求解最大割问题的交叉熵算法

交叉熵方法（Cross Entropy）是近几年发展而来的一种启发式方法,在求解组合优化问题中显示出其简单有效的特点,将运用交叉熵方法（CE）寻求图论中一个典型的NP困难问题—最大割问题的最优解。为了解决最大割问题,CE方法借助Bernoulli分布的思想,将一个确定性的网络转换成一个具有一定随机性的关联网络,接下来首先按照一个多维的Bernoulli概率分布生成样本,同时计算出随机割;其次,基于前一步的数据,更新Bernoulli概率分布P参数,使得分布参数逐步逼近最优值产生最大割的稳定估计值。数值实验表明,CE方法具有很好的稳定性和收敛性,最终也获得了比较好的近似解。     

Numerical method of estimating the maximal likelihood of a smooth parametric manifold

Consideration was given to the numerical estimation of the maximum likelihood for the parameter vector describing a smooth manifold. Estimation is based on the results of observing motion of a dynamic plant whose trajectory belongs to this manifold and is measured with random errors having normal distribution with certain parameters. Application of the maximum likelihood method to such problems gives rise to the problem of nonlinear highdimensionality programming. Some constructive analytical results obtained enable significant reduction in the problem dimensionality. The problem of identifying the plane of motion of a dynamic plant was examined.     

Efficiently extracting and classifying objects for analyzing color documents

Conventional objects extraction method are not efficient for color document image with large graphics. For example, the projection profile and connected component based methods scanning the large graphics many times. To display the large graphics are extracted, conventional methods use rectangle to represent it. Thus, scanning into the large graphics is time-consuming. In this paper, a novel system for efficiently analyzing color documents is proposed to solve above mentioned problem. The proposed system includes color transformation, background color determination, objects extraction by top-down method, and objects classification without parameters. The proposed color document analysis system is efficient because it scans only background pixels such that the temporal complexity is O (NB), where NB is the total number of background color pixels. Results of this study demonstrate that this system is more effective and efficient than other methods. Moreover, the proposed algorithm can be run in an embedded environment (such as a mobile device) and processed in real-time system due to its simplicity and efficiency.     

A scalable,parallel algorithm for maximal clique enumeration

The problem of maximal clique enumeration (MCE) is to enumerate all of the maximal cliques in a graph. Once enumerated, maximal cliques are widely used to solve problems in areas such as 3-D protein structure alignment, genome mapping, gene expression analysis, and detection of social hierarchies. Even the most efficient serial MCE algorithms require large amounts of time to enumerate the maximal cliques in networks arising from these problems that contain hundreds, thousands, or larger numbers of vertices. The previous attempts to provide practical solutions to the MCE problem through parallel implementation have had limited success, largely due to a number of challenges inherent to the nature of the MCE combinatorial search space. On the one hand, MCE algorithms often create a backtracking search tree that has a highly irregular and hard-or-impossible to predict structure; therefore, almost any static decomposition of the search tree by parallel processors results in highly unbalanced processor execution times. On the other hand, the data-intensive nature of the MCE problem often makes naive dynamic load distribution strategies that require extensive data movement prohibitively expensive. As a result, good scaling of the overall execution time of parallel MCE algorithms has been reported for only up to a couple hundred processors. In this paper, we propose a parallel, scalable, and memory-efficient MCE algorithm for distributed and/or shared memory high performance computing architectures, whose runtime scales linearly for thousands of processors on real-world application graphs with hundreds and thousands of nodes. Its scalability and efficiency are attributed to the proposed: (a) representation of the search tree decomposition to enable parallelization; (b) parallel depth-first backtracking search to both constrain the search space and minimize memory requirement; (c) least stringent synchronization to minimize data movement; and (d) on-demand work stealing intelligently coupled with work stack splitting to minimize computing elements’ idle time. To the best of our knowledge, the proposed parallel MCE algorithm is the first to achieve a linear scaling runtime using up to 2048 processors on Cray XT machines for a number of real-world biological networks.     

Separating mixtures of probability distributions with the grid method of moments and the grid maximal likelihood method

We consider the so-called grid methods for approximate statistical separation of probability distribution mixtures based on (i) minimizing the disparity between theoretical and empirical moments and (ii) maximizing the grid likelihood function. We show that problems of type (i) can be reduced to linear programming problems. For a numerical solution of problems of type (ii) we offer the “truncated” EM algorithm and the conditional gradient algorithm. We show results of a comparative study of the suggested approaches’ efficiency based on solving the decomposition problem for the volatility function of financial indices. We give examples of volatility decompositions for the CAC 40 index.     

Theoretical underpinnings for maximal clique enumeration on perturbed graphs

The problem of enumerating the maximal cliques of a graph is a computationally expensive problem with applications in a number of different domains. Sometimes the benefit of knowing the maximal clique enumeration (MCE) of a single graph is worth investing the initial computation time. However, when graphs are abstractions of noisy or uncertain data, the MCE of several closely related graphs may need to be found, and the computational cost of doing so becomes prohibitively expensive.Here, we present a method by which the cost of enumerating the set of maximal cliques for related graphs can be reduced. By using the MCE for some baseline graph, the MCE for a modified, or perturbed, graph may be obtained by enumerating only the maximal cliques that are created or destroyed by the perturbation. When the baseline and perturbed graphs are relatively similar, the difference set between the two MCEs can be overshadowed by the maximal cliques common to both. Thus, by enumerating only the difference set between the baseline and perturbed graphs’ MCEs, the computational cost of enumerating the maximal cliques of the perturbed graph can be reduced.We present necessary and sufficient conditions for enumerating difference sets when the perturbed graph is formed by several different types of perturbations. We also present results of an algorithm based on these conditions that demonstrate a speedup over traditional calculations of the MCE of perturbed, real biological networks.     

Computing stable poses of piecewise smooth objects

When a three dimensional object is known to be lying on a planar surface, its pose is restricted from six to three degrees of freedom. Computer vision algorithms can exploit the few stable poses of modeled objects to simplify scene interpretation and more accurately determine object location. This paper presents necessary and sufficient conditions for the pose of a piecewise smooth curved three-dimensional object to be stable. For objects whose surfaces are represented by implicit algebraic equations, these conditions can be expressed as systems of polynomial equations that are readily solved by homotopy continuation. Examples from the implemented algorithm are presented.     

Efficient enumeration of words in regular languages

The cross-section enumeration problem is to list all words of length n$n$ in a regular language L$L$ in lexicographical order. The enumeration problem is to list the first m$m$ words in L$L$ according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n+t$n+t$, where t$t$ is the output size. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorithms for both enumeration problems. We discuss some shortcomings of the enumeration algorithm found in the Grail computation package. In the practical domain, we modify Mäkinen’s enumeration algorithm to get an algorithm that is usually the most efficient in practice. We performed an extensive performance analysis of the new and previously known enumeration and cross-section enumeration algorithms and found when each algorithm is preferable.     

The method of forced enumeration for nondeterministic automata

Summary Every family of languages, recognized by nondeterministic L(n) tape-bounded Turing machines, where L(n)logn, is closed under complement. As a special case, the family of context-sensitive languages is closed under complement. This solves the open problem from [4].This research was supported by the grant SP2V I-1-5/08     

Reconstruction of piecewise planar objects from point clouds

This article discusses the reverse engineering problem of reconstructing objects with planar faces. We will present the main geometric features of a modeling system which are the detection of planar faces and the generation of a cad model. The algorithms are applied to the problem of reconstruction of buildings from airborne laser scanner data.     

The satisfiability problem in regular CNF-formulas

 In this paper we deal with the propositional satisfiability (SAT) problem for a kind of multiple-valued clausal forms known as regular CNF-formulas and extend some known results from classical logic to this kind of formulas. We present a Davis–Putnam-style satisfiability checking procedure for regular CNF-formulas equipped with suitable data structures and prove its completeness. Then, we describe a series of experiments for regular random 3-SAT instances. We observe that, for the regular 3-SAT problem with this procedure, there exists a threshold of the ratio of clauses to variables such that (i) the most computationally difficult instances tend to be found near the threshold, (ii) there is a sharp transition from satisfiable to unsatisfiable instances at the threshold and (iii) the value of the threshold increases as the number of truth values considered increases. Instances in the hard part provide benchmarks for the evaluation of regular satisfiability solvers.     

The method of dominants in the problem of ranking interval objects specified by three points

A method for ranking interval objects (ordering them by preference) is proposed and analyzed; these objects are nonreusable, and the results of their use are represented by pessimistic, optimistic, and most probable estimates. The method is based on the approximation of the binary probability preference relation by a binary preference relation with respect to a specially designed characteristic-dominant based on the three estimates indicated above. The method is verified using statistical modeling (the Monte Carlo method). It is shown that the proposed method ensures sufficiently high approximation accuracy in most cases.     

The complexity of restricted regular expressions and the synthesis problem for finite automata

It is known that for every restricted regular expression of length n there exists a nondeterministic finite automaton with n + 1 states giving rise to the upper bound of 2ⁿ + 1 on the number of states of the corresponding reduced automaton. In this note we show that this bound can be attained for all n ? 2, i.e., the upper bound 2ⁿ + 1 is optimal. An observation is then made about the synthesis problem for nondeterministic finite automata.     

A solution of the syntactical induction-inference problem for regular languages

A Teacher knows a regular language L(G), in the form of a finite state acceptor. A method is described for selecting a set of examples, strings X, each in L(G) as inputs to the Pupil. The Set X is mapped into a lattice W (in Pupil) of finite state machines. A mapping is defined from pairs of machines in the lattice W into strings y, each of which serves as a ”crucial experiment”. The Teacher is asked to decide if the string y belongs to L(G). The process then repeats or terminates.This procedure is shown to converge (if Teacher answers truthfully) to a finite state acceptor accepting only strings of L(G)(which obviously may be brought into canonical, minimal state form). However, this process does not depend on state minimization as an inference method.The only necessary condition for the inference process is that every move (edge) of that finite state acceptor U(X) chosen to correspond to L(G) must be applied at least once in generating some string x in X. A proof is given that if the Teacher answers correctly, the Pupil will infer a machine behaviorally equivalent to the original acceptor U.Elements of the lattice W are constructed by successive refinement of the partitions of the state set of the initial finite state machine U(X). Pairs are chosen in an ordered process and converted to deterministic and completely specified machines, if necessary. The two machines are tested for behavioral equivalence. If they are equivalent, one is eliminated. If not, a testing string y belonging to one machine, but not the other, is constructed and output to the teacher. If y belongs to L(G), one machine is eliminated. If not, y is tested by the Pupil against a sequence of machines generated internally. If only one machine is left, the process terminates, otherwise two new candidate machines are chosen. The algorithm described is relatively simple and easy to understand, but does not necessarily produce a minimal time solution.     

On the consistency of line-drawings, obtained by projections of piecewise planar objects

This paper deals with line-drawings, obtained from images of piecewise planar objects after edge detection. Such images are used, e.g., for navigation and recognition. In order to be a possible image of a three dimensional piecewise planar object, it has to obey some projective conditions. Criteria for a line-drawing to be correct is given in this paper, along with methods to find possible interpretations. In real life situations, due to digitization errors and noise, a line-drawing in general does not obey the geometric conditions imposed by the projective imaging process. Under various optimality conditions, algorithms are presented for the correction of such distorted line-drawings.This work has been done within the ESPRIT-BRA project VIVA.