Showing papers on "Prim's algorithm published in 2012"
17 Jan 2012
TL;DR: An algorithm is given that outputs a (2, e)-estimate of the size of a minimum vertex cover whose query complexity and running time are O(n) · poly(1/e) and the result is nearly optimal.
Abstract: We give a nearly optimal sublinear-time algorithm for approximating the size of a minimum vertex cover in a graph G. The algorithm may query the degree deg(v) of any vertex v of its choice, and for each 1 ≤ i ≤ deg(v), it may ask for the ith neighbor of v. Letting VCopt(G) denote the minimum size of vertex cover in G, the algorithm outputs, with high constant success probability, an estimate [EQUATION] such that [EQUATION], where e is a given additive approximation parameter. We refer to such an estimate as a (2, e)-estimate. The query complexity and running time of the algorithm are O([EQUATION] · poly(1/e)), where d denotes the average vertex degree in the graph. The best previously known sublinear algorithm, of Yoshida et al. (STOC 2009), has query complexity and running time O(d4/e2), where d is the maximum degree in the graph. Given the lower bound of Ω(d) (for constant e) for obtaining such an estimate (with any constant multiplicative factor) due to Parnas and Ron (TCS 2007), our result is nearly optimal.In the case that the graph is dense, that is, the number of edges is Θ(n2), we consider another model, in which the algorithm may ask, for any pair of vertices u and v, whether there is an edge between u and v. We show how to adapt the algorithm that uses neighbor queries to this model and obtain an algorithm that outputs a (2, e)-estimate of the size of a minimum vertex cover whose query complexity and running time are O(n) · poly(1/e).
97 citations
01 Jun 2012
TL;DR: This paper proposes a simple and efficient population-based iterated greedy algorithm for tackling the minimum weight vertex cover problem and shows that this algorithm outperforms current state-of-the-art approaches.
Abstract: Given an undirected, vertex-weighted graph, the goal of the minimum weight vertex cover problem is to find a subset of the vertices of the graph such that the subset is a vertex cover and the sum of the weights of its vertices is minimal. This problem is known to be NP-hard and no efficient algorithm is known to solve it to optimality. Therefore, most existing techniques are based on heuristics for providing approximate solutions in a reasonable computation time. Population-based search approaches have shown to be effective for solving a multitude of combinatorial optimization problems. Their advantage can be identified as their ability to find areas of the space containing high quality solutions. This paper proposes a simple and efficient population-based iterated greedy algorithm for tackling the minimum weight vertex cover problem. At each iteration, a population of solutions is established and refined using a fast randomized iterated greedy heuristic based on successive phases of destruction and reconstruction. An extensive experimental evaluation on a commonly used set of benchmark instances shows that our algorithm outperforms current state-of-the-art approaches.
60 citations
TL;DR: A learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown and the superiority of the proposed algorithm over the well-known existing methods both in terms of the number of samples and the running time of algorithm is shown.
Abstract: During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention it merits. This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable. This becomes more difficult if we assume that the probability distribution function of the edge weight is unknown. In this paper, we propose a learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown. The proposed algorithm taking advantage of learning automata determines the edges that must be sampled at each stage. As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight. The proposed learning automata-based sampling method decreases the number of samples that need to be taken from the graph by reducing the rate of unnecessary samples. Experimental results show the superiority of the proposed algorithm over the well-known existing methods both in terms of the number of samples and the running time of algorithm.
56 citations
TL;DR: In this article, a trade-off between the size of the separator and the sharpness with which we can fix the sizes of the two sides of the partition was proved. But the trade-offs were not discussed in this paper.
Abstract: Many divide-and-conquer algorithms employ the fact that the vertex set of a graph of bounded treewidth can be separated in two roughly balanced subsets by removing a small subset of vertices, referred to as a separator. In this paper we prove a trade-off between the size of the separator and the sharpness with which we can fix the size of the two sides of the partition. Our result appears to be a handy and powerful tool for the design of exact and parameterized algorithms for NP-hard problems. We illustrate that by presenting two applications.
Our first application is a O(2 n+o(n))-time algorithm for the Degree Constrained Spanning Tree problem: find a spanning tree of a graph with the maximum number of nodes satisfying given degree constraints. This problem generalizes some well-studied problems, among them Hamiltonian Path, Full Degree Spanning Tree, Bounded Degree Spanning Tree, and Maximum Internal Spanning Tree.
The second application is a parameterized algorithm with running time O(16 k+o(k)+n O(1)) for the k-Internal Out-Branching problem: here the goal is to compute an out-branching of a digraph with at least k internal nodes. This is a significant improvement over the best previously known parameterized algorithm for the problem by Cohen et al. (J. Comput. Syst. Sci. 76:650–662, 2010), running in time O(49.4k +n O(1)).
47 citations
TL;DR: It is shown that Connected Feedback Vertex Set can be solved in time O(2O(k)nO(1)) on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O( 1)})$ on graphs excluding a fixed graph H as a minor.
Abstract: We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists F?V, |F|?k, such that G[V?F] is a forest and G[F] is connected.
We show that Connected Feedback Vertex Set can be solved in time O(2 O(k) n O(1)) on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O(1)})$ on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses, as a subroutine, a parameterized algorithm for Group Steiner Tree, a well studied variant of Steiner Tree. We find the algorithm for Group Steiner Tree of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.
46 citations
22 Jul 2012
TL;DR: In this article, a minimal spanning tree algorithm for distribution networks configurations is proposed, which is based on the power losses' minimization in order to select a new configuration, keeping a radial configuration.
Abstract: A minimal spanning tree algorithm for distribution networks configurations is proposed. The paper approaches the formulation by the power losses' minimization in order to select a new configuration, keeping a radial configuration. This type of problem becomes a non-differentiable, mixed integer, and highly combinatorial in nature. The Kruskal's algorithm is used to determine the minimum spanning tree, which has the characteristic to run in polynomial time.
37 citations
TL;DR: An ant-based algorithm to find low cost degree-constrained spanning trees (DCST) is presented, which employs a set of ants which traverse the graph and identify aSet of candidate edges, from which a DCST is constructed.
Abstract: The degree-constrained minimum spanning tree (DCMST) problem is the problem of finding the minimum cost spanning tree in an edge weighted complete graph such that each vertex in the spanning tree has degree ≤ d for some d ≥ 2. The DCMST problem is known to be NP-hard. This paper presents an ant-based algorithm to find low cost degree-constrained spanning trees (DCST). The algorithm employs a set of ants which traverse the graph and identify a set of candidate edges, from which a DCST is constructed. Local optimization algorithms are then used to further improve the DCST. Extensive experiments using 612 problem instances show many improvements over existing algorithms.
32 citations
TL;DR: This work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn and significantly improves the straightforward O(n^3) dynamic programming approach, and provides an O( n^2) time algorithm.
26 citations
TL;DR: This paper studies two optimization problems having roots in the domain of optical networks, referred to as MBV and MDS, which seek a spanning tree T of G with the minimum number of branch vertices.
22 citations
17 Jan 2012
TL;DR: An algorithm is presented for the degree-constrained MST problem where for every vertices v, the edges adjacent to v have to be independent in a given matroid, such that for every vertex v, it suffices to remove at most 8 edges from the spanning tree to satisfy the matroidal degree constraint at v.
Abstract: We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints A famous example thereof is the classical degree-bounded MST problem, where for every vertex v, a simple upper bound on the degree is imposed Iterative rounding/relaxation algorithms became the tool of choice for degree-constrained network design problems A cornerstone for this development was the work of Singh and Lau [19], who showed that for the degree-bounded MST problem, one can find a spanning tree violating each degree bound by at most one unit and with cost at most the cost of an optimal solution that respects the degree boundsHowever, current iterative rounding approaches face several limits when dealing with more general degree constraints, where several linear constraints are imposed on the edges adjacent to a vertex v For example, when a partition of the edges adjacent to v is given and only a fixed number of elements can be chosen out of each set of the partition, current approaches might violate each of the constraints at v by a constant, instead of violating the whole family of constraints at v by at most a constant number of edges Furthermore, previous iterative rounding approaches are not suited for degree constraints where some edges are in a super-constant number of constraintsWe extend iterative rounding/relaxation approaches, both conceptually as well as in their analysis, to address these limitations Based on these extensions, we present an algorithm for the degree-constrained MST problem where for every vertex v, the edges adjacent to v have to be independent in a given matroid The algorithm returns a spanning tree of cost at most OPT, such that for every vertex v, it suffices to remove at most 8 edges from the spanning tree to satisfy the matroidal degree constraint at v
22 citations
Patent•
18 Jul 2012
TL;DR: The Maximum Resilience (MR) algorithm as discussed by the authors minimizes the probability that a node is disconnected from the controller in case of a failure in the network by minimizing the weight of the controller.
Abstract: The invention is a routing algorithm characteristic that minimizes the weight, meaning that the probability that a node is disconnected from the controller in case of a failure in the network is minimized. The first algorithm used in the invention is an approximation algorithm for finding the controller routing tree that provides maximum resilience in the network. The algorithm is referred to herein as the Maximum Resilience (MR) algorithm. The heuristic MR algorithm selects a shortest-path tree as a starting point and modifies the tree in order to improve resilience. The output of the MR algorithm is not necessarily a shortest-path tree, but provides more resilience compared to the initial tree. The RASP algorithm provides a shortest-path tree with improved network resilience compared to other possible shortest-path trees.
01 Nov 2012
TL;DR: A decentralized learning automata-based algorithm creates spanning trees that honor the diameter constraint and confirms the superiority of the algorithm over other heuristics in terms of both speed and solution quality.
Abstract: Given a graph G and a bound d ? 2, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of minimum weight subject to the constraint that its diameter does not exceed d This problem is NP-hard; several heuristics have been proposed to find near-optimal solutions to it in reasonable times A decentralized learning automata-based algorithm creates spanning trees that honor the diameter constraint The algorithm rewards a tree if it has the smallest weight found so far and penalizes it otherwise As the algorithm proceeds, the choice probability of the tree converges to one; and the algorithm halts when this probability exceeds a predefined value Experiments confirm the superiority of the algorithm over other heuristics in terms of both speed and solution quality
TL;DR: The presented algorithm can be modified to solve the DC-MST (Delay Constrained-Minimum Spanning Tree) problem presented by Lee and Atiquzzaman (2007) and the MRCT (Minimum Routing Cost Tree)problem presented by Cambos and Ricardo (2008), given as the applications of the presented algorithm.
Abstract: In this paper, least-cost minimum spanning tree (LC-MST) problem is defined as a method to construct a minimum cost spanning tree that has the least-cost edges in the network by using the distance (cost) matrix. The paper presents a new algorithm based on the distance matrix to solve the LC-MST problem. The studied cases show that the presented algorithm is efficient to solve the LC-MST problem in less time. Also, the presented algorithm can be modified to solve the DC-MST (Delay Constrained-Minimum Spanning Tree) problem presented by Lee and Atiquzzaman (2007) and the MRCT (Minimum Routing Cost Tree) problem presented by Cambos and Ricardo (2008), given as the applications of the presented algorithm.
TL;DR: In this paper, a 2-approximation algorithm for the unweighted case has been proposed, and the best approximation ratio known for the weighted case is 3, which is the best known approximation ratio.
Abstract: The minimum cost-tree cover problem is to compute a minimum cost-tree T in a given connected graph G with costs on the edges, such that the vertices spanned by T form a vertex cover for G. The problem is supposed to occur in applications of vertex cover and in edge-dominating sets when additional connectivity is required for solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the 3-approximation algorithms for such cases are far from practical due to their inefficiency.In this article we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost-tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST); and, to determine which leaves to trim, it uses both the primal-dual schema and an instance layering technique adapted from the local ratio method.
31 May 2012
TL;DR: Based on the results of research, Prim's algorithm computation time in finding the minimum spanning tree of a weighted graph will grow up along with increasing the number of points/vertices and thenumber of sides of the weighted graph.
Abstract: In this study, the algorithm used is Prim’s algorithm—an algorithm in graph theory to seek a minimum spanning tree for a weighted connected graph. The program used is a program created with Delphi 7 programming language used for searching the minimum spanning tree of a graph model with the weight of each form of distance/length connecting the points/vertices. Then display the information search process sequence of minimum spanning tree, the total number of minimum length and the resulting computing time to determine the efficiency of Prim’s algorithm. Based on the results of research, Prim's algorithm computation time in finding the minimum spanning tree of a weighted graph will grow up along with increasing the number of points/vertices and the number of sides of the weighted graph. Keywords:Prim’s Algorithm, Graph model, Minimum Spanning Tree
TL;DR: 2 heuristic-based algorithms used for MRCT, to start at a spanning tree and step by step improve edges to obtain better spanning tree, are proposed.
Abstract: Minimum routing cost spanning tree - MRCT is one of spanning tree optimization problems having many applications in network design. In general cases, the problem is proved as NP-hard. This paper is going to propose 2 heuristic-based algorithms used for MRCT. The general idea of those algorithms is to start at a spanning tree and step by step improve edges to obtain better spanning tree. We conducted experiment implemetations for these proposals and obtained better result than the result of current approximate algorithms.
Proceedings Article•
29 May 2012TL;DR: A P2MP energy-saving routing design using Prim's algorithm to reduce the energy consumption of the transport network for multipoint services and reduces number of links up to 57% in 40 node network is developed.
Abstract: We develop a P2MP energy-saving routing design using Prim's algorithm to reduce the energy consumption of the transport network for multipoint services. By computer simulation, it is shown the developed algorithm provides an energy-saving topology within 1 second and reduces number of links up to 57% in 40 node network.
TL;DR: This paper presents some modification of the Blair and Manne algorithm for finding the center of a tree network in the distributed, self-stabilizing environment that finds weighted centroid, which is direct generalization of the former one for tree networks with positive weights on nodes.
Abstract: In this paper we present some modification of the Blair and Manne algorithm for finding the center of a tree network in the distributed, self-stabilizing environment. Their algorithm finds n/2 -separator of a tree. Our algorithm finds weighted centroid, which is direct generalization of the former one for tree networks with positive weights on nodes. Time complexity of both algorithms is O(n2), where n is the number of nodes in the network.
01 Dec 2012
TL;DR: A new Steiner tree algorithm called branch-based multi-cast (BBMC) is proposed for this study, which produces exactly the same P2MP tree as MPH, and the algorithm speed of BBMC is much faster than that of MPH because BBMC does not use Dijkstra's algorithm in its algorithm process and drastically reduces the number of accesses to the F-heaps.
Abstract: There are many polynomial-time heuristic Steiner tree algorithms since seeking the minimum point to multi point (P2MP) tree in a network, which is known as the Steiner problem in networks (SPN), is nondeterministic polynomial time complete. Takahashi and Matsuyama's minimum-cost path heuristic algorithm (MPH) is widely applied to various multicast services. MPH has to run Dijkstra's algorithm m times in its algorithm process, where m is the number of end nodes of the multicast tree. By using Fibonacci heaps (F-heaps), the time complexity of MPH is O(m(l + n log n)), where l is the number of links and n is the number of nodes on the network. A new Steiner tree algorithm called branch-based multi-cast (BBMC) is proposed for this study, which produces exactly the same P2MP tree as MPH does. BBMC shortens MPH's average time complexity to O((log m)(l + n log n)). In addition, the algorithm speed of BBMC is much faster than that of MPH because BBMC does not use Dijkstra's algorithm in its algorithm process and drastically reduces the number of accesses to the F-heaps. MPH's processing time increases proportionally to m, especially when m is large, but BBMC's processing time is almost independent from m. The speed of BBMC is about the same as that of the destination-driven multi-cast algorithm (DDMC), which has a time complexity of O(l + n log n), though BBMC produces a P2MP tree with a tree cost much smaller than that of DDMC.
19 Apr 2012
TL;DR: A Lagrangian Relaxation algorithm is proposed for approximating the lower bounds of the Min-Degree Constrained Minimum Spanning Tree Problem, and a parallel Subgradient Method is implemented, attempting to speed up the computation of the Lagrangia Dual bounds.
Abstract: Given an edge weighted undirected graph G and a positive integer d, the Min-Degree Constrained Minimum Spanning Tree Problem (MDMST) asks for a minimum cost spanning tree of G, such that each vertex is either a leaf or has degree at least d in the tree. The strongest known MDMST lower bounds, provided by a reformulation by intersection, are very expensive to be evaluated directly, by Linear Programming solvers. Therefore, we propose a Lagrangian Relaxation algorithm for approximating them. The reformulation makes use of a large number of variables and the relaxation involves the dualization of a large number of constraints. Attempting to speed up the computation of the Lagrangian Dual bounds, we implemented a parallel Subgradient Method. We also introduced a Lagrangian heuristic based on a Local Branching algorithm. With the proposed methods, respectively 26 and 14 new best upper and lower bounds are presented.
01 Jan 2012
TL;DR: This paper finds the solution for the problem, that A.V.M.V., Sri Pushpam College, (Autonomous), Poondi, Thanjavur District, South India need to connect updated intercom lines connecting all the departments using fuzzy shortest route algorithm.
Abstract: In computer science, there are many algorithm that finds a minimum spanning tree for a connected weighted undirected fuzzy graph. This means it finds a subset of the edge- set that forms a fuzzy spanning tree that includes every vertex, where the total weight of all the edges in the fuzzy tree is minimized. Generally algorithm has many applications, such as landline (intercom) phone connection to a particular college in order to minimize the shortest distance, which applies Nearest Neighbor Algorithm, Sorted Edges Algorithm, Kruskal's Algorithm to a randomly weighted fuzzy graph. In this paper, we find the solution for the problem, that A.V.V.M. Sri Pushpam College, (Autonomous), Poondi, Thanjavur District, South India need to connect updated intercom lines connecting all the departments using fuzzy shortest route algorithm. The problem is to minimize the amount of new line using Kruskal's Algorithm with fuzzy graph. These algorithm continuously increases the size of a fuzzy tree, one edge at a time, starting with a fuzzy tree consisting of a single vertex, until it spans all vertices of the fuzzy graph.
01 Sep 2012
TL;DR: A new genetic algorithm based on spanning tree-based encoding for the well-known MAX CUT problem is proposed and could obtain performance improvement on sparse graphs, which appear in real-world applications such as social networks and systems biology.
Abstract: Most of previous genetic algorithms for solving graph problems have used vertex-based encoding. In this paper, we introduce spanning tree-based encoding instead of vertex-based encoding for the well-known MAX CUT problem. We propose a new genetic algorithm based on this new type of encoding. We conducted experiments on benchmark graphs and could obtain performance improvement on sparse graphs, which appear in real-world applications such as social networks and systems biology, when the proposed methods are compared with ones using vertex-based encoding.
04 Jul 2012
TL;DR: The algorithm for determining how many vertices should be installed in a certain period in such a way so that the cost of installation is minimum is discussed.
Abstract: Given one center already set, The Multi Period Degree Constrained Minimum Spanning Tree Problem (MPDCMST) is a problem of determining how many vertices (can be computers, cities, and so on) should be installed in a certain period in such a way so that the cost of installation is minimum. After all the periods done, all of the vertices must be in the network, and still the cost of installation must be the minimum. In addition, the network itself has a degree restriction in every vertex which limits the number of links that incident to. In this paper we will discuss the algorithm we have developed and give results on 600 random table data. Keywords: multi period, degree constrained, minimum spanning tree
Posted Content•
TL;DR: This paper deals with generation of all possible spanning trees in increasing cost of a weighted graph using one matrix called Difference Weighted Circuit Matrix; it is little bit modification of FCM.
Abstract: The most popular algorithms for generation of minimal spanning tree are Kruskal and Prim algorithm. Many algorithms have been proposed for generation of all spanning tree. This paper deals with generation of all possible spanning trees in increasing cost of a weighted graph. This approach uses one matrix called Difference Weighted Circuit Matrix; it is little bit modification of FCM.
01 Jan 2012
TL;DR: A modified version of prim's algorithm which is a minimum spanning tree algorithm, where root node is chosen with minimum edge weight so that from the beginning of forest creation, only minimum weight edges are included.
Abstract: 1 Abstract— This paper proposes a modified version of prim's algorithm which is a minimum spanning tree algorithm. Minimum spanning tree algorithms are greedy algorithms as they choose the best path available at that moment. Prim's algorithm chooses a root node randomly and starts processing it but choosing any node randomly as a root node is not efficient. So, in modified prim's algorithm, root node is chosen with minimum edge weight so that from the beginning of forest creation, only minimum weight edges are included. Minimum spanning tree is generated differently as of prim's algorithm. Although modified prim's algorithm is a special case of original prims algorithm with randomly chosen node is of minimum weight. With this modification in original prims algorithm, modified prim's algorithm maintains the complexity same as original prim's algorithm.
01 Jan 2012
TL;DR: A fuzzy spanning tree with maximum flow is constructed, which is equivalent to an undirected graph by algorithmic representation, and in general, the flow equivalent fuzzy tree is not unique.
Abstract: By introducing, the new concept fuzzy edge cut-set, multiple sources and sinks of fuzzy graphs and with arc and vertex capacities of fuzzy graphs , simple variations of the maximal flow problem is introduced. A maximum flow matrix is constructed by a spanning tree using vertex condensation process. Also, in this paper a fuzzy spanning tree with maximum flow is constructed, which is equivalent to an undirected graph by algorithmic representation. In general, the flow equivalent fuzzy tree is not unique.
Journal Article•
TL;DR: The algorithm involves choosing the minimum edge that connects each disjoint component of the graph, until a single component is formed, which is the minimum spanning tree of the given graph.
Abstract: This paper presents an approach to finding the minimum spanning tree for simple undirected graphs and undirected multi-graphs. The algorithm involves choosing the minimum edge that connects each disjoint component of the graph, until a single component is formed. This single component is the minimum spanning tree of the given graph. The approach we take is a slight modification to Sollin’s algorithm.
23 Mar 2012
TL;DR: Wang et al. as discussed by the authors adopted width first search in local bound, which can reduce redundant search packet in some scope, while it won't occupy much network resource in message exchange because of scope is small.
Abstract: To improve information retrieval speed, it is the key of minimizing traffic and every required visit peer on the view of reducing traffic, combining the merit of width first search won't lead to redundant and P2P network's dynamic feature, We advanced adopting width first search in local bound--Broad first minimum spanning tree search. It can reduce redundant search packet in some scope. Meanwhile, It won't occupy much network resource in message exchange because of scope is small. The way have good feature in expansibility and robustness. It can adapt to dynamic change in P2P network.
Journal Article•
TL;DR: Experiment indicated that the method can keep the boundary of region while merging "over-segmentation" regions quickly and effectively, and it is effective for remote sensing images of complex and large size.
Abstract: To solve the problem of over-segmentation caused by noise when applying watershed segmentation based on morpho-logy,a new regions merging method is proposed.Based on the minimum spanning tree algorithm(prim,kruskal,boruvka),segmented region is regarded as the vertex of a graph,adjacent regions are regarded as the edges whose weight is determined by the difference between the segmented region and adjacent region,regions merging is completed by setting the appropriate threshold and iteration times.Experiment indicated that the method can keep the boundary of region while merging"over-segmentation" regions quickly and effectively,and it is effective for remote sensing images of complex and large size.