Comparison of Greedy Algorithms for Decision Tree Optimization

The Steiner tree problem is one of the fundamental optimization problems in distributed graph algorithms. Recently Saikia and Karmakar [27] proposed a deterministic distributed algorithm for the Steiner tree problem that constructs a Steiner tree in \(O(S + \sqrt{n} \log ^* n)\) rounds whose cost is optimal upto a factor of \(2(1 - 1/\ell )\), where n and S are the number of nodes and shortest path diameter [17] respectively of the given input graph and \(\ell \) is the number of terminal leaf nodes in the optimal Steiner tree. The message complexity of the algorithm is \(O(\varDelta (n - t) S + n^{3/2})\), which is equivalent to \(O(mS + n^{3/2})\), where \(\varDelta \) is the maximum degree of a vertex in the graph, t is the number of terminal nodes (we assume that \(t < n\)), and m is the number of edges in the given input graph. This algorithm has a better round complexity than the previous best algorithm for Steiner tree construction due to Lenzen and Patt-Shamir [21]. In this paper we present a deterministic distributed algorithm which constructs a Steiner tree in \(\tilde{O}(S + \sqrt{n})\) rounds and \(\tilde{O}(mS)\) messages and still achieves an approximation factor of \(2(1 - 1/\ell )\). Note here that \(\tilde{O}(\cdot )\) notation hides polylogarithmic factors in n. This algorithm improves the message complexity of Saikia and Karmakar’s algorithm by dropping the additive term of \(O(n^{3/2})\) at the expense of a logarithmic multiplicative factor in the round complexity. Furthermore, we show that for sufficiently small values of the shortest path diameter \((S=O(\log n))\), a \(2(1 - 1/\ell )\)-approximate Steiner tree can be computed in \(\tilde{O}(\sqrt{n})\) rounds and \(\tilde{O}(m)\) messages and these complexities almost coincide with the results of some of the singularly-optimal minimum spanning tree (MST) algorithms proposed in [9, 12, 23].

A Classification Prediction Analysis of Flight Cancellation Based on Spark

The study of algorithms for decision tree construction was initiated in 1960s. The first algorithms are based on the separation heuristic [13, 31] that at each step tries dividing the set of objects as evenly as possible. Later Garey and Graham [28] showed that such algorithm may construct decision trees whose average depth is arbitrarily far from the minimum. Hyafil and Rivest in [35] proved NP-hardness of DT problem that is constructing a tree with the minimum average depth for a diagnostic problem over 2-valued information system and uniform probability distribution. Cox et al. in [22] showed that for a two-class problem over information system, even finding the root node attribute for an optimal tree is an NP-hard problem.

In this paper, a differential-evolution-based approach implementing a global search strategy to find a near-optimal axis-parallel decision tree is introduced. In this paper, the internal nodes of a decision tree are encoded in a real-valued chromosome, and a population of them evolves using the training accuracy of each one as its fitness value. The height of a complete binary decision tree whose number of internal nodes is not less than the number of attributes in the training set is used to compute the chromosome size, and a procedure to map a feasible axis-parallel decision tree from one chromosome is applied, which uses both the smallest-position-value rule and the training instances. The best decision tree in the final population is refined replacing some leaf nodes with sub-trees to improve its accuracy. The differential evolution algorithm has been successfully applied in conjunction with several supervised learning methods to solve numerous classification problems, due to it exhibiting a good tradeoff between its exploitation and exploration skills, and to the best of our knowledge, it has not been utilized to build axis-parallel decision trees. To obtain reliable estimates of the predictive performance of this approach and to compare its results with those achieved by other methods, a repeated stratified ten-fold cross-validation procedure is applied in the experimental study. A statistical analysis of these results suggests that our approach is better as a decision tree induction method as compared with other supervised learning methods. Also our results are comparable to those obtained with random forest and one multilayer-perceptron-based classifier.

Total Path Length and Number of Terminal Nodes for Decision Trees

Improved distributed approximation for Steiner tree in the CONGEST model

The decision‐tree (DT) algorithm is a very popular and efficient data‐mining technique. It is non‐parametric and computationally fast. Besides forming interpretable classification rules, it can select features on its own. In this article, the feature‐selection ability of DT and the impacts of feature‐selection/extraction on DT with different training sample sizes were studied by using AVIRIS hyperspcetral data. DT was compared with three other feature‐selection methods; the results indicated that DT was an unstable feature selector, and the number of features selected by DT was strongly related to the sample size. Trees derived with and without feature‐selection/extraction were compared. It was demonstrated that the impacts of feature selection on DT were shown mainly as a significant increase in the number of tree nodes (14.13–23.81%) and moderate increase in tree accuracy (3.5–4.8%). Feature extraction, like Non‐parametric Weighted Feature Extraction (NWFE) and Decision Boundary Feature Extraction (DBFE), could enhance tree accuracy more obviously (4.78–6.15%) and meanwhile a decrease in the number of tree nodes (6.89–16.81%). When the training sample size was small, feature‐selection/extraction could increase the accuracy more dramatically (6.90–15.66%) without increasing tree nodes.

The construction of a spanning tree is a fundamental task in distributed systems which allows to resolve other tasks (i.e., routing, mutual exclusion, network reset). In this paper, we are interested in the problem of constructing a Breadth First Search (BFS) tree. Stabilization is a versatile technique which ensures that the system recover a correct behavior from an arbitrary global state resulting from transient faults. A fully polynomial algorithm has a round complexity in O(da) and a step complexity in O(nb) where d and n are the diameter and the number of nodes of the network and a and b are constants. We present the first fully polynomial stabilizing algorithm constructing a BFS tree under a distributed daemon. Moreover, as far as we know, it is also the first fully polynomial stabilizing algorithm for spanning tree construction. Its round complexity is in O(d2) and its step complexity is in O(n6). To our knowledge, since in general the diameter of a network is much smaller than the number of nodes (log(n) in average instead of n), this algorithm reaches the best compromise of the literature between the complexities in terms of rounds and in terms of steps.

Path-finding is a fundamental problem in computer games, and its efficiency is mainly determined by the number of nodes it will expand. A* algorithm is unsuitable for path-finding on large map under limited computer sources and real-time demand, because the number of nodes it will expand grows fast with the size of the search space. HPA* can greatly improve the efficiency by generating abstract graph of the given map to memorize the map information before doing pathfinding. Through evenly partitioning the map as preprocessing, it can also reduce the influence of terrain factor on the output. As a result, it finds near optimal paths instead of optimal ones. And the evenly partition on the map doesnt consider the terrain distribution, which may still cause resource waste to some extent. In this paper, we present DT-HPA* (Hierarchical Path-Finding A* based on Decision Tree), a hierarchical path-finding approach on the map which has been divided by decision tree. This approach views each point on the map as an instance, and divides the map according to cut-points of continuous valued decision tree. The result of division is that the map is cut into some rectangular regions in different size, and retains the regions contain a kind of terrain. The experimental results show that, compared to HPA*, DT-HPA* can find more optimal paths with fewer detected nodes.KeywordsGame intelligenceHierarchical path-findingInformation entropyDecision treeDT-HPA*

Linial, London and Rabinovich [16] and Aumann and Rabani [3] proved that the min-cut max-flow ratio for general maximum concurrent flow problems (when there are k commodities) is O(logfe). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are poly-logarithmic in k for a much broader class of multicommodity flow and cut problems. Our structural results are motivated by the meta question: Suppose we are given a poly(log n) approximation algorithm for a flow or cut problem when can we give a poly(log k) approximation algorithm for a generalization of this problem to a Steiner cut or flow problem? Thus we require that these approximation guarantees be independent of the size of the graph, and only depend on the number of commodities (or the number of terminal nodes in a Steiner cut problem). For many natural applications (when k = n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o(1)</sup> ) this yields much stronger guarantees. We construct vertex-sparsifiers that approximately preserve the value of all terminal min-cuts. We prove such sparsifiers exist through zero-sum games and metric geometry, and we construct such sparsifiers through oblivious routing guarantees. These results let us reduce a broad class of multicommodity-type problems to a uniform case (on k nodes) at the cost of a loss of a poly (log k) in the approximation guarantee. We then give poly(log k) approximation algorithms for a number of problems for which such results were previously unknown, such as requirement cut, 1-multicut, oblivious 0-extension, and natural Steiner generalizations of oblivious routing, min-cut linear arrangement and minimum linear arrangement.

An efficient algorithm for optimal pruning of decision trees

One of the major limitation of using the back-propagation neural network and its variants in real applications are that the number of hidden nodes is unknown. It is usually estimated by trial-and-error and thus it is inefficient. The paper proposes an algorithm to determine the number of hidden nodes based on the input data. The dynamic expansion and contraction approach (DECA), which comes from dynamic programming, is used to determine the optimal number of hidden nodes. The object function minimises the number of hidden nodes while the constraints are a pre-defined error. A short interval of train/test interleaving is used to minimise the learning time and avoid over-training the network. The algorithm is applicable to the neural network used for function approximation as well as pattern classification. >

Stock Classification Prediction Based on Spark

Simple or proxy production models are potentially very useful and tractable because they are computationally attractive whilst still providing insight to the decision at hand. Useful and tractable models are required for supporting high-quality decisions in uncertain, complex, and computationally demanding contexts. A key decision for development planning is: what is the optimal time to initiate an Improved-Oil-Recovery (IOR) process. We aim to illustrate the implementation and application of a useful and tractable approach for the analysis of the optimal IOR switch time using a two-factor production model and Least-Squares Monte Carlo (LSM) simulation. The two-factor production model contains only two parameters for each recovery phases. One parameter describes how much recovery efficiency a recovery mechanism can ultimately achieve whilst the other describes how fast the recovery efficiency increases. The simplicity of the model makes it computationally attractive. The LSM algorithm is an approximate dynamic programming approach, which allows for learning over time. It provides a near-optimal solution for the IOR switch time problem. The Value-Of-Information (VOI) framework—a powerful decision-analysis tool—provides an estimate of the value of learning. Closed-Loop Reservoir Management (CLRM) is considered to be a state-of-the-art approach to solving for the optimal IOR switch time. However, this approach can produce a suboptimal solution as the CLRM approach considers only uncertainties and actions reflecting currently available information but not those uncertainties and actions arising from future information. The dynamic programming approach used here considers both the impact of the information obtained before a decision is made and the impact of the information that might be obtained to support future decisions. We conclude that a dynamic programming approach, such as the LSM algorithm, can significantly improve both the timing and value of decisions, leading to a significant increase in a field's economic performance. Furthermore, the two-factor model combined with the LSM algorithm is tractable and provides useful insight into the IOR switch time problem. The novelties provided by this work are: developing and illustrating the structure of the IOR switch time problem in a decision tree, demonstrating and discussing the suboptimality of the CLRM solution, developing and illustrating the detailed steps of applying the LSM algorithm for the IOR switch time decision, and implementing the two-factor model combined with the LSM algorithm for analyzing the optimal IOR switch time.

Mobile ad-hoc network is dynamic nature because each node moves freely in the network. In MANET we can't predict node motion and traffic load of each node, so number of nodes are ideal and number of node are vary loaded that leads the problem of congestion onto the network, here we design a survey paper related various congestion control under the MANET that work provide the congestion free as well as congestion avoidance techniques from network. In this survey we identify multipath routing and load aware technique both are provide more reliable as well as load aware of each node so minimize the data drop but all given approach are use routing base congestion control, through this survey we identify that congestion control through dynamic queue management technique, here we given about problem statement about dynamic queue base approach for congestion control and simulation parameter. In further we design proposed work and proposed algorithm and simulate through all network parameter base for performance evaluation.