Measuring and repairing inconsistency in probabilistic knowledge bases

In this paper we present a family of measures aimed at determining the amount of inconsistency in probabilistic knowledge bases. Our approach to measuring inconsistency is graded in the sense that we consider minimal adjustments in the degrees of certainty (i.e., probabilities in this paper) of the statements necessary to make the knowledge base consistent. The computation of the family of measures we present here, in as much as it yields an adjustment in the probability of each statement that restores consistency, provides the modeler with possible repairs of the knowledge base. The case example that motivates our work and on which we test our approach is the knowledge base of CADIAG-2, a well-known medical expert system.     

Bandwidth of bipartite permutation graphs in polynomial time

We give the first polynomial-time algorithm that computes the bandwidth of bipartite permutation graphs. Bandwidth is an NP-complete graph layout problem that is notorious for its difficulty even on small graph classes. For example, it remains NP-complete on caterpillars of hair length at most 3, a very restricted subclass of trees. Much attention has been given to designing approximation algorithms for computing the bandwidth, as it is NP-hard to approximate the bandwidth of general graphs with a constant factor guarantee. The problem is considered important even for approximation on restricted classes, with several distinguished results in this direction. Prior to our work, polynomial-time algorithms for exact computation of bandwidth were known only for caterpillars of hair length at most 2, chain graphs, cographs, and most interestingly, interval graphs.     

可满足性（SAT）问题的概率研究

本文首先构造了随机均匀产生的d-SAT问题的概率模型,然后给出了SAT问题的解的个数的均值的计算公式,使用矩方法研究了解空间的元素满足方程的概率以及在临界点方程有解的概率和极限性质,最后确定n/m=Td=ln(2)/(ln2^d/2^d-1)是其解的平均个数的临界点,并且当n/m=rd时,方程有解的概率随着m→∞而趋于0。     

The firefighter problem for graphs of maximum degree three

We show that the firefighter problem is NP-complete for trees of maximum degree three, but in P for graphs of maximum degree three if the fire breaks out at a vertex of degree at most two.     

The computational complexity of the elimination problem in generalized sports competitions

Consider a sports competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The computational complexity of this question depends on the way scores are allocated according to the outcome of a match. For competitions with at most 3 different outcomes of a match the complexity is already known. In practice there are many competitions in which more than 3 outcomes are possible. We determine the complexity of the above problem for competitions with an arbitrary number of different outcomes. Our model also includes competitions that are asymmetric in the sense that away playing teams possibly receive other scores than home playing teams.     

Solving the split equality problem without prior knowledge of operator norms

The split equality problem has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Moudafi proposed an alternating CQ algorithm and its relaxed variant to solve it. However, to employ Moudafi’s algorithms, one needs to know a priori norm (or at least an estimate of the norm) of the bounded linear operators (matrices in the finite-dimensional framework). To estimate the norm of an operator is very difficult, but not an impossible task. It is the purpose of this paper to introduce a projection algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any priori information about the operator norms. We also practise this way of selecting stepsizes for variants of the projection algorithm, including a relaxed projection algorithm where the two closed convex sets are both level sets of convex functions, and a viscosity algorithm. Both weak and strong convergence are investigated.     

On the on-line rent-or-buy problem in probabilistic environments

Fujiwara and Iwama [In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)] first integrated probability distribution into the classical competitive analysis to study the rental problem. They assumed that the future inputs are drawn from an exponential distribution, and obtained the optimal competitive strategy and the competitive ratio by the derivative method. In this paper, we introduce the interest rate and tax rate into the continuous model of Fujiwra and Iwama [In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)]. Moreover, we use the forward difference method in different probabilistic environments to consider discrete leasing models both with and without the interest rate. We not only give the optimal competitive strategies and their competitive ratios in theory, but also give numerical results. We find that with the introduction of the interest rate and tax rate, the uncertainty involved in the process of decision making will diminish and the optimal purchasing date will be put off.     

一类多维0-1背包问题的约束归并方法

提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。     

On the complexity of computing treelength

We resolve the computational complexity of determining the treelength of a graph, thereby solving an open problem of Dourisboure and Gavoille, who introduced this parameter, and asked to determine the complexity of recognizing graphs of a bounded treelength Dourisboure and Gavoille (2007) [6]. While recognizing graphs with treelength 1 is easily seen as equivalent to recognizing chordal graphs, which can be done in linear time, the computational complexity of recognizing graphs with treelength 2 was unknown until this result. We show that the problem of determining whether a given graph has a treelength at most k is NP-complete for every fixed k≥2, and use this result to show that treelength in weighted graphs is hard to approximate within a factor smaller than . Additionally, we show that treelength can be computed in time O^∗(1.7549ⁿ) by giving an exact exponential time algorithm for the Chordal Sandwich problem and showing how this algorithm can be used to compute the treelength of a graph.     

A practical map labeling algorithm

The map labeling problem is a classical problem of cartography. There is a theoretically optimal approximation algorithm A. Unfortunately A is useless in practice as it typically produces results that are intolerably far off the optimal size. On the other hand there are heuristics with good practical results.

In this paper we present an algorithm B that (1) guarantees the optimal approximation quality and runtime behaviour of A, and (2) yields results significantly closer to the optimum than the best heuristic known so far.

The sample data used in the experimental evaluation consists of three different classes of random problems and a selection of problems arising in the production of groundwater quality maps by the authorities of the City of Munich.     

Boole''s conditions of possible experience and reasoning under uncertainty

Consider a set of logical sentences together with probabilities that they are true. These probabilities must satisfy certain conditions for this system to be consistent. It is shown that an analytical form of these conditions can be obtained by enumerating the extreme rays of a polyhedron. We also consider the cases when (i) intervals of probabilities are given, instead of single values; and (ii) best lower and upper bounds on the probability of an additional logical sentence to be true are sought. Enumeration of vertices and extreme rays is used. Each vertex defines a finear expression and the maximum (minimum) of these defines a best possible lower (upper) bound on the probability of the additional logical sentence to be true. Each extreme ray leads to a constraint on the probabilities assigned to the initial set of logical sentences. Redundancy in these expressions is studied. Illustrations are provided in the domain of reasoning under uncertainty.     

强部分逆网络流问题

Abstract. In this paper,a new model for inverse network flow problems,robust partial inverseproblem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution becomeoptimal under new coefficients. It has been shown that the robust partial inverse spanning treeproblem can be formulated as a combinatorial linear program,while the robust partial inverseminimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.     

3-正则图的分割问题是NP-完全问题

证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.     

A new kind of graph coloring

A proper k-coloring C¹,C²,…,C^k of a graph G is called strong if, for every vertex uV(G), there exists an index i{1,2,…,k} such that u is adjacent to every vertex of Cⁱ. We consider classes of strongly k-colorable graphs and show that the recognition problem of is NP-complete for every k4, but it is polynomial-time solvable for k=3. We give a characterization of in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring.     

关于3－正则子图问题的一个注记

这篇注记证明判断一个图是否有３－正则子图的问题，即使对于节点次不超过４的平面图，仍然是ＮＰ－完全的。而且，此结果是最好的可能。     

Pendants-median支撑树及其一个相关问题:复杂性和算法

The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3).     

基于部分基变量的LP问题矩阵算法

基于部分基变量提出了LP问题的矩阵算法. 该算法以最优基矩阵的一个充分必要条件为基础,首先将一个初始矩阵转化为右端项和检验数均满足要求的矩阵,再转为检验数满足要求的基矩阵,最后转化为最优基矩阵.该算法具有使用范围广、计算规模小、计算过程简化、计算机易于实现的优势.矩阵算法的核心运算是求逆矩阵的运算,提出了矩阵算法的求逆问题,讨论并给出了求逆快速算法,该算法充分利用了矩阵算法迭代过程中提供的原来的逆矩阵的信息经过简单的变换得到新的逆矩阵,该算法比直接求逆法计算效率更高.