A simple algorithm for generating neuronal dendritic trees

A simple, efficient algorithm is presented for generating the codewords of all neuronal dendritic trees with a given number of terminal nodes. Furthermore, a procedure is developed for deciding if different codewords respond to topologically equivalent trees.     

An efficient algorithm for finding the CSG representation of a simple polygon

Modeling two-dimensional and three-dimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary.We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedronP are based on the half-spaces supporting the faces ofP. For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practicalO(n logn) algorithm for doing this boundary-to-CSG conversion for a simple polygon ofn sides. We also prove that such nice formulae do not always exist for general polyhedra in three dimensions.The first author would like to acknowledge the support of the National Science Foundation under Grants CCR87-00917 and CCR90-02352. The fourth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the first author was visiting the DEC Systems Research Center.     

Binary tree of SVM: a new fast multiclass training and classification algorithm

We present a new architecture named Binary Tree of support vector machine (SVM), or BTS, in order to achieve high classification efficiency for multiclass problems. BTS and its enhanced version, c-BTS, decrease the number of binary classifiers to the greatest extent without increasing the complexity of the original problem. In the training phase, BTS has N-1 binary classifiers in the best situation (N is the number of classes), while it has log/sub 4/3/((N+3)/4) binary tests on average when making a decision. At the same time the upper bound of convergence complexity is determined. The experiments in this paper indicate that maintaining comparable accuracy, BTS is much faster to be trained than other methods. Especially in classification, due to its Log complexity, it is much faster than directed acyclic graph SVM (DAGSVM) and ECOC in problems that have big class number.     

Triangulating multiply-connected polygons: A simple, yet efficient algorithm.

We present a new, simple, yet efficient algorithm for triangulating multiply-connected polygons. The algorithm requires sorting only local concave minima (sags). The order in which triangles are created mimics a flooding process of the interior of the polygon. At each stage, the algorithm analyses the positions and neighborhoods of two vertices only, and possibly checks for active sags, so as to determine which of five possible actions to take. Actions are based on a local decomposition of the polygon into monotonic regions, or gorges (raise the water level in the current gorge, spill into an adjacent gorge, jump to the other bank of a filled gorge, divide a gorge into two, and fill a gorge to its top). The implementation is extremely simple and numerically robust for a large class of polygons. It has been tested on millions of cases as a preprocessing step of a walkthrough and inspection program for complex mechanical and architectural scenes. Extensive experimental results indicate that the observed complexity in terms of the number of vertices, remains under in all cases.     

A simple,efficient degree raising algorithm for B-spline curves

This paper presents a new algorithm to compute the degree-raised version of a spline. The new algorithm is as fast as the best existing algorithm, but is much easier to understand and to implement. The new control vertices of the degree-raised spline are obtained simply by a series of knot insertions followed by a series of knot deletions.     

The giving tree: constructing trees for efficient offline and online multi-robot coverage

This paper discusses the problem of building efficient coverage paths for a team of robots. An efficient multi-robot coverage algorithm should result in a coverage path for every robot, such that the union of all paths generates a full coverage of the terrain and the total coverage time is minimized. A method underlying several coverage algorithms, suggests the use of spanning trees as base for creating coverage paths. However, overall performance of the coverage is heavily dependent on the given spanning tree. This paper focuses on the challenge of constructing a coverage spanning tree for both online and offline coverage that minimizes the time to complete coverage. Our general approach involves building a spanning tree by growing sub-trees from the initial location of the robots. This paper first describes a polynomial time tree-construction algorithm for offline coverage. The use of this algorithm is shown by extensive simulations to significantly improve the coverage time of the terrain even when used as a basis for a simple, inefficient, coverage algorithm. Second, this paper provides an algorithm for online coverage of a finite terrain based on spanning-trees, that is complete and guarantees linear time coverage with no redundancy in the coverage. In addition, the solutions proposed by this paper guarantee robustness to failing robots: the offline trees are used as base for robust multi-robot coverage algorithms, and the online algorithm is proven to be robust.     

代数约简的知识粒度表示及其高效算法

首先提出了修正相对粒度计算公式,给出其单调性证明以及等号成立的充要条件;然后证明了保持修正相对粒度不变是保持正区域不变的充要条件,并给出代数约简的知识粒度表示;最后讨论了现有相对粒度与修正相对粒度之间的关系,利用修正相对粒度的单调性给出计算属性重要性定义及其递归计算公式,进而利用基排序思想计算等价类,设计出一种计算决策表代数约简的高效算法.实验结果表明该算法是可行且高效的.     

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

Given a relation ?? ? ?? × ?? on a set ?? of objects and a set ?? of attributes, the AOC-poset (Attribute/Object Concept poset), is the partial order defined on the “introducers” of objects and attributes in the corresponding concept lattice. In this paper, we present Hermes, a simple and efficient algorithm for building an AOC-poset which runs in O(m i n{n m, n ^α }), where n is the number of objects plus the number of attributes, m is the size of the relation, and n ^α is the time required to perform matrix multiplication (currently α = 2.376). Finally, we compare the runtime of Hermes with the runtime of other algorithms computing the AOC-poset: Ares, Ceres and Pluton. We characterize the cases where each algorithm is the more relevant.     

An efficient algorithm for computing moments on a block representation of a grey-scale image

Computing lower order moments is important in image processing. Suppose the input grey image with size N×N has been compressed into the block representation where the number of blocks is K, commonly K<N² due to the compression effect. This correspondence presents an efficient algorithm for computing lower order moments on the block representation directly. Our proposed algorithm takes O(K) time which is proportional to the number of blocks. Experimental results reveal the computational advantage of our proposed algorithm. In addition, the results of this paper can be viewed as a generalization of the previous result by Spiliotis and Mertzios for computing lower order moments from the binary image domain to the grey image domain.     

Resolution correction: A simple and efficient algorithm with error analysis

A new procedure to correct experimental spectra for instrumental resolution is described. A-priori knowledge is not used, in contrast to other deconvolution methods; consequently the range of applications is very wide, while the necessary computations are simple. Use is being made of the Fast Fourier Transform technique, which makes the method suitable to process large amounts of data. Not only the propagation of the random statistical errors but also the contribution from systematic errors, which arise in any method, is estimated. The validity of the method is demonstrated by means of numerical tests taken from different sources in the literature.     

Bonsai: A compact representation of trees

This paper shows how trees can be stored in a very compact form, called ‘Bonsai’, using hash tables. A method is described that is suitable for large trees that grow monotonically within a predefined maximum size limit. Using it, pointers in any tree can be represented within 6 + [log₂n] bits per node where n is the maximum number of children a node can have. We first describe a general way of storing trees in hash tables, and then introduce the idea of compact hashing which underlies the Bonsai structure. These two techniques are combined to give a compact representation of trees, and a practical methodology is set out to permit the design of these structures. The new representation is compared with two conventional tree implementations in terms of the storage required per node. Examples of programs that must store large trees within a strict maximum size include those that operate on trie structures derived from natural language text. We describe how the Bonsai technique has been applied to the trees that arise in text compression and adaptive prediction, and include a discussion of the design parameters that work well in practice.     

SQR: a simple quantum representation of infrared images

A simple quantum representation (SQR) of infrared images is proposed based on the characteristic that infrared images reflect infrared radiation energy of objects. The proposed SQR model is inspired from the Qubit Lattice representation for color images. Instead of the angle parameter of a qubit to store a color as in Qubit Lattice representation, probability of projection measurement is used to store the radiation energy value of each pixel for the first time in this model. Since the relationship between radiation energy values and probability values can be quantified for the limited radiation energy values, it makes the proposed model more clear. In the process of image preparation, only simple quantum gates are used, and the performance comparison with the latest flexible representation of quantum images reveals that SQR can achieve a quadratic speedup in quantum image preparation. Meanwhile, quantum infrared image operations can be performed conveniently based on SQR, including both the global operations and local operations. This paper provides a basic way to express infrared images in quantum computer.     

VideoGraph: a non-linear video representation for efficient exploration

In this paper we introduce VideoGraph, a novel non-linear representation for scene structure of a video. Unlike classical linear sequential organization, VideoGraph concentrates the video content across the time line by structuring scenes and materializes with two-dimensional graph, which enables non-linear exploration on the scenes and their transitions. To construct VideoGraph, we adopt a sub-shot induced method to evaluate the spatio-temporal similarity between shot segments of video. Then, scene structure is derived by grouping similar shots and identifying the valid transitions between scenes. The final stage is to represent the scene structure using a graph with respect to scene transition topology. Our VideoGraph can provide a condensed representation in the scene level and facilitate a non-linear manner to browse videos. Experimental results are presented to demonstrate the effectiveness and efficiency by using VideoGraph to explore and access the video content.     

eXploratory K-Means: A new simple and efficient algorithm for gene clustering

In this paper, a novel gene expression clustering method known as eXploratory K-Means (XK-Means) is proposed. The method is based on the integration of the K-Means framework, and an exploratory mechanism to prevent premature convergence of the clustering process. Experimental results reveal that the performance of XK-Means in grouping gene expressions, measured in terms of speed, error and stability, is superior to existing methods that are based on evolutionary algorithm. In addition, the complexity of the proposed method is lower and the method can be easily implemented in practice.     

Optimal representation of the minimum spanning tree algorithm in associative parallel processors

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–13, July–August, 1995.     

TurboTree: a fast algorithm for minimal trees

A branch and bound algorithm is described for searching rapidly for minimal length trees from biological data. The algorithm adds characters one at a time, rather than adding taxa, as in previous branch and bound methods. The algorithm has been programmed and is available from the authors. A worked example is given with 33 characters and 15 taxa. About 8 x 10(12) binary trees are possible with 15 taxa but the branch and bound program finds the minimal tree in less than 5 min on an IBM PC.     

A simple algorithm for three-dimensional finite element analysis of contact problems

This paper addresses the numerical solution of three-dimensional frictionless contact problems by a finite element method. The two-body contact problem is considered in the context of fully non-linear kinematics. The impenetrability constraint is satisfied via a classical penalty formulation. The contacting surfaces are discretized by means of projections of the interacting element faces onto suitably chosen flat surfaces. Attention is focused on the efficiency of the overall algorithm. Numerical simulations are conducted for a series of test problems to assess the performance of the proposed methodology.     

A simple and efficient algorithm for determining the symmetries of polyhedra

In this paper we present a simple and efficient algorithm for determining the rotational symmetries of polyhedral objects in O(m²) time using O(m) space, where m represents the number of edges of the object. Our algorithm is an extension of Weinberg's algorithm for determining isomorphisms of planar triply connected graphs. The symmetry information detected by our algorithm can be utilized for various purposes in artificial intelligence, robotics, assembly planning and machine vision.     

DBC: a condensed representation of frequent patterns for efficient mining

Given a large set of data, a common data mining problem is to extract the frequent patterns occurring in this set. The idea presented in this paper is to extract a condensed representation of the frequent patterns called disjunction-bordered condensation (DBC), instead of extracting the whole frequent pattern collection. We show that this condensed representation can be used to regenerate all frequent patterns and their exact frequencies. Moreover, this regeneration can be performed without any access to the original data. Practical experiments show that the DBCcan be extracted very efficiently even in difficult cases and that this extraction and the regeneration of the frequent patterns is much more efficient than the direct extraction of the frequent patterns themselves. We compared the DBC with another representation of frequent patterns previously investigated in the literature called frequent closed sets. In nearly all experiments we have run, the DBC have been extracted much more efficiently than frequent closed sets. In the other cases, the extraction times are very close.