Showing papers on "Prim's algorithm published in 2013"

Prime Object Proposals with Randomized Prim's Algorithm

Abstract: Generic object detection is the challenging task of proposing windows that localize all the objects in an image, regardless of their classes. Such detectors have recently been shown to benefit many applications such as speeding-up class-specific object detection, weakly supervised learning of object detectors and object discovery. In this paper, we introduce a novel and very efficient method for generic object detection based on a randomized version of Prim's algorithm. Using the connectivity graph of an image's super pixels, with weights modelling the probability that neighbouring super pixels belong to the same object, the algorithm generates random partial spanning trees with large expected sum of edge weights. Object localizations are proposed as bounding-boxes of those partial trees. Our method has several benefits compared to the state-of-the-art. Thanks to the efficiency of Prim's algorithm, it samples proposals very quickly: 1000 proposals are obtained in about 0.7s. With proposals bound to super pixel boundaries yet diversified by randomization, it yields very high detection rates and windows that tightly fit objects. In extensive experiments on the challenging PASCAL VOC 2007 and 2012 and SUN2012 benchmark datasets, we show that our method improves over state-of-the-art competitors for a wide range of evaluation scenarios.

A local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning

Abstract: We study the design of local algorithms for massive graphs A local graph algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph We present a local clustering algorithm Our algorithm finds a good cluster---a subset of vertices whose internal connections are significantly richer than its external connections---near a given vertex The running time of our algorithm, when it finds a nonempty local cluster, is nearly linear in the size of the cluster it outputs The running time of our algorithm also depends polylogarithmically on the size of the graph and polynomially on the conductance of the cluster it produces Our clustering algorithm could be a useful primitive for handling massive graphs, such as social networks and web-graphs As an application of this clustering algorithm, we present a partitioning algorithm that finds an approximate sparsest cut with nearly optimal balance Our algorithm takes time nearly linear in the number edges of the graph

An O(c^k n) 5-Approximation Algorithm for Treewidth

Abstract: We give an algorithm that for an input n-vertex graph G and integer k > 0, in time O(ckn) either outputs that the tree width of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for tree width which runs in time single-exponential in k and linear in n. Tree width based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single-exponential in the tree width and linear in the input size.

New heuristic approaches for the dominating tree problem

Abstract: Given an undirected, connected and edge-weighted graph, the dominating tree problem (DTP) seeks on this graph a tree with minimum total edge weight such that each vertex of the graph is either in this tree or adjacent to a vertex in this tree. The DTP is a NP-Hard problem. In the literature only two heuristics for this problem are proposed so far in spite of the fact that it has several practical applications in the field of wireless sensor networks. In this paper, we propose one heuristic and two swarm intelligence techniques, viz. an artificial bee colony algorithm and an ant colony optimization algorithm for the DTP. Computational results show the effectiveness of our approaches.

Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem

Abstract: An inverse minimum spanning tree problem makes 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, the concept of uncertain α-minimum spanning tree is initiated for minimum spanning tree problem with uncertain edge weights. Using different decision criteria, two uncertain programming models are presented to formulate a specific inverse minimum spanning tree problem with uncertain edge weights involving a sum-type model and a minimax-type model. By means of the operational law of independent uncertain variables, the two uncertain programming models are transformed to their equivalent deterministic models which can be solved by classic optimization methods. Finally, some numerical examples on a traffic network reconstruction problem are put forward to illustrate the effectiveness of the proposed models.

A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation.

Abstract: The minimum spanning tree (MST) problem is to find minimum edge connected subsets containing all the vertex of a given undirected graph. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications. Moreover in previous studies, DNA molecular operations usually were used to solve NP-complete head-to-tail path search problems, rarely for NP-hard problems with multi-lateral path solutions result, such as the minimum spanning tree problem. In this paper, we present a new fast DNA algorithm for solving the MST problem using DNA molecular operations. For an undirected graph with n vertex and m edges, we reasonably design flexible length DNA strands representing the vertex and edges, take appropriate steps and get the solutions of the MST problem in proper length range and O(3m+n) time complexity. We extend the application of DNA molecular operations and simultaneity simplify the complexity of the computation. Results of computer simulative experiments show that the proposed method updates some of the best known values with very short time and that the proposed method provides a better performance with solution accuracy over existing algorithms.

Solving Minimum Vertex Cover Problem Using Learning Automata

Abstract: Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed algorithm, each vertex of graph is equipped with a learning automaton that has two actions in the candidate or non- candidate of the corresponding vertex cover set. Due to characteristics of learning automata, this algorithm significantly reduces the number of covering vertices of graph. The proposed algorithm based on learning automata iteratively minimize the candidate vertex cover through the update its action probability. As the proposed algorithm proceeds, a candidate solution nears to optimal solution of the minimum vertex cover problem. In order to evaluate the proposed algorithm, several experiments conducted on DIMACS dataset which compared to conventional methods. Experimental results show the major superiority of the proposed algorithm over the other methods.

VANET Cluster-on-Demand Minimum Spanning Tree (MST) Prim clustering algorithm

Abstract: Vehicle to Vehicle (V2V) communication offers great potential as far as information dissemination in VANETs is concerned. Research has shown that clustering vehicles and relaying information through cluster-heads (CHs) has several advantages over allowing all the vehicles to broadcast the information. Forming and maintaining stable clusters as well as ensuring good QoS in intra-cluster communications has always been a great challenge. In this paper we present a VANET Cluster-onDemand (CoD) Minimum Spanning Tree (MST) Prim algorithm which clusters vehicles taking into consideration the intra-cluster QoS. Matlab simulation results of the algorithm applied to real traffic data has shown the algorithm’s ability to successfully form clusters with good QoS. The algorithm has also been shown to compare very well with Dijkstra’s algorithm which is one of the best clustering algorithms. Keywords-Dijkstra’s algorithm, Minimum spanning tree (MST), Prim algorithm, Vehicular ad hoc networks (VANETs)

The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs

Abstract: The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor's prices. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.

Degree constrained minimum spanning tree problem: a learning automata approach

Abstract: Degree-constrained minimum spanning tree problem is an NP-hard bicriteria combinatorial optimization problem seeking for the minimum weight spanning tree subject to an additional degree constraint on graph vertices. Due to the NP-hardness of the problem, heuristics are more promising approaches to find a near optimal solution in a reasonable time. This paper proposes a decentralized learning automata-based heuristic called LACT for approximating the DCMST problem. LACT is an iterative algorithm, and at each iteration a degree-constrained spanning tree is randomly constructed. Each vertex selects one of its incident edges and rewards it if its weight is not greater than the minimum weight seen so far and penalizes it otherwise. Therefore, the vertices learn how to locally connect them to the degree-constrained spanning tree through the minimum weight edge subject to the degree constraint. Based on the martingale theorem, the convergence of the proposed algorithm to the optimal solution is proved. Several simulation experiments are performed to examine the performance of the proposed algorithm on well-known Euclidean and non-Euclidean hard-to-solve problem instances. The obtained results are compared with those of best-known algorithms in terms of the solution quality and running time. From the results, it is observed that the proposed algorithm significantly outperforms the existing method.

Hardware and software implementations of prim's algorithm for efficient minimum spanning tree computation

Abstract: Minimum spanning tree (MST) problems play an important role in many networking applications, such as routing and network planning. In many cases, such as wireless ad-hoc networks, this requires efficient high-performance and low-power implementations that can run at regular intervals in real time on embedded platforms. In this paper, we study custom software and hardware realizations of one common algorithm for MST computations, Prim’s algorithm. We specifically investigate a performance-optimized realization of this algorithm on reconfigurable hardware, which is increasingly present in such platforms.

A global optimization algorithm for solving the minimum multiple ratio spanning tree problem

Abstract: This paper studies the sum-of-ratios version of the classical minimum spanning tree problem. We describe a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on randomly generated complete and sparse graph instances.

Modified Vertex Support Algorithm: A New approach for approximation of Minimum vertex cover

Abstract: Graph related problems mostly belong to NP class and minimum vertex cover is one of them. Minimum vertex cover is focus point for researchers since last decade due to its vast areas of application. In this research paper we have presented a modified form of approximation algorithm for minimum vertex cover which makes use of data structure proposed already named vertex support. We changed the way of selection slightly from vertex support algorithm, vertices attached to minimum support node play very critical role in selection of vertices for minimum vertex cover and we used this in our algorithm. Using our approach we managed to reduce worst case approximation ratio of VSA which is 1.583 to 1.064, this is very major change in providing results with simplicity. Results are also compared with MDG and NOVAC in order to demonstrate the efficiency of selecting vertices in this manner. Simplicity in design can help in applying it in time restricted environments.

An Improved Exact Algorithm for Undirected Feedback Vertex Set.

Abstract: A feedback vertex set in an undirected graph is a subset of vertices removal of which leaves a graph with no cycles. Razgon (SWAT 2006) gave a 1.8899 n nO(1)-time algorithm for finding a minimum feedback vertex set in an n-vertex undirected graph, which is the first exact algorithm for the problem that breaks the trivial barrier of 2 n . Later, Fomin et al. (Algorithmica 2008) improved the result to 1.7548 n nO(1). In this paper, we further improve the result to 1.7356 n nO(1). Our algorithm is analyzed by using the measure-and-conquer method. After showing some properties of the problem, we get improvements by introducing a new measure scheme on the structure of reduced graphs.

A learning automata based approach to the bounded-diameter minimum spanning tree problem

Abstract: The bounded diameter minimum spanning tree (BDMST) problem aims at finding the minimum weight spanning tree subject to a predefined diameter constraint. Due to the NP-hardness of the BDMST problem, several heuristic and meta-heuristic approaches have been proposed to find a near optimal solution in a reasonable time. In this article, a distributed algorithm is proposed for solving the BDMST problem based on learning automata. Generally, the proposed algorithm consists of two main phases. In the former phase, the proposed algorithm forms the action-set of learning automata and paths from the root to every other node. The latter phase constructs different spanning trees until it finds the optimum one. To show the performance of the proposed algorithm, it is compared with one of the well-known methods. Experimental results confirm the superiority of the proposed algorithm both in terms of the computational complexity and the weight of the spanning tree.

An FPT algorithm for Tree Deletion Set

Abstract: We give a 5 k n O(1) fixed-parameter algorithm for determining whether a given undirected graph on n vertices has a subset of at most k vertices whose deletion results in a tree. Such a subset is a restricted form of a feedback vertex set. While parameterized complexity of feedback vertex set problem and several of its variations have been well studied, to the best of our knowledge, this is the first fixed-parameter algorithm for this version of feedback vertex set.

A self-stabilizing 3-approximation for the maximum leaf spanning tree problem in arbitrary networks

Abstract: The maximum leaf spanning tree (MLST) is a good candidate for constructing a virtual backbone in self-organized multihop wireless networks, but is practically intractable (NP-complete). Self-stabilization is a general technique that permits to recover from catastrophic transient failures in self-organized networks without human intervention. We propose a fully distributed self-stabilizing approximation algorithm for the MLST problem in arbitrary topology networks. Our algorithm is the first self-stabilizing protocol that is specifically designed to approximate an MLST. It builds a solution whose number of leaves is at least 1/3 of the maximum possible in arbitrary graphs. The time complexity of our algorithm is O(n 2) rounds.

A Hybrid-Heuristics Algorithm for k-Minimum Spanning Tree Problems

Abstract: A combinatorial optimization problem, namely k-Minimum Spanning Tree Problem (KMSTP), is to find a subtree with exactly k edges in an undirected graph G, such that the sum of edges’ weights is minimal. This chapter provides a Hybrid algorithm using Memetic Algorithm (MA) as a diversification strategy for Tabu Search (TS) to solve KMSTPs. The genetic operator in the proposed MA is based on dynamic programming, which efficiently finds the optimal subtree in a given tree. The experimental results show that the proposed algorithm is superior to several exiting algorithms in terms of solution accuracy and that the algorithm updates some best known solutions that were found by existing algorithms.

A Survey on Methods for finding Min-Cut Tree

Abstract: In this paper we have discussed all existing approaches to solve the problem for calculating the min-cut tree of an undirected edge-weighted graph and present a new approximation algorithm for constructing the minimum-cut tree. We discussed Gomory-Hu algorithm. The algorithm proposed by Gomory and Hu has time complexity O(V*time complexity of finding a min s-t cut). We also have discussed Ford-Fulkerson method. Running time of Ford-Fulkerson algorithm is O(ve 2 ). The asymptotically fastest maximumflow algorithms are based on push-relabel method and have the running time of O(V 3 ). M. Stoer and F. Wagner have given a simple and compact algorithm for finding the minimum cut of a graph. The algorithm is remarkably simple and has the fastest running time so far the algorithm consists of |V| - 1 identical phases each of which requires O(|e| + |V| log |V|) time yielding an overall running time of O(|V||e| + log |V|). We present a new approximation algorithm for constructing the minimum cut tree. We calculate an upperbound value for each node in the graph. We define the upper bound value of each node as the value of cut which separates this node from rest of the graph and our algorithm runs in O(V 2 .logV + V 2 .d), where V is the number of vertices in the given graph and d is the degree of the graph. It is a significant improvement over time complexities of existing solutions. However, because of an assumption it does not produce correct result for all sorts of graphs but for the dense graphs success rate is more than 90%. Moreover in the unsuccessful cases, the deviation from actual result is very less (usually for less than 5% pairs) and for most of the pairs we obtain correct values of max-flow or min-cut.

An Efficient Implementation of Kruskal's and Reverse-Delete Minimum Spanning Tree Algorithm

Abstract: This paper suggests a method to reduce the number of performances of Kruskal and Reverse-delete algorithms. Present Kruskal and Reverse-delete algorithms verify whether the cycle occurs within the edges of the graph. For this reason, they have problems of unnecessarily performing extra algorithms from the edges, even though they`ve already obtained the minimum spanning tree. This paper, first of all, suggests the 1st method which reduces the no. of performances by introducing stop point criteria of algorithm, but at the same time, performs algorithms from all the edges, just like how Kruskal and Reverse-delete algorithms. Next, it suggests the 2nd method which finds the minimum spanning tree from the remaining edges after getting rid of all the unnecessary edges which are considered not to affect the minimum spanning tree. These suggested methods have an effect of terminating algorithm at least 1.4 times and at most 3.86times than Kruskal and Reverse-delete algorithms, when applied to the real graphs. We have found that the 2nd method of the Reverse-delete algorithm has the fastest speed in terminating an algorithm, among 4 algorithms which are results of the 2 suggested methods being applied to 2 algorithms.

Design and Analysis of Minimum Spanning Tree in Euclidean Plane

Abstract: N points are given in the Euclidean plane, and the minimum spanning tree problem seeks for a minimum spanning tree interconnecting the n points so that there is only one path between any two points. One of the classic and frequently-used algorithms for minimum spanning tree problem is Prim's algorithm, but it consumes large time and space complexity for the plane minimum spanning tree problem is of O(n2) numbers of edges. Luckily, it was proved that the plane minimum spanning tree is a sub-graph of Delaunay triangulation for the given points in the plane, and the number of edges in the triangulation is O(n). This motivates us to efficiently compute the Delaunay triangulation of the given points and then find the minimum spanning tree in the triangulation. This paper presents an algorithm based on the divide and conquer for Delaunay triangulation together with the Prim's algorithm to produce an O(nlogn) algorithm for minimum spanning tree problem in the plane, implements the visual graphic interface with various selected algorithms for plane minimum spanning tree and compares their running time.

A Minimum Cut Algorithm Using Maximum Adjacency Merging Method of Undirected Graph

Abstract: Given weighted graph  , the minimum cut problem is classified with source  and sink  or without  and  . Given undirected weighted graph without  and  , Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs  times. Given graph with  and  , Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from  to  . If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with  and  . This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs  times and successfully divides  into disjoint  and  sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within

IKCAP: An Improved K-means Clustering Algorithm Based on Prim ⋆

Abstract: In k-means clustering algorithm, it remains a problem that the initial cluster centers are selected randomly. To deal with the randomness problem, the Prim minimum spanning tree is introduced to the initial center selection of K-means clustering algorithm. Firstly, the prim method is used to find the minimum spanning tree for the randomly generated points, then a group of points are selected as the initial center which has the maximum sum of the weights and all weights have little difference. Finally, we propose an improved K-means clustering algorithm based on prim. Simulation results show that, compared with NKM (Normal K-Means) algorithm, our algorithm improves the accuracy and reduces the data iterations.

The Iterative Minimum Cost Spanning Tree Problem

Abstract: The minimum cost spanning tree problem consists in constructing a network of minimum cost that connects all agents to the source and distributes the cost among the agents in a fair way. We develop a framework for the iterative minimum cost spanning tree problem. In the iterative setting, agents arrive over time and desire to be connected to a source in different rounds in order to receive a service from the source. We provide an algorithm for the iterative minimum cost spanning tree problem in order to connect the agents from the different rounds to the source in a minimal way. Moreover, we discuss the complexity of the algorithm. To divide the cost of the constructed network among the agents in a fair way we propose different charge rules. One class of charge rules is defined in such a way that the inefficiency of the network, caused by agents joining in different rounds, is equally divided among the agents who use the network. A second class of charge rules charges the incoming agents as much as possible such that previously connected agents can be reimbursed. However, we want to avoid that agents are better off by construction their own network. Furthermore, we prove that the charge rules satisfy several properties. This provides the basis for comparing the charge rules and allows for assessment of their fairness in a particular situation.

Minimum Spanning Tree with Rough Weights

Abstract: In many real world problems related to weighted graphs, the input data corresponding to the weights are often imprecise due to incomplete or non-obtainable information. Finding the minimum spanning tree of such type of connected graphs is a challenge. This paper is introduced to find minimum spanning tree on a connected graph where the edges have rough weights.

Application of Kruskal Algorithm Based on Union-find Sets in Subway Planning

Abstract: Minimum spanning tree has very good characteristics and been used extensively.This paper aims at three important op erations of Kruskal algorithm,sorting,adding edge as well as avoiding cycle,the later two operations are realized on the basis of union-find sets,then,the issue of cycle in the construction of minimum spanning tree is also solved with union-find sets and sorting.Kruskal algorithm based on union-find sets provides a solution for the planning of Changsha subway system.

K-Edge-Connectivity: a new Approach of finding Minimum Spanning Tree Ordered Minimum Spanning Tree (OMST)

Abstract: While forming reliable communication networks, we must guarantee is that, after failure of a node or link, the surviving network still allows communication between all other nodes by choosing alternate path which gives strict requirement on the connectivity of the corresponding graph. For a general network design problem it is required that the underlying network to be resilient to link failures is known as the edge- connectivity survivable network design problem. In this paper we present a method called Ordered Minimum Spanning Tree (OMST) used to parallelize efficiently Kruskal's Minimum Spanning Forest algorithm. This algorithm is known for exhibiting inherently sequential characteristics. More specifically, the strict order by which the algorithm checks the edges of a given graph is the main reason behind the lack of explicit parallelism. Our proposed scheme attempts to overcome the imposed restrictions and improve the performance of the algorithm.