Probability logic and optimization SAT: The PSAT and CPA models

Both probabilistic satisfiability (PSAT) and the check of coherence of probability assessment (CPA) can be considered as probabilistic counterparts of the classical propositional satisfiability problem (SAT). Actually, CPA turns out to be a particular case of PSAT; in this paper, we compare the computational complexity of these two problems for some classes of instances. First, we point out the relations between these probabilistic problems and two well known optimization counterparts of SAT, namely Max SAT and Min SAT. We then prove that Max SAT with unrestricted weights is NP-hard for the class of graph formulas, where Min SAT can be solved in polynomial time. In light of the aforementioned relations, we conclude that PSAT is NP-complete for ideal formulas, where CPA can be solved in linear time.     

Probability logic and optimization SAT: The PSAT and CPA models

Both probabilistic satisfiability (PSAT) and the check of coherence of probability assessment (CPA) can be considered as probabilistic counterparts of the classical propositional satisfiability problem (SAT). Actually, CPA turns out to be a particular case of PSAT; in this paper, we compare the computational complexity of these two problems for some classes of instances. First, we point out the relations between these probabilistic problems and two well known optimization counterparts of SAT, namely Max SAT and Min SAT. We then prove that Max SAT with unrestricted weights is NP-hard for the class of graph formulas, where Min SAT can be solved in polynomial time. In light of the aforementioned relations, we conclude that PSAT is NP-complete for ideal formulas, where CPA can be solved in linear time.     

随机正则(k,r)-SAT问题的可满足临界

研究k-SAT问题实例中每个变元恰好出现r=2s次,且每个变元对应的正、负文字都出现s次的严格随机正则（k,r）-SAT问题.通过构造一个特殊的独立随机实验,结合一阶矩方法,给出了严格随机正则（k,r）-SAT问题可满足临界值的上界.由于严格正则情形与正则情形的可满足临界值近似相等,因此得到了随机正则（k,r）-SAT问题可满足临界值的新上界.该上界不仅小于当前已有的随机正则（k,r）-SAT问题的可满足临界值上界,而且还小于一般的随机k-SAT问题的可满足临界值.因此,这也从理论上解释了在相变点处的随机正则（k,r）-SAT问题实例通常比在相应相变点处同规模的随机k-SAT问题实例更难满足的原因.最后,数值分析结果验证了所给上界的正确性.     

Protecting data privacy through hard-to-reverse negative databases

A set DB of data elements can be represented in terms of its complement set, known as a negative database. That is, all of the elements not in DB are represented, and DB itself is not explicitly stored. This method of representing data has certain properties that are relevant for privacy enhancing applications. The paper reviews the negative database (NDB) representation scheme for storing a negative image compactly, and proposes using a collection of NDBs to represent a single DB, that is, one NDB is assigned for each record in DB. This method has the advantage of producing negative databases that are hard to reverse in practice, i.e., from which it is hard to obtain DB. This result is obtained by adapting a technique for generating hard-to-solve 3-SAT formulas. Finally we suggest potential avenues of application.     

Probabilistic Default Reasoning with Conditional Constraints

We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of z-, lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as reference-class reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of reference-class reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of z-, lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of z- and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational complexity.     

取定s的严格d-正则随机(3,2s)-SAT问题的可满足临界

3-CNF公式的随机难解实例生成对于揭示3-SAT问题的难解实质和设计满足性测试的有效算法有着重要意义.对于整数k>2和s>0,如果在一个k-CNF公式中每个变量正负出现次数均为s,则称该公式是严格正则（k,2s）-CNF公式.受严格正则（k,2s）-CNF公式的结构特征启发,提出每个变量正负出现次数之差的绝对值均为d的严格d-正则（k,2s）-CNF公式,并使用新提出的SDRRK2S模型生成严格d-正则随机（k,2s）-CNF公式.取定整数5<s<11,模拟实验显示,严格d-正则随机（3,2s）-SAT问题存在SAT-UNSAT相变现象和HARD-EASY相变现象.因此,立足于3-CNF公式的随机难解实例生成,研究了严格d-正则随机（3,2s）-SAT问题在s取定时的可满足临界.通过构造一个特殊随机实验和使用一阶矩方法,得到了严格d-正则随机（3,2s）-SAT问题在s取定时可满足临界值的一个下界.模拟实验结果验证了理论证明所得下界的正确性.     

The Complexity of Read-Once Resolution

We investigate the complexity of deciding whether a propositional formula has a read-once resolution proof. We give a new and general proof of Iwama–Miynano's theorem which states that the problem whether a formula has a read-once resolution proof is NP-complete. Moreover, we show for fixed k2 that the additional restriction that in each resolution step one of the parent clauses is a k-clause preserves the NP-completeness. If we demand that the formulas are minimal unsatisfiable and read-once refutable then the problem remains NP-complete. For the subclasses MU(k) of minimal unsatisfiable formulas we present a pol-time algorithm deciding whether a MU(k)-formula has a read-once resolution proof. Furthermore, we show that the problems whether a formula contains a MU(k)-subformula or a read-once refutable MU(k)-subformula are NP-complete.     

Probabilistic π-Calculus and Event Structures

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.     

The <Emphasis Type="Italic">k</Emphasis>-Track Assignment Problem on Partial Orders

The k-track assignment problem is a scheduling problem in which a collection of jobs, represented by intervals, are to be processed by k machines. Two different jobs can be processed by the same machine only if the corresponding intervals do not overlap. We give a compact formulation of the problem and state some polyhedral results for the associated polytope, working in the more general context where job compatibility stems not necessarily from intervals but rather from an arbitrary strict partial order.This authors research was financially supported by the Portuguese Foundation for Science and Technology (FCT).     

Using B<Superscript>+</Superscript>-trees for processing of line segments in large spatial databases

Points, lines, and regions are the three basic entities for constituting vector-based objects in spatial databases. Many indexing methods (G-tree, K-D-B tree, Quad-tree, PMR-tree, Grid-file, R-tree, and so on) have been widely discussed for handling point or region data. These traditional methods can efficiently organize point or region objects in a space into a hashing or hierarchical directory. They provide efficient access methods to meet the requirement of accurate retrievals. However, two problems are encountered when their techniques are applied to deal with line segments. The first is that representing line segments by means of point or region objects cannot exactly and properly preserve the spatial information about the proximities of line segments. The second problem is derived from the large dead space and overlapping areas in external and internal nodes of the hierarchical directory caused by the use of rectangles to enclose line objects. In this paper, we propose an indexing structure for line segments based on B ⁺ -tree to remedy these two problems. Through the experimental results, we demonstrate that our approach has significant improvement over the storage efficiency. In addition, the retrieval efficiency has also been significantly prompted as compared to the method using R-tree index scheme. These improvements derive mainly from the proposed data processing techniques and the new indexing method.     

A linear-time algorithm for finding a sparsek-connected spanning subgraph of ak-connected graph

We show that anyk-connected graphG = (V, E) has a sparsek-connected spanning subgraphG = (V, E) with ¦E¦ =O(k¦V¦) by presenting anO(¦E¦)-time algorithm to find one such subgraph, where connectivity stands for either edge-connectivity or node-connectivity. By using this algorithm as preprocessing, the time complexities of some graph problems related to connectivity can be improved. For example, the current best time boundO(max{k ²¦V¦^1/2,k¦V¦}¦E¦) to determine whether node-connectivityK(G) of a graphG = (V, E) is larger than a given integerk or not can be reduced toO(max{k ³¦V¦^3/2,k ²¦V¦²}).The first author was partially supported by the Grant-in-Aid for Encouragement of Young Scientists of the Ministry of Education, Science and Culture of Japan and by the subvention to young scientists by the Research Foundation of Electrotechnology of Chubu.     

基于节点1-邻居图相似性的社会网络匿名技术

利用传统的k匿名技术在社会网络中进行隐私保护时会存在聚类准则单一、图中数据信息利用不足等问题.针对该问题,提出了一种利用Kullback-Leibler (KL)散度衡量节点1-邻居图相似性的匿名技术(anonymization techniques for measuring the similarity of node 1-neighbor graph based on Kullback-Leibler divergence, SNKL).根据节点1-邻居图分布的相似性对原始图节点集进行划分,按照划分好的类进行图修改,使修改后的图满足k匿名,完成图的匿名发布.实验结果表明, SNKL方法与HIGA方法相比在聚类系数上的改变量平均降低了17.3%,同时生成的匿名图与原始图重要性节点重合度保持在95%以上.所提方法在有效保证隐私的基础上,可以显著的降低对原始图结构信息的改变.     

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective.     

The effect to diagnostic accuracy of decision tree classifier of fuzzy and k-NN based weighted pre-processing methods to diagnosis of erythemato-squamous diseases

This paper presents a novel method for differential diagnosis of erythemato-squamous disease. The proposed method is based on fuzzy weighted pre-processing, k-NN (nearest neighbor) based weighted pre-processing, and decision tree classifier. The proposed method consists of three parts. In the first part, we have used decision tree classifier to diagnosis erythemato-squamous disease. In the second part, first of all, fuzzy weighted pre-processing, which can improved by ours, is a new method and applied to inputs erythemato-squamous disease dataset. Then, the obtained weighted inputs were classified using decision tree classifier. In the third part, k-NN based weighted pre-processing, which can improved by ours, is a new method and applied to inputs erythemato-squamous disease dataset. Then, the obtained weighted inputs were classified via decision tree classifier. The employed decision tree classifier, fuzzy weighted pre-processing decision tree classifier, and k-NN based weighted pre-processing decision tree classifier have reached to 86.18, 97.57, and 99.00% classification accuracies using 20-fold cross validation, respectively.     

Strongly Hamiltonian laceability of the even k-ary n-cube

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks can be viewed as the subclasses of the k-ary n-cubes include the cycle, the torus and the hypercube. A bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path joining every two vertices which are in distinct partite sets. A bipartite graph G is strongly Hamiltonian laceable if it is Hamiltonian laceable and there exists a path of length N − 2 joining each pair of vertices in the same partite set, where N = |V(G)|. We prove that the k-ary n-cube is strongly Hamiltonian laceable for k is even and n  2.     

On Complexity of Computation of Partial Derivatives of Boolean Functions Realized by Zhegalkin Polynomials

The combinational complexity of a system of partial derivatives in the basis of linear functions is established for a Boolean function of n variables that is realized by a Zhegalkin polynomial. An algorithm whose complexity equals 3ⁿ – 2ⁿ modulo 2 additions is proposed for computation of all partial derivatives of such a function from the coefficients of its Zhegalkin polynomial.     

Improving the space cost of <Emphasis Type="Italic">k</Emphasis>-NN search in metric spaces by using distance estimators

Similarity searching in metric spaces has a vast number of applications in several fields like multimedia databases, text retrieval, computational biology, and pattern recognition. In this context, one of the most important similarity queries is the k nearest neighbor (k-NN) search. The standard best-first k-NN algorithm uses a lower bound on the distance to prune objects during the search. Although optimal in several aspects, the disadvantage of this method is that its space requirements for the priority queue that stores unprocessed clusters can be linear in the database size. Most of the optimizations used in spatial access methods (for example, pruning using MinMaxDist) cannot be applied in metric spaces, due to the lack of geometric properties. We propose a new k-NN algorithm that uses distance estimators, aiming to reduce the storage requirements of the search algorithm. The method stays optimal, yet it can significantly prune the priority queue without altering the output of the query. Experimental results with synthetic and real datasets confirm the reduction in storage space of our proposed algorithm, showing savings of up to 80% of the original space requirement.

Choice of approximator and design of penalty function for an approximate dynamic programming based control approach

This paper investigates the choice of function approximator for an approximate dynamic programming (ADP) based control strategy. The ADP strategy allows the user to derive an improved control policy given a simulation model and some starting control policy (or alternatively, closed-loop identification data), while circumventing the ‘curse-of-dimensionality’ of the traditional dynamic programming approach. In ADP, one fits a function approximator to state vs. ‘cost-to-go’ data and solves the Bellman equation with the approximator in an iterative manner. A proper choice and design of function approximator is critical for convergence of the iteration and the quality of final learned control policy, because an approximation error can grow quickly in the loop of optimization and function approximation. Typical classes of approximators used in related approaches are parameterized global approximators (e.g. artificial neural networks) and nonparametric local averagers (e.g. k-nearest neighbor). In this paper, we assert on the basis of some case studies and a theoretical result that a certain type of local averagers should be preferred over global approximators as the former ensures monotonic convergence of the iteration. However, a converged cost-to-go function does not necessarily lead to a stable control policy on-line due to the problem of over-extrapolation. To cope with this difficulty, we propose that a penalty term be included in the objective function in each minimization to discourage the optimizer from finding a solution in the regions of state space where the local data density is inadequately low. A nonparametric density estimator, which can be naturally combined with a local averager, is employed for this purpose.     

An Analytic Study of Two Probabilistic Models for Establishing Ad Hoc WLANs

Two contention-based algorithms are proposed in this paper for establishing ad hoc Wireless Local Area Networks (WLANs). They are named uniform and geometric, respectively, based on the nature of the probabilistic model in the decision making process used in each algorithm. The main performance consideration in this paper is the network setup time each algorithm requires. It is shown that the network setup time is an explicit function of the total solicitation rounds required. The paper is, therefore, focused on deriving the distribution of the total solicitation rounds needed for setting up a network. It is shown analytically that the performance of uniform is better than that of geometric. It also derives the asymptotic lower and upper bounds for the average setup times for uniform.     

基于KD树的信息发布隐私保护

随着医疗信息共享服务的发展,越来越多的患者病历信息被发布出来,敌手通过患者属性推断患者的隐私信息,从而造成患者隐私泄露.基于上述需求,提出基于KD树的隐私保护数据发布算法.利用KD树的性质,对每一维所在属性的泛化值进行分解,直到所有属性的泛化值不能分解,以确保每个叶子节点的所有属性的泛化值的区域达到最小,以减少信息损失.在对等价元组属性分解期间,对每个节点敏感属性值个数做l多样性约束,以降低隐私泄漏风险.实验结果表明,方案可以减少隐私泄露风险和信息损失.