Showing papers on "Prim's algorithm published in 2014"
TL;DR: In this article, the authors consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment, where the robot repeatedly performs a closed walk on the graph, and define the weighted latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance of that vertex.
Abstract: In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent regions of interest, edge lengths give travel times between regions and the vertex weights give the importance of each region. As the robot repeatedly performs a closed walk on the graph, we define the weighted latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance (vertex weight) of that vertex. Our goal is to find a closed walk that minimizes the maximum weighted latency of any vertex. We show that there does not exist a polynomial time algorithm for the problem. We then provide two approximation algorithms; an O(logn)-approximation algorithm and an O(logIG)-approximation algorithm, where IG is the ratio between the maximum and minimum vertex weights. We provide simulation results which demonstrate that our algorithms can be applied to problems consisting of thousands of vertices and a case study for patrolling a city for crime.
92 citations
08 Jul 2014
TL;DR: In this paper, an n-vertex graph, a tree decomposition of width w, and an integer t are used to decide whether the input graph has treedepth at most t in time 2 O(wt) ·n.
Abstract: The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which—given as input an n-vertex graph, a tree decomposition of width w, and an integer t—decides whether the input graph has treedepth at most t in time 2 O(wt) ·n. We use this to construct further algorithms which do not require a tree decomposition as part of their input: A simple algorithm which decides treedepth in linear time for a fixed t, thus answering an open question posed by Ossona de Mendez and Nesetřil as to whether such an algorithm exists, a fast algorithm with running time \(2^{O(t^2)} \cdot n\) and an algorithm for chordal graphs with running time 2 O(t logt)·n.
68 citations
TL;DR: A symmetric compact reformulation was presented, devised with the application of an Intersection Reformulation Technique to the directed model, which proved to be much stronger than the previous models, but evaluating its bounds is very time consuming.
18 citations
TL;DR: A memetic algorithm is introduced that quickly generates chromosomes with specific characteristics and a wise application of recent local search procedures based on k‐diamonds and outperforms two other metaheuristics recently proposed in the literature for this problem.
Abstract: Given an undirected and vertex weighted graph G=V,E,w, the Weighted Feedback Vertex Set Problem consists of finding the subset Fi¾?V of vertices, with minimum weight, whose removal results in an acyclic graph. Finding the minimum feedback vertex set in a graph is an important combinatorial problem that has a variety of real applications. In this article, we introduce a memetic algorithm for this problem. We propose an efficient greedy procedure that quickly generates chromosomes with specific characteristics and a wise application of recent local search procedures based on k-diamonds. Computational results show that the proposed algorithm outperforms the effectiveness of two other metaheuristics recently proposed in the literature for this problem. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 644, 339-356 2014
12 citations
TL;DR: An improved genetic algorithm, which encodes the minimum spanning trees of large-scale rural highway network layout with Prufer array with a method which can reduce the length of chromosome and substitutes for traditional crossover and mutation operations.
Abstract: For the layout problem of rural highway network, which is often characterized by a cluster of geographically dispersed nodes, neither the Prim algorithm nor the Kruskal algorithm can be readily applied, because the calculating speed and accuracy are by no means satisfactory. Rather than these two polynomial algorithms and the traditional genetic algorithm, this paper proposes an improved genetic algorithm. It encodes the minimum spanning trees of large-scale rural highway network layout with Prufer array, a method which can reduce the length of chromosome; it decodes Prufer array by using an efficient algorithm with time complexity o(n) and adopting the single transposition method and orthoposition exchange method, substitutes for traditional crossover and mutation operations, which can effectively overcome the prematurity of genetic algorithm. Computer simulation tests and case study confirm that the improved genetic algorithm is better than the traditional one.
11 citations
28 Nov 2014-The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
TL;DR: 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 and helps to solve complex network MST problem easily, efficiently and effectively is developed.
Abstract: . 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.
9 citations
TL;DR: In this paper, two spanning tree problems in an undirected, simple graph are addressed: finding a spanning tree that minimizes the number of branch vertices (MBV) and minimizing the degree sum of branches (MDS).
Abstract: A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier.
8 citations
TL;DR: It is shown that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m, 2m, a result connected to a conjecture of Graham and Häggkvist that implies that the bipartition classes of the base tree of a random tree have roughly equal size.
Abstract: We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Haggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size. © Cambridge University Press 2013.
8 citations
TL;DR: A fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria, and a fuzzy simulation for computing credibility is designed and embedded into a genetic algorithm to produce some hybrid intelligent algorithms.
Abstract: An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights In this paper, a type of fuzzy inverse minimum spanning tree problem is introduced from a LAN reconstruction problem, where the weights of edges are assumed to be fuzzy variables The concept of fuzzy α-minimum spanning tree is initialized, and subsequently a fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria In order to solve the two fuzzy models, a fuzzy simulation for computing credibility is designed and then embedded into a genetic algorithm to produce some hybrid intelligent algorithms Finally, some computational examples are given to illustrate the effectiveness of the proposed algorithms
7 citations
TL;DR: An algorithm is presented which finds a spanning tree with at least k leaves in time O*(3.4575k) which improves the currently best algorithm, and the estimation of the running time is done by using a non-standard measure.
Abstract: The problem of finding a spanning tree in an undirected graph with a maximum number of leaves is known to be NP-hard. We present an algorithm which finds a spanning tree with at least k leaves in time O*(3.4575k) which improves the currently best algorithm. The estimation of the running time is done by using a non-standard measure. The present paper is one of the still few examples that employ the Measure & Conquer paradigm of algorithm analysis in the area of Parameterized Algorithmics.
6 citations
09 Oct 2014
TL;DR: In this paper, a modified BFS algorithm is proposed to traverse the graphs, which we may not traverse with existing BFS completely but the output may contain multiple trees forming a spanning forest.
Abstract: Given a graph G={V, E} and a distinguished source vertex `s', the traditional BFS algorithm systematically explores the edges of G to discover every vertex that is reachable from the source vertex `s' and it produces a “Breadth - First - Tree” with root `s'. The Breadth-First-Tree formed after running the traditional algorithm may not visit all the vertices in some graphs for instance Directed cyclic and acyclic graphs. As a consequence the traversing may be incomplete. With modified BFS algorithm we can traverse the graphs, which we may not traverse with existing BFS completely but the output may contain multiple trees forming a spanning forest.
TL;DR: In this article, the authors proposed three algorithms for constructing vertex cover in wireless sensor networks, which are an adaption of the Parnas & Ron's algorithm, a greedy approach that finds a vertex cover by using the degrees of the nodes, and a weighted matching algorithm is used.
Abstract: Vertex covering has important applications for wireless sensor networks such as monitoring link failures, facility location, clustering, and data aggregation. In this study, we designed three algorithms for constructing vertex cover in wireless sensor networks. The first algorithm, which is an adaption of the Parnas & Ron's algorithm, is a greedy approach that finds a vertex cover by using the degrees of the nodes. The second algorithm finds a vertex cover from graph matching where Hoepman's weighted matching algorithm is used. The third algorithm firstly forms a breadth-first search tree and then constructs a vertex cover by selecting nodes with predefined levels from breadth-first tree. We show the operation of the designed algorithms, analyze them, and provide the simulation results in the TOSSIM environment. Finally we have implemented, compared and assessed all these approaches. The transmitted message count of the first algorithm is smallest among other algorithms where the third algorithm has turned out to be presenting the best results in vertex cover approximation ratio.
TL;DR: In this article, the authors show that the problem is NP-complete even for series-parallel graphs, and give a pseudo-polynomial time algorithm to solve the problem for a given seriesparallel graph G.
Abstract: Let G be a graph with a single source w, assigned a positive integer called the supply. Every vertex other than w is a sink, assigned a nonnegative integer called the demand. Every edge is assigned a positive integer called the capacity. Then a spanning tree T of G is called a spanning distribution tree if the capacity constraint holds when, for every sink v, an amount of flow, equal to the demand of v, is sent from w to v along the path in T between them. The spanning distribution tree problem asks whether a given graph has a spanning distribution tree or not. In the paper, we first observe that the problem is NP-complete even for series-parallel graphs, and then give a pseudo-polynomial time algorithm to solve the problem for a given series-parallel graph G.
Patent•
07 May 2014
TL;DR: In this paper, a cluster tree hierarchical wireless sensor network routing method with optimized energy efficiency is proposed, which includes the first step of automatically and dynamically organiing clustering during a cluster construction period, the second step of carrying out random selection on cluster head nodes according to the energy balance principle through the consideration on node energy factors, the third step of utilizing a minimum spanning tree Prim algorithm to construct a CH hierarchical network route, namely, points in the Prim algorithm correspond to the CH nodes selected in a WSN, and the weights of sides correspond to energy weighting distances between
Abstract: The invention discloses a cluster tree hierarchical wireless sensor network routing method with the optimized energy efficiency. The method includes the first step of automatically and dynamically organiing clustering during a cluster construction period, the second step of carrying out random selection on cluster head nodes according to the energy balance principle through the consideration on node energy factors, the third step of utilizing a minimum spanning tree Prim algorithm to construct a cluster tree hierarchical network route, namely, points in the Prim algorithm correspond to the cluster head nodes selected in a wireless sensor network, and the weights of sides correspond to energy weighting distances between the cluster head nodes, and the fourth step of constructing the cluster head nodes to a multi-hop routing network structure. Through the protocol, the cluster heads are reasonably selected in the application of the wireless sensor network which is powered through the energy harvesting technology, and consequently effective utilization of energy can be achieved, the communication cost between the nodes is reduced, the problem of the premature death of the cluster head nodes due to long-distance communication is solved, and the prolonging of the lifetime of the whole network is facilitated; in addition, the application of the spanning tree algorithm enhances the expandability of the protocol.
TL;DR: In this paper an algorithm based on the cost perturbation method and adapted to the analysed problem has been proposed and the results of numerical experiments testing the effectiveness of the proposed algorithm are contained and it is compared with algorithms known in the literature.
Abstract: This paper analyses the problem of finding a robust spanning tree. The problem consists of determining a minimum spanning tree of a graph with uncertain edge costs. We should determine a spanning tree that minimizes the difference in costs between the tree selected and the optimal tree. While doing this, all possible realizations of the edge costs should be taken into account. This issue belongs to the class of NP-hard problems. In this paper an algorithm based on the cost perturbation method and adapted to the analysed problem has been proposed. The paper also contains the results of numerical experiments testing the effectiveness of the proposed algorithm and compares it with algorithms known in the literature. The research is based on a large number of various test examples taken from the literature.
Posted Content•
TL;DR: Minimal Partitioning (MP) algorithm, an innovative algorithm for enumerating all the spanning trees in an undirected graph is presented and it is reported that MP algorithm outperforms other algorithm by $O(V)$ time complexity.
Abstract: In this thesis, Minimal Partitioning (MP) algorithm, an innovative algorithm for enumerating all the spanning trees in an undirected graph is presented.
While MP algorithm uses a computational tree graph to traverse all possible spanning trees by the edge exchange technique, it has two unique properties compared to previous algorithms. In the first place, the algorithm maintains a state of minimal partition size in the spanning tree due to edge deletion. This is realized by swapping peripheral edges, more precisely leaf edges, in most of edge exchange operations. Consequently, the main structure of the spanning trees is preserved during the steps of the enumeration process. This extra constraint proves to be advantageous in many applications where the partition size is a factor in the solution cost. Secondly, we introduce, and utilize, the new concept of edge promotion: the exchanged edges always share one end. Practically, and as a result of this property, the interface between the two partitions of the spanning tree during edge exchange has to be maintained from one side only.
For a graph $G(V,E)$, MP algorithm requires $O(log V+E/V)$ expected time and $OV log V)$ worst case time for generating each spanning tree. MP algorithm requires a total expected space limit of $O(E log V)$ with worst case limit of $O(EV)$. Like all edge exchange algorithms, MP algorithm retains the advantage of compacted output of $O(1)$ per spanning tree by listing the relative differences only.
Three sample real-world applications of spanning trees enumeration are explored and the effects of using MP algorithm are studied. Namely: construction of nets of polyhedra, multi-robots spanning tree routing, and computing the electric current in edges of a network. We report that MP algorithm outperforms other algorithm by $O(V)$ time complexity.
DOI•
01 Jan 2014
TL;DR: A Minimum Spanning Tree algorithm for GPUs is presented, its implementation discussed, and its efficiency evaluated on GPU and multicore architectures.
Abstract: Standard parallel computing operations are considered in the context of algorithms for solving 3D graph problems which have applications, e.g., in vertex finding in HEP. Exploiting GPUs for tree-accumulation and graph algorithms is challenging: GPUs offer extreme computational power and high memory-access bandwidth, combined with a model of fine-grained parallelism perhaps not suiting the irregular distribution of linked representations of graph data structures. Achieving data-race free computations may demand serialization through atomic transactions, inevitably producing poor parallel performance. A Minimum Spanning Tree algorithm for GPUs is presented, its implementation discussed, and its efficiency evaluated on GPU and multicore architectures.
14 Nov 2014
TL;DR: The results have shown that the proposed algorithm can yield better solutions especially on dense graphs for solving the minimum vertex cover problem.
Abstract: The minimum vertex cover (MVC) problem is a well-studied NP-Complete problem and has various applications. In this paper, a new heuristic approach has been proposed to find the minimum vertex cover of a graph. The proposed algorithm has been tested on random graphs and BHOSLIB instances. The results have shown that the proposed algorithm can yield better solutions especially on dense graphs for solving the minimum vertex cover problem.
03 Apr 2014
TL;DR: This empirical study found that Alom's algorithm performs consistently better than the other algorithms for all types of graphs, regardless of their class and number of vertices in the graph, while approximation algorithms show the worst performance for very large graphs.
Abstract: There are several vertex cover algorithms proposed for the solution of well-known NP-complete class problem of computing vertex cover. The Vertex Cover problem is important to address as it has various real world applications viz. Wireless Communication Network, Airline Communication Network, Terrorist Communication Network, etc. In this paper, we present a comparative evaluation of different existing algorithms like approximation, list, greedy and Alom's for most efficiently computing vertex cover over a variety of large graphs. Our empirical study found that Alom's algorithm performs consistently better than the other algorithms for all types of graphs, regardless of their class and number of vertices in the graph, while approximation algorithms show the worst performance for very large graphs.
Journal Article•
TL;DR: A Double-Weighted Graph Model considering multiple entrances and exits for tourist scenic area, and the weights of both vertexes and edges of the proposed model can be selected and weighted dynamically, and an optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm is proposed.
Abstract: When visiting multiple tourist scenic spots, a recommended travel line is usually the most effective route designed for tourists according to the actual road situations. In the field of intelligent tourism navigation, a traditional recommended travel line is mainly generated by path planning algorithm automatically, considering thescenic spots' positions and road networks based on graph model. Normally, the traditional algorithms firstly map scenic spots(which belong to certain scenic area) into points of interests(POIs),and map the road network that links these POIs into a line collection, then build the corresponding graph model. But when a scenic spot has a limited area and involves multiple entrances or exits(for example buildings with multiple indoor space), the traditional described mechanism for single point coordinates is difficult to reflect these structural features. In reality, scenic area path planning is widely applied in the field of mobile tourism guide recently, especially for pedestrians. There exist significant differences between theoretical optimal paths and actual optimal paths, sincetouristsare inclined to have more choices. In order to solve this problem, this paper analyzed various influences on the process of path planning, caused by scenic spots' own structural features(such as the size, shape and entrance),and focused on the influences of multiple entrances or exits located within the scenic area. Then,we proposed a Double-Weighted Graph Model considering multiple entrances and exits for tourist scenic area, and the weights of both vertexes and edges of the proposed model can be selected and weighted dynamically. Next, we discussed the building method for the model, and proposed an optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm. Experimental results show that the optimal planned travel line derived from this proposed model and algorithms is considerably reasonable, and the travelling order and travelling distance can be further optimized.
TL;DR: An efficient implementation of Kruskal's algorithm to obtain a minimum spanning tree is presented, reducing the depth of the tree of the node set by making the nodes in the path to root be the child node of the root of combined tree.
Abstract: In this paper, we present an efficient implementation of Kruskal's algorithm to obtain a minimum spanning tree. The proposed method utilizes the union-find data structure, reducing the depth of the tree of the node set by making the nodes in the path to root be the child node of the root of combined tree. This method can reduce the depth of the tree by shortening the path to the root and lowering the level of the node. This is an efficient method because if the tree's depth reduces, it could shorten the time of finding the root of the tree to which the node belongs. The performance of the proposed method is evaluated through the graphs generated randomly. The results showed that the proposed method outperformed the conventional method in terms of the depth of the tree. ▸
TL;DR: The present minimum spanning tree algorithm works on all the edges of the graph, however, the suggested algorithm reduces the edges population size by means of applying a method of deleting maximum weight edges in advance from vertices with more than 2 valencies.
14 Jul 2014
TL;DR: In this article, a graph theory for solving constrained minimum spanning tree problem is proposed to reduce the change machine costs, shorten production cycle and improve production efficiency for semiconductor assembly and testing system.
Abstract: The production of semiconductor assembly and testing is wide variety, and the cost of produce time of switch between different products is not the same, which could lead to its utilization is lower, production cycle longer. Thus lot release control plays an important role for improving utilization and shorter production cycle for semiconductor assembly and testing system. In this paper, we modeled as a graph theory for solving constrained minimum spanning tree problem. Using mainstream Prim algorithm, we solve it to give each product sequence and specific lot release time. It have solved the extra time problem that caused by blinding lot release, and finally, through applied research we verified the effectiveness and superiority of it. The proposed strategy can reduce the change machine costs, shorten production cycle and improve production efficiency. c 2014 IEEE.
TL;DR: This paper focuses on the influence on the process of path planning caused by scenic spots' own structural features such as multiple entrances or exits, and proposes a doubleweighted Graph Model, for the weight of both vertexes and edges of proposed Model can be selected dynamically.
Abstract: When tourists visiting multiple tourist scenic spots, the travel line is usually the most effective road network according to the actual tour process, and maybe the travel line is different from planned travel line. For in the field of navigation, a proposed travel line is normally generated automatically by path planning algorithm, considering the scenic spots' positions and road networks. But when a scenic spot have a certain area and have multiple entrances or exits, the traditional described mechanism of single point coordinates is difficult to reflect these own structural features. In order to solve this problem, this paper focuses on the influence on the process of path planning caused by scenic spots' own structural features such as multiple entrances or exits, and then proposes a doubleweighted Graph Model, for the weight of both vertexes and edges of proposed Model can be selected dynamically. And then discusses the model building method, and the optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm. Experimental results show that the optimal planned travel line derived from the proposed model and algorithm is more reasonable, and the travelling order and distance would be further optimized.
TL;DR: A fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property, and reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.
Abstract: This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge per vertex . Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.
01 Jan 2014
TL;DR: An algorithm base on firefly algorithm is suggested for solving the issue of minimum Steiner tree and the results of tests show that suggested algorithm compare to reported methods as genetic algorithm & ant colony enjoys more proficiency.
Abstract: The issue of finding minimum Steiner tree in a valuable graph is finding a tree by least cost on graph which involves special loop naming terminal. This issue is out of NP-Complete issues, therefore, several approximate algorithms as genetic algorithm, ant colony, learning automata &etc has reported. In this paper an algorithm base on firefly algorithm is suggested for solving the issue of minimum Steiner tree. The results of tests show that suggested algorithm compare to reported methods as genetic algorithm & ant colony enjoys more proficiency.
TL;DR: An Advanced AOI-cast algorithm based on PCA is presented, which gains a greater improvement on multicast efficiency, and achieves better scalability of P2P-based NVEs.
Abstract: Voronoi-based Overlay Network (VON) has been proposed that promises to maintain high overlay topology consistency in a bandwidth-efficient manner. VoroCast constructs a spanning tree across all AOI neighbors based on Voronoi diagrams, while FiboCast dynamically adjusts the messaging range by a Fibonacci sequence. VoroCast improves the AOI scalability of P2P-based NVEs. However, one potential drawback of the schemes is that the child node degrees are only based on peers' positions, but not node capacities. Since each node in VoroCast has different capacity, packet loss will be unavoidable. VoroCast may lead to lower multicast efficiency in AOI. To these problems, an Advanced AOI-cast algorithm based on PCA is presented. In the algorithm, node capacity is related to node CPU (c), node bandwidth (b) and node memory (m), and the node capacity is calculated according to the PCA. An undirected graph is formed through all the nodes in the AOI and the edge weights are calculated by the Gaussian function. Through the prim algorithm, to generate the minimum spanning tree of the weighted undirected graph, and the minimum spanning tree is used as the final multicast tree. The message is delivered through the multicast tree. The simulation results show that the algorithm gains a greater improvement on multicast efficiency, and achieves better scalability.
01 Jan 2014
TL;DR: Based the on Google Earth, the undirected graph of Tangshan tourist sites are established, optimal traveling rout are explored by Prim algorithm and improved Prim algorithm.
Abstract: It is important to design the optimal travel route for the traveler. In this paper, based the on Google Earth, the undirected graph of Tangshan tourist sites are established, optimal traveling rout are explored by Prim algorithm and improved Prim algorithm.
TL;DR: Test results have shown that the algorithm Prim MST ability to determine the primary distribution grid is much better if based on the geographical conditions of a region, and Prim's algorithm graph computation time in generating the MSTbased on the data that is not based onThe contour and contour data are quadratic.
Abstract: Determination of the minimum spanning tree are widely used to solve optimization problems of finding solutions to problems that require minmum. In the electricity distribution network, minimum spanning tree (MST) is used to find the minimum length of cable for electricity network system becomes more optimal. Minimum weight of a MST primary distribution power network is strongly influenced by the geographical conditions of a region in the form of contour data. This research was done by designing a model of primary distribution power network graph in accordance with the data obtained. In finding the minimum weight for each side of the network graph should include parameters elevation, high point / node, and the distance between points / nodes. Furthermore, the graph is done by computer calculation and simulation to get the electricity distribution network primary MST using Prim's algorithm with the help of ArcView GIS 3.3 program through the avenue script. Prim's algorithm included in the category of good or efficient algorithms, because the shape of polynomial time complexity in n, where n is a measure of the number of vertices or sides. Based on the test results have shown that the algorithm Prim MST ability to determine the primary distribution grid is much better if based on the geographical conditions of a region. In addition, Prim's algorithm graph computation time in generating the MST based on the data that is not based on the contour and contour data are quadratic. Keywords: minimum spanning tree, prim's algorithm, contours, complexity time