial to-be-connected graph by each recovered line, a charged node and a target node; B) performing repeated combination until connected sub-graph aggregation is finished to form connected sub-graphs; C) searching for a shortest connection path that connects all the connected sub-graphs by utilizing a prim algorithm, and establishing a connected graph containing all to-be-recovered power supply points; and D) setting a line state on the connection path on the connected graph to be 1 according to the connected graph containing all the to-be-recovered power supply points, thereby realizing connectivity correction. The method for effectively correcting non connected individuals into connected individuals according to a connectivity correction algorithm based on an agglomerative hierarchical clustering algorithm and the prim algorithm is high in calculation speed, small in number of iterations, high in convergence speed, relatively high in stability and relatively small in calculation result fluctuation, and has very high adaptability and good application prospects.
01 Jan 2016
TL;DR: This work proposes a Distributed Minimum Spanning Tree based Information Exchange (DMSTIE) strategy, which helps in collecting the load information of the nodes through the edges formed during the Distributed minimum Spanning tree ( DMST) process.
Abstract: Distributed system has an inherent problem of unevenly distributed load. The possible solution to this problem is load balancing. For the above purpose it is very important to have updated information about the load status of the nodes comprising the system. This work proposes a Distributed Minimum Spanning Tree based Information Exchange (DMSTIE) strategy. The strategy helps in collecting the load information of the nodes through the edges formed during the Distributed Minimum Spanning Tree (DMST) process. Based on the information about the system state various load balancing approach can be applied for transferring extra load over the underutilized nodes. An MST based approach results in the information collection and eventually dispatch of load efficiently in terms of communication and computation.
01 Jan 2016
TL;DR: A new methodology is designed and developed to find minimum spanning tree using subtraction and remainder procedure, which also uses Greedy approach.
Abstract: Efficient routing problem exists from several years. Spanning tree plays very important role to design routing algorithms efficiently. To obtain the minimum cost a minimum spanning tree is formed from the given graph. Greedy technique plays important role to generate minimum spanning tree. Several approaches exists to solve minimum spanning tree but in this paper a new methodology is designed and developed to find minimum spanning tree using subtraction and remainder procedure. This procedure also uses Greedy approach. The main objective is to present a new way to find minimum spanning tree. An example is also given to understand the procedure in efficient way.
09 May 2016
TL;DR: The application of a software tool based on graph theory to analyze and solve problems of the shortest routes, using the algorithms of Prim, Kruskal and Tabu is described.
Abstract: This article describes the application of a software tool based on graph theory to analyze and solve problems of the shortest routes, using the algorithms of Prim, Kruskal and Tabu. For the development of this application the following elements were used: Visual Studio 2010, GraphSharp and QuickGraph. TO create this tool, a class structure that would support the graphics was established:1) PocGraph: represents the graph; 2) PocEdge: represents the edges of the graph; and 3 ) PocVertex: represents the nodes or vertices of the graph. The Prim algorithm worked with the aim of finding the shortest spanning tree; while Kruskal’s algorithm, in order to find the minimal tree from TSP instances . Tabu Search method is applied to find the minimum closed road connecting all the vertices or nodes. The Tabu Search algorithm was designed to minimize the routes from an initial solution which is modified to obtain the result.
TL;DR: Using a special kind of interval tree, it is shown how to compute the vertex connectivity and to maintain the tree in log time when a new interval is added or an existing interval is deleted.
Abstract: A graph is called an interval graph with a set of vertices representing intervals on a line such that there is an edge ∈ if and only if intervals and intersect. In this paper, we are concerned in the vertex connectivity, one of various characteristics of the graph. Specifically, the vertex connectivity of an interval graph is represented by the overlapping of intervals. Also we propose an efficient algorithm to compute the vertex connectivity on the fully dynamic environment in which the vertices or the edges are inserted or deleted. Using a special kind of interval tree, we show how to compute the vertex connectivity and to maintain the tree in log time when a new interval is added or an existing interval is deleted. 키워드 : 선분 그래프, 정점 연결성, 완전 동적, 선분 트리, 알고리즘, 선분 Key word : interval graph, vertex connectivity, fully dynamic, interval tree, algorithm, interval Journal of the Korea Institute of Information and Communication Engineering 한국정보통신학회논문지(J. Korea Inst. Inf. Commun. Eng.) Vol. 20, No. 2 : 415~420 Feb. 2016
Patent•
17 Aug 2016
TL;DR: In this article, an optical synchronous network clock link planning method was proposed, which comprises the following steps of inputting network element information parameters, and using a minimum spanning tree Prim algorithm to determine the master clock link with the priority being 1; meanwhile, determining the array set V of each network element sequentially adding into the minimum spanning trees; determining the minimum ring passing through the first element network element V1 in the array sets V according to the network topology network element connection relationship; if the minimum rings exists, traversing each network elements in the minimum circle, and
Abstract: The invention discloses an optical synchronous network clock link planning method, which comprises the following steps of inputting network element information parameters, and using a minimum spanning tree Prim algorithm to determine the master clock link with the priority being 1; meanwhile, determining the array set V of each network element sequentially adding into the minimum spanning tree; determining the minimum ring passing through the first element network element V1 in the array set V according to the network topology network element connection relationship; if the minimum ring exists, traversing each network element in the minimum ring, and planning a spare clock link with the priority being 2 for each network element; if the minimum ring does not exist, planning the spare clock link of the first element network element to be consistent with the master clock link; updating the array set V; deleting the planned network elements of the spare clock link; repeating the steps until the planning of all network elements is completed. The intelligent planning is realized; the problems of complexity, unreliability and the like of artificial planning are solved; the master and spare clock links of the single PRC master and slave synchronous networks can be effectively planned; the work efficiency is greatly improved.