Minimum Tree Research Articles

Evidence against planting lodgepole pine monocultures in the cedar-hemlock forests of southeastern British Columbia

Single-species planting of lodgepole pine (Pinus contorta var. latifolia) following clear-cut logging or wildfire has been common throughout interior British Columbia, Canada, but health problems with the species have been documented as it grows beyond the juvenile stage. We examined damage and stocking in twenty-seven 15to 30-yearold lodgepole pine plantations that were previously declared free growing in the highly productive cedar–hemlock forests in southeastern British Columbia, where lodgepole pine is absent from many primary forests. In order to be free growing, stands must meet minimum tree density, height, damage and brush competition criteria as legislated by the Provincial government. Overall, 44 per cent of lodgepole pine trees had unacceptable damage (causing them to be rejected as crop trees), and as a direct result, one-third of the plantations were no longer defined as free growing because there were insufficient crop trees remaining. Natural regeneration of other tree species partially compensated for the unhealthy pine. Logistic regression and odds ratio analysis associated increasing risk of damage from western gall rust with increasing soil moisture, more northerly aspects and mechanical site preparation, and decreasing risk with pre-commercial thinning treatment. Risk of damage from snow and ice was associated with increasing mean annual precipitation, decreasing longitude and broadcast burning. Risk of bear damage was associated with increasing soil moisture, pre-commercial thinning treatment and broadcast burning. Based on our results, we recommend that single-species planting of lodgepole pine be curtailed in the Interior Cedar–Hemlock zone in southeastern British Columbia.

Obstacle-Avoiding Algorithm in X-Architecture Based on Discrete Particle Swarm Optimization for VLSI Design

Obstacle-avoiding Steiner minimal tree (OASMT) construction has become a focus problem in the physical design of modern very large-scale integration (VLSI) chips. In this article, an effective algorithm is presented to construct an OASMT based on X-architecturex for a given set of pins and obstacles. First, a kind of special particle swarm optimization (PSO) algorithm is proposed that successfully combines the classic genetic algorithm (GA), and greatly improves its own search capability. Second, a pretreatment strategy is put forward to deal with obstacles and pins, which can provide a fast information inquiry for the whole algorithm by generating a precomputed lookup table. Third, we present an efficient adjustment method, which enables particles to avoid all the obstacles by introducing some corner points of obstacles. Finally, an excellent refinement method is discussed to further enhance the quality of the final routing tree, which can improve the quality of the solution by 7.93% on average. To our best knowledge, this is the first time to specially solve the single-layer obstacle-avoiding problem in X-architecture. Experimental results show that the proposed algorithm can further shorten wirelength in the presence of obstacles. And it achieves the best solution quality in a reasonable runtime among the existing algorithms.

A Genetic Algorithm Based Minimal Maximal Load Tree Routing Algorithm in Wireless Sensor Networks

The key issue of static routing algorithms is how to construct an energy efficient routing tree that is utilized during the whole network duration in order to extend network lifetime. In this paper, we have illuminated that, in applications that define network lifetime as the time when the first sensor dies, the optimal routing tree should be the routing tree with minimal maximal load of all sensors and named such trees the Minimal Maximal Load Tree (MMLT). Since the procedure of constructing a routing tree is complex and the number of possible routing trees in a network is very huge, we have proposed a genetic algorithm (GA) based algorithm to obtain approximate Minimal Maximal Load Tree (MMLT). Each individual corresponds to a routing tree, and the fitness function is defined as the maximal load of all sensors in accordance with the routing tree that the individual corresponds to. Thus, approximate MMLT is obtained and network lifetime is extended. Simulation results show that our proposed algorithm notably extends network lifetime.

Minimum Average Distance Clique Trees

Chordal graphs have been extensively studied and have applications in various fields, including computational biology, sparse matrix computation, and graphical models. They are characterized by the existence of clique trees, whose vertices correspond to the maximal cliques of a chordal graph. In many applications, it is the clique tree of the chordal graph that is of greatest utility. In general, the number of clique trees can grow exponentially with the size of the chordal graph, and in some applications, particular clique trees have greater utility; we want additional criteria to select the most useful clique tree(s). A natural criterion in phylogenetics (and perhaps elsewhere) is that of compactness. In this paper, we formalize this criterion as the average distance between nodes, and present a characterization of clique trees that satisfies this criterion. We also develop a polynomial-time algorithm to find such a clique tree, and show that any minimum average-distance clique tree of a chordal graph c...

GIẢI THUẬT KIẾN SONG SONG GIẢI BÀI TOÁN CÂY KHUNG NHỎ NHẤT CÓ BẬC BỊ CHẶN

GIẢI THUẬT KIẾN SONG SONG GIẢI BÀI TOÁN CÂY KHUNG NHỎ NHẤT CÓ BẬC BỊ CHẶN

A Multicast Sparse-Grooming Algorithm Based on Network Coding in WDM Networks

AbstractTo improve the limited number of wavelength utilization and decrease the traffic blocking probability in sparse-grooming wavelength-division multiplexing (WDM) networks, a multicast sparse-grooming algorithm based on network coding (MCSA-NC) is put forward to solve the routing problem for dynamic multicast requests in this paper. In the proposed algorithm, a traffic partition strategy, that the coarse-granularity multicast request with grooming capability on the source node is split into several fine-granularity multicast requests, is designed so as to increase the probability for traffic grooming successfully in MCSA-NC. Besides considering that multiple destinations should receive the data from source of the multicast request at the same time, the traditional transmission mechanism is improved by constructing edge-disjoint paths for each split multicast request. Moreover, in order to reduce the number of wavelengths required and further decrease the traffic blocking probability, a light-tree reconfiguration mechanism is presented in the MCSA-NC, which can select a minimal cost light tree from the established edge-disjoint paths for a new multicast request.

Variation in Tree, Foliage, Phenological and Pollen Characters of Low Chill Peach Germplasm Accessions under Mid-hills of Himachal Pradesh

The present investigation was carried out in the department of Fruit Science, Dr Y S Parmar University of Horticulture and Forestry, Nauni, Solan, HP, India. Ten peach genotypes namely Tropic Sweet, Saharanpur Prabhat, Earli Grande, Flordaprince, Tropic Snow, Flordaglo, Valle Grande, Tropic Beauty, Pratap and Florda Grande were evaluated for their tree, foliage, floral and pollen characteristics. Valle Grande recorded maximum tree height (2.73 m) whereas, minimum tree height (1.83 m) was recorded in Flordaprince. Shedding of leaf started from 29th October (Tropic Sweet) and extended till 20th November (Tropic Beauty). Time of full bloom extended from 24th January in Saharanpur Prabhat and Pratap to 2nd February in Tropic Snow and Flordaglo. The longest duration (39 days) of flowering was recorded in Pratap and shortest (28 days) in Tropic Sweet and Earli Grande. Pollen viability ranged from 93.82% to 98.93% when tested by 1.0% acetocarmine and 84.19 to 97.70% by 0.1% erythrosin B. In vitro pollen germination varied from 62.26% to 90.39%.

Optimization of Cable Layout Design in a Wind Farm: A Hybrid Approach

In this paper, a hybrid algorithm based on modified Ants Colony Optimization (ACO) and Artificial Immune Algorithm (AIA) for solving the Steiner Minimal Tree Problem (SMTP) is introduced. Since the Steiner Tree Problem is NP-hard, we design an algorithm to construct high quality Steiner trees in a short time which is suitable for real time multicast routing in networks. After the breadth - first traversal of the minimal graph obtained by ACO, the terminal points are divided into different convex hull sets, and the full Steiner tree is structured from the convex hull sets partition. The Steiner points can be vaccinated by AIA to get an optimal graph. The average optimization effect of AIA is shorter than the minimal graph obtained using ACO, and the performance of the algorithm is shown. We give an example of application in wind farm network design.

Dynamic Prediction of Minimal Trees in Large-Scale Parallel Game Tree Search

Dynamic Prediction of Minimal Trees in Large-Scale Parallel Game Tree Search

Efficient Multicast Routing on BCube-Based Data Centers

Multicast group communication has many advantages in data centers and thus is widely used by many applications. It can efficiently reduce the network traffic and improve the application throughput. For the multicast application in data centers, an essential problem is how to find a minimal multicast tree, which has been proved to be NP-hard. In this paper, we propose an approximation tree-building method for the minimal multicast problem, named HD （Hamming Distance）-based multicast tree. Consider that many new network structures have been proposed for data centers. We choose three representative ones, including BCube, FBFLY, and HyperX, whose topological structures can be regarded as the generalized hypercube. Given a multicast group in BCube, the HD-based method can jointly schedule the path from each of receiver to the only sender among multiple disjoint paths; hence, it can quickly construct an efficient multicast tree with the low cost. The experimental results demonstrate that our method consumes less time to construct an efficient multicast tree, while considerably reduces the cost of the multicast tree compared to the representative methods. Our approach for BCube can also be adapted to other generalized hypercube network structures for data centers after minimal modifications.

Improve and Optimize Query Recommendation System by MST Algorithm and its MapReduce Implementation

Query recommendation as an important tool to enhance the user search efficiency has gradually become a hotspot. In the context of big data, using the MapReduce programming model, combined with distributed minimum spanning tree algorithm, a parallel query recommended method based on MapReduce was proposed in this paper. The final results show that the efficiency of query recommendation was greatly improved through parallel computing.

Efficient Multilayer Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Geometric Reduction

Given a set of pin-vertices, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects all the pin-vertices possibly through Steiner points using vertical and horizontal segments with the minimal wirelength and without intersecting any obstacle. To deal with multiple routing layers and preferred routing orientations, we consider the multilayer obstacle-avoiding rectilinear Steiner minimal tree (ML-OARSMT) problem and the obstacle-avoiding preferred direction Steiner tree (OAPD-ST) problem. First, we prove that the multilayer case is theoretically different from the 2D one, and propose a reduction to transform a multilayer instance into a 3D instance. Based on the reduction, we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics, for the ML-OARSMT problem and the OAPD-ST problem. Furthermore, we develop an advanced Steiner point selection to avoid inferior Steiner points and to improve the solution quality. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.

MTC: A Fast and Robust Graph-Based Transductive Learning Method.

Despite the great success of graph-based transductive learning methods, most of them have serious problems in scalability and robustness. In this paper, we propose an efficient and robust graph-based transductive classification method, called minimum tree cut (MTC), which is suitable for large-scale data. Motivated from the sparse representation of graph, we approximate a graph by a spanning tree. Exploiting the simple structure, we develop a linear-time algorithm to label the tree such that the cut size of the tree is minimized. This significantly improves graph-based methods, which typically have a polynomial time complexity. Moreover, we theoretically and empirically show that the performance of MTC is robust to the graph construction, overcoming another big problem of traditional graph-based methods. Extensive experiments on public data sets and applications on web-spam detection and interactive image segmentation demonstrate our method's advantages in aspect of accuracy, speed, and robustness.

Key-node-based local search discrete artificial bee colony algorithm for obstacle-avoiding rectilinear Steiner tree construction

The obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem is a fundamental problem in very large-scale integrated circuit physical design and can be reduced to the Steiner tree problem in graphs (GSTP), which can be solved by using three types of common methods: classic heuristics, local search algorithms, or computational intelligence algorithms. However, classic heuristics have poor solution qualities; local search algorithms easily fall into the problem of the local optimum; and the searching effects of the existing computational intelligence algorithms are poor for this problem. In order to improve the solution quality, we propose a novel discrete artificial bee colony algorithm for constructing an obstacle-avoiding rectilinear Steiner tree. We first generate the escape graph for the OARSMT problem. Then, we search for a near-optimal solution consisting of some edges of escape graph by using the discrete ABC algorithm. We apply a key-node neighborhood configuration for the local search strategy and introduce two local search operators. We then naturally use a key-node-based encoding scheme for representing the feasible solution and obtain a tight searching scope. We employ a modified classic heuristic as the encoder that can produce a feasible solution. Experiments conducted on both general GSTP and very large-scale integrated circuit instances reveal the superior performance of the proposed method in terms of the solution quality among the state-of-the-art algorithms.

Minimum Cost Bandwidth Guaranteed Multicast Routing in Multi-channel Multi-radio Wireless Mesh Networks

Multicast communication is an important service in wireless mesh networks (WMNs). It covers a broad range of applications, including data distribution, video conferencing, and distance learning. In this paper, we discuss the issue of bandwidth guaranteed multicast routing in multi-channel multi-radio WMNs. The problem of our concern is to construct a tree per multicast session such that the cost of the system, which is defined as the amount of total consumed bandwidth, is minimized. In order to solve the problem efficiently, we design Bandwidth Guaranteed Minimum Cost Tree construction (BGMCT) algorithm. Our algorithm yields cost-effective solutions as it exploits the wireless broadcast advantage (WBA) property of the wireless medium. In the proposed algorithm, we have developed two strategies for constructing minimum cost trees. Firstly, the number of the relay nodes in each tree is minimized. Secondly, the amount of overlapping between the shortest paths which connect different destinations of each session to its source node, is taken into account. The simulation results demonstrate that our algorithm outperforms existing solutions. Moreover, BGMCT provides near to optimal outcomes in a reasonable time.

Multilayer obstacle-avoiding x-architecture steiner minimal tree construction based on particle swarm optimization.

As the basic model for very large scale integration routing, the Steiner minimal tree (SMT) can be used in various practical problems, such as wire length optimization, congestion, and time delay estimation. In this paper, an effective algorithm based on particle swarm optimization is presented to construct a multilayer obstacle-avoiding X-architecture SMT (ML-OAXSMT). First, a pretreatment strategy is presented to reduce the total number of judgments for the routing conditions around obstacles and vias. Second, an edge transformation strategy is employed to make the particles have the ability to bypass the obstacles while the union-find partition is used to prevent invalid solutions. Third, according to the feature of ML-OAXSMT problem, we design an edge-vertex encoding strategy, which has the advantage of simple and effective. Moreover, a penalty mechanism is proposed to help the particle bypass the obstacles, and reduce the generation of via at the same time. Experimental results show that our algorithm from a global perspective of multilayer structure can achieve the best solution quality among the existing algorithms. Finally, to our best knowledge, we redefine the edge cost and then construct the obstacle-avoiding preferred direction X-architecture Steiner tree, which is the first work to address this problem and can offer the theory supports for chip design based on non-Manhattan architecture.

SOLVING THE RECTILINEAR STEINER MINIMAL TREE PROBLEM WITH A BRANCH AND CUT ALGORITHM

This paper presents a new branch-and-cut algorithm that allows us to reduce the solution time of the concatenation phase of the rectilinear Steiner minimal tree problem in the plane. Our branch-and-cut algorithm is used on an integer programming formulation using what we call cutsec, and sec constraints. We present implementation details of our branch-and-cut program called NEOSteiner and provide computational results on test instances from the SteinLib library.

A new model to imitate the foraging behavior of Physarum polycephalum on a nutrient-poor substrate

Abstract Researches on Physarum polycephalum show that methods inspired by the primitive unicellular organism can construct an efficient network and solve some complex problems in graph theory. Current models simulating the intelligent behavior of Physarum are mainly based on Hagen–Poiseuille Law and Kirchhoff Law, reaction–diffusion, Cellular Automaton and multi-agent approach. In this paper, based on an assumption that the plasmodium of Physarum forages for food along the gradient of chemo-attractants on a nutrient-poor substrate, a new model is proposed to imitate its intelligent foraging behavior. The key point of the model is that the growth of Physarum is determined by the simple particle concentration field relating the distance to food source and the shape of food source on a nutrient-poor substrate. To verify this model, numerical experiments are conducted according to Adamatzky׳s experiment. Results in spanning tree construction by this model are almost the same as those of Physarum and Oregonator model. The proposed model can also imitate Physarum to avoid repellents. Furthermore, the Euclidean Spanning tree built by this model is similar to its corresponding Minimal Euclidean Spanning tree.

On the clustered Steiner tree problem

We investigate the Clustered Steiner tree problem on metric graphs, which is a variant of the Steiner minimum tree problem. In this problem, the required vertices are partitioned into clusters, and the subtrees spanning different clusters must be disjoint in a feasible clustered Steiner tree. In this paper, it is shown that the problem is NP-hard even if the inter-cluster tree and all the local topologies are given, where a local topology specifies the tree structure of required vertices in the same cluster. We show that the Steiner ratio of this problem is lower and upper bounded by three and four, respectively. We also propose a $$(\rho +2)$$(?+2)-approximation algorithm, where $$\rho $$? is the approximation ratio for the Steiner minimum tree problem, and the approximation ratio can be improved to $$\rho +1$$?+1 if the local topologies are given. Two variants of this problem are also studied. When the goal is to minimize the inter-cluster cost and ignore the cost of local trees, the problem can be solved in polynomial time. But it is NP-hard if we ask for the minimum cost of local trees among all solutions with minimum inter-cluster cost.

Optimization of underground mine development system using fuzzy shortest path length algorithm

Graphic mine design elements denote physical entities such as shafts, declines, and drives. Ore deposits are often composed of independent orebodies that must be interconnected into one integrated system. In this paper, we examine a case where access points to orebodies lie in the Euclidean plane. The key question is how to interconnect these points at minimal cost. This design problem is modeled as a network and the solution technique is outlined. We supposed that the locations of access points had been previously determined. To define the ore reserves in each orebody, we used linguistic variables and their transformation to fuzzy triangular numbers. At first, we used Kruskal’s algorithm to identify the minimum spanning tree. After that, by inserting Steiner points we defined a Steiner minimal tree as the global minimum. In a network created in such a way, it is necessary to locate a point called the major mass concentration point to which excavated ore will be delivered; from there, the excavated ore will be hauled or hoisted to a surface breakout point via an optimal development system. In this paper, we use the fuzzy shortest path length procedure to select an optimal development system.