On Integrality, Stability and Composition of Dicycle Packings and Covers

Given a digraph D, the minimum integral dicycle cover problem (known also as the minimum feedback arc set problem) is to find a minimum set of arcs that intersects every dicycle; the maximum integral dicycle packing problem is to find a maximum set of pairwise arc disjoint dicycles. These two problems are NP-complete.Assume D has a 2-vertex cut. We show how to derive a minimum dicycle cover (a maximum dicycle packing) for D, by composing certain covers (packings) of the corresponding pieces. The composition of the covers is simple and was partially considered in the literature before. The main contribution of this paper is to the packing problem. Let be the value of a minimum integral dicycle cover, and * () the value of a maximum (integral) dicycle packing. We show that if = then a simple composition, similar to that of the covers, is valid for the packing problem. We use these compositions to extend an O(n³) (resp., O(n⁴)) algorithm for finding a minimum integral dicycle cover (resp., packing) from planar digraphs to K_3,3-free digraphs (i.e., digraphs not containing any subdivision of K_3,3).However, if , then such a simple composition for the packing problem is not valid. We show, that if the pieces satisfy, what we call, the stability property, then a simple composition does work. We prove that if = * holds for each piece, then the stability property holds as well. Further, we use the stability property to show that if = * holds for each piece, then = * holds for D as well.     

Efficient Heuristics for Orientation Metric and Euclidean Steiner Tree Problems

We consider Steiner minimum trees (SMT) in the plane, where only orientations with angle , 0 i – 1 and an integer, are allowed. The orientations define a metric, called the orientation metric, , in a natural way. In particular, ₂ metric is the rectilinear metric and the Euclidean metric can beregarded as metric. In this paper, we provide a method to find an optimal SMT for 3 or 4 points by analyzing the topology of SMT's in great details. Utilizing these results and based on the idea of loop detection first proposed in Chao and Hsu, IEEE Trans. CAD, vol. 13, no. 3, pp. 303–309, 1994, we further develop an O(n²) time heuristic for the general SMT problem, including the Euclidean metric. Experiments performed on publicly available benchmark data for 12 different metrics, plus the Euclidean metric, demonstrate the efficiency of our algorithms and the quality of our results.     

Local Optimality and Its Application on Independent Sets for k-claw Free Graphs

Given a graph G = (V,E), we define the locally optimal independent sets asfollows. Let S be an independent set and T be a subset of V such that S T = and (S) T, where (S) is defined as the neighbor set of S. A minimum dominating set of S in T is defined as T_D(S) T such that every vertex of S is adjacent to a vertex inTD(S) and TD(S) has minimum cardinality. An independent setI is called r-locally optimal if it is maximal and there exists noindependent set S V\I with |ID (S)| r such that|S| >|I (S)|.In this paper, we demonstrate that for k-claw free graphs ther-locally optimal independent sets is found in polynomial timeand the worst case is bounded by , where I and I* are a locally optimal and an optimal independent set,respectively. This improves the best published bound by Hochbaum (1983) bynearly a factor of two. The bound is proved by LP duality and complementaryslackness. We provide an efficientO(|V|^r+3) algorithm to find an independent set which is notnecessarily r-locally optimal but is guarantteed with the above bound. Wealso present an algorithm to find a r-locally optimal independent set inO(|V|^r(k-1)+3) time.     

On the Tightness of the Alternating-Cycle Lower Bound for Sorting by Reversals

We give a theoretical answer to a natural question arising from a few years of computational experiments on the problem of sorting a permutation by the minimum number of reversals, which has relevant applications in computational molecular biology. The experiments carried out on the problem showed that the so-called alternating-cycle lower bound is equal to the optimal solution value in almost all cases, and this is the main reason why the state-of-the-art algorithms for the problem are quite effective in practice. Since worst-case analysis cannot give an adequate justification for this observation, we focus our attention on estimating the probability that, for a random permutation of n elements, the above lower bound is not tight. We show that this probability is low even for small n, and asymptotically (1/n⁵), i.e., O(1/n⁵) and (1/n⁵). This gives a satisfactory explanation to empirical observations and shows that the problem of sorting by reversals and its alternating-cycle relaxation are essentially the same problem, with the exception of a small fraction of pathological instances, justifying the use of algorithms which are heavily based on this relaxation. From our analysis we obtain convenient sufficient conditions to test if the alternating-cycle lower bound is tight for a given instance. We also consider the case of signed permutations, for which the analysis is much simpler, and show that the probability that the alternating-cycle lower bound is not tight for a random signed permutation of m elements is asymptotically (1/m²).     

Are g.p.a. and ethics related?

This article reports results of a study of some 200 college-aged students at California State University. Ethical values are measured using a subset of the well-known and frequently used Rokeach Value Survey. Using nonparametric statistical analysis, four value measures, and four different consistent tests of significance and probability, the research data, perhaps disappointedly for many observers including the authors, reveal that there is no relationship between college grade point average and student ethics. Statistical analysis was done on g.p.a. splits of less than 3.0 versus 3.0 or more and also on g.p.a. data for 2.5 or less versus 3.5 or more. In all cases, there are no significant relationships between high or low grade point averages and scores on ethical value rankings.     

Codes of conduct in Hong Kong organisations

This paper first reviews the literature on the role of codes of conduct for organisations in Hong Kong in their attempts to manage increasingly complex ethical problems and issues. It shows that, although valuable foundations exist upon which to build, research and understanding of the subject is at it's embryonic stage. Social Psychology literature is examined to investigate what lessons those concerned with the study of ethics may learn and the work of Hofstede, as seminal in the area of work-related values, is emphasised in this context.Following Hofstede's proposals for strategies for operationalizing¹ constructs about human values, a content analysis² was conducted on a pilot sample of codes provided by Hong Kong organisations. The results show three clearly identified clusters of organisations with common formats. The first group, described as Foreign Legal, emphasises legal compliance, has criteria for invoking penalties and consists of foreign-owned, large multinational organisations. Companies in the second cluster have codes which, except in the case of a couple of larger organisations, mainly follow the Independent Commission Against Corruption's (ICAC) standard format. The third cluster, described as the Bank Network, also appear to largely conform to a format: the Hong Kong Banking Association's guidelines.Further analysis conducted here of the Hong Kong codes indicates the important role of emic teleological values³, such as trust and reputation, amongst indigenous organisations, rather than the amorality suggested by an earlier study (Dolecheck and Bethke, 1990). These results support the proposition that Hong Kong ethical perspectives are culture bound⁴, as there appear to be different emphases than revealed in an American study (Stevens, 1994), which identified an emphasis in the US codes upon introverted organisational issues and a failure to espouse deontological values⁵.The conclusion is that designing a research programme on business values in Hong Kong requires reference to studies of values in cross-cultural psychology generally and to Hofstede's work in particular. It also supports the need for indigenous research and models in this field which avoid the ethnocentrism inherent in much Western theory and research.     

Algorithm for the Cost Edge-Coloring of Trees

Let C be a set of colors, and let be a cost function which assigns a real number (c) to each color C in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors. In this paper we give an efficient algorithm to find an optimal edge-coloring of a given tree T, that is, an edge-coloring f of T such that the sum of costs (f(e)) of colors f(e) assigned to all edges e is minimum among all edge-colorings of T. The algorithm takes time O(n²) if n is the number of vertices and is the maximum degree of T.     

Approximation Algorithms for Quadratic Programming

We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m=1, we rigorously show that an -minimizer, where error (0, 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1/). For m 2, we present a polynomial-time (1- )-approximation algorithm as well as a semidefinite programming relaxation for this problem. In addition, we present approximation algorithms for solving QP under the box constraints and the assignment polytope constraints.     

Acccounting and Volksgeist – Teritorial Claims on Accounting Regulation

In this paper, it is argued that international diversityin the rules governing corporate accountability is afunction of the desire to preserve local jurisdictionsby maintaining national distinctiveness. Successiveattempts at regulatory harmonisation in Europe havemet considerable resistance, starting with Savignysappeal to the spirit of the people (Volksgeist)and ending with the notion of subsidiarity. In thispaper, territorial claims on regulation are exploredin the context of the rules governing asset revaluation,where there are still almost as many required methodsof accounting in the European Union as there aremember states. The paper rejects the conventionalexplanation that such differences are culture-bound,and instead suggests that the continued existence ofnational rules in accounting reflects the pursuit ofautonomy by individual states and the self-interestof national regulators.     

On Shortest k-Edge-Connected Steiner Networks in Metric Spaces

Given a set of points P in a metric space, let l(P) denote the ratio of lengths between the shortest k-edge-connected Steiner network and the shortest k-edge-connected spanning network on P, and let r = inf l(P) P for k 1. In this paper, we show that in any metric space, r 3/4 for k 2, and there exists a polynomial-time -approximation for the shortest k-edge-connected Steiner network, where = 2 for even k and = 2 + 4/(3k) for odd k. In the Euclidean plane, and .     

Compression Theorems and Steiner Ratios on Spheres

Suppose AiBiCi (i = 1, 2) are two triangles of equal side lengths lying on spheres i with radii r1, r2 (r1 < r2) respectively. First we prove the existence of a map h: A1B1C1 A2B2C2 so that for any two points P1, Q1 in A1B1C1,¦P1Q1¦¦h(P1)h(Q1)¦. Moreover, if P1, Q1 are not on the same side, then the inequality strictly holds. This compression theorem can be applied to compare the minimum of a variable in triangles on two spheres. Hence, one of the applications of the compression theorem is the study of Steiner minimal tress on spheres. The Steiner ratio is the largest lower bound for the ratio of the lengths of Steiner minimal trees to minimal spanning trees for point sets in a metric space. Using the compression theorem we prove that the Steiner ratio on spheres is the same as on the Euclidean plane, namely .     

Mind Engineering for Value-Based Order

This paper tries to trace the background of the modern business paradigm. A business mind dominating the social mind has been the root cause of unethicality in an order, according to this paper. The solution could come from the liberation of the social mind through a process of mind engineering at the individual level. The paper suggests an active mechanism to inculcate values through a systematic process of mind engineering.     

On Approximate Graph Colouring and MAX-k-CUT Algorithms Based on the θ-Function

The problem of colouring a k-colourable graph is well-known to be NP-complete, for k 3. The MAX-k-CUT approach to approximate k-colouring is to assign k colours to all of the vertices in polynomial time such that the fraction of `defect edges' (with endpoints of the same colour) is provably small. The best known approximation was obtained by Frieze and Jerrum (1997), using a semidefinite programming (SDP) relaxation which is related to the Lovász -function. In a related work, Karger et al. (1998) devised approximation algorithms for colouring k-colourable graphs exactly in polynomial time with as few colours as possible. They also used an SDP relaxation related to the -function.In this paper we further explore semidefinite programming relaxations where graph colouring is viewed as a satisfiability problem, as considered in De Klerk et al. (2000). We first show that the approximation to the chromatic number suggested in De Klerk et al. (2000) is bounded from above by the Lovász -function. The underlying semidefinite programming relaxation in De Klerk et al. (2000) involves a lifting of the approximation space, which in turn suggests a provably good MAX-k-CUT algorithm. We show that of our algorithm is closely related to that of Frieze and Jerrum; thus we can sharpen their approximation guarantees for MAX-k-CUT for small fixed values of k. For example, if k = 3 we can improve their bound from 0.832718 to 0.836008, and for k = 4 from 0.850301 to 0.857487. We also give a new asymptotic analysis of the Frieze-Jerrum rounding scheme, that provides a unifying proof of the main results of both Frieze and Jerrum (1997) and Karger et al. (1998) for k 0.     

Fundamentals of Health Risk Assessment. Use,Derivation, Validity and Limitations of Safety Indices

We investigated the way results of human health risk assessments are used, and the theory used to describe those methods, sometimes called the NAS paradigm. Contrary to a key tenet of that theory, current methods have strictly limited utility. The characterizations now considered standard, Safety Indices such as Acceptable Daily Intake, Reference Dose, and so on, usefully inform only decisions that require a choice between two policy alternatives (e.g., approve a food additive or not), decided solely on the basis of a finding of safety. Risk is characterized as the quotient of one of these Safety Indices divided by an estimate of exposure: a quotient greater than one implies that the situation may be considered safe. Such decisions are very widespread, both in the U. S. federal government and elsewhere. No current method is universal; different policies lead to different practices, for example, in California's Proposition 65, where statutory provisions specify some practices. Further, an important kind of human health risk assessment is not recognized by this theory: this kind characterizes risk as likelihood of harm, given estimates of exposure consequent to various decision choices. Likelihood estimates are necessary whenever decision makers have many possible decision choices and must weigh more than two societal values, such as in EPA's implementation of conventional air pollutants. These estimates can not be derived using current methods; different methods are needed. Our analysis suggests changes needed in both the theory and practice of human health risk assessment, and how what is done is depicted.     

Democratizing Risk Management: Successful Public Involvement in Local Water Management Decisions

This paper discusses a successful public involvement effort that addressed and resolved several highly controversial water management issues involving environmental and flood risks associated with an electrical generation facility in British Columbia. It begins with a discussion of concepts for designing public involvement, summarizing research that indicates why individuals and groups may find it difficult to make complex choices. Reasons for public involvement, and the range of current practices are discussed. Next, four principles for designing group decision process are outlined, emphasizing decision-aiding concepts that include value-focused thinking and adaptive management. The next sections discuss the Alouette River Stakeholder Committee process in terms of objectives, participation, process, methods for structuring values and creating alternatives, information sources, and results. Discussion and conclusions complete the paper.     

Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

Given an undirected multigraph G = (V, E) and two positive integers and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an -edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn²) time for any fixed and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G.     

Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming

Two primal-dual affine scaling algorithms for linear programming are extended to semidefinite programming. The algorithms do not require (nearly) centered starting solutions, and can be initiated with any primal-dual feasible solution. The first algorithm is the Dikin-type affine scaling method of Jansen et al. (1993b) and the second the classical affine scaling method of Monteiro et al. (1990). The extension of the former has a worst-case complexity bound of O(₀nL) iterations, where ₀ is a measure of centrality of the the starting solution, and the latter a bound of O(₀nL²) iterations.     

Approximation and Exact Algorithms for RNA Secondary Structure Prediction and Recognition of Stochastic Context-free Languages

For a basic version (i.e., maximizing the number of base-pairs) of the RNA secondary structure prediction problem and the construction of a parse tree for a stochastic context-free language, O(n³) time algorithms were known. For both problems, this paper shows slightly improved O(n³(log log n)^1/2/(log n)^1/2) time exact algorithms, which are obtained by combining Valiant's algorithm for context-free recognition with fast funny matrix multiplication. Moreover, this paper shows an O(n^2.776 + (1/)^O(1)) time approximation algorithm for the former problem and an O(n^2.976 log n + (1/)^O(1)) time approximation algorithm for the latter problem, each of which has a guaranteed approximation ratio 1 – for any positive constant , where the absolute value of the logarithm of the probability is considered as an objective value in the latter problem. The former algorithm is obtained from a non-trivial modification of the well-known O(n³) time dynamic programming algorithm, and the latter algorithm is obtained by combining Valiant's algorithm with approximate funny matrix multiplication. Several related results are shown too.     

Power Assignment for <Emphasis Type="Italic">k</Emphasis>-Connectivity in Wireless Ad Hoc Networks

The problem Min-Power k-Connectivity seeks a power assignment to the nodes in a given wireless ad hoc network such that the produced network topology is k-connected and the total power is the lowest. In this paper, we present several approximation algorithms for this problem. Specifically, we propose a 3k-approximation algorithm for any k, a (k + 12H (k)) -approximation algorithm for k(2k–1) n where n is the network size, a (k+2(k + 1)/2) -approximation algorithm for 2 k7, a 6-approximation algorithm for k = 3, and a 9-approximation algorithm for k = 4.This work is supported in part by Hong Kong Research Grant Council under grant No. CityU 1149/04E.This work is partially supported by NSF CCR-0311174.     

Business student ethical values anew in the 1990s

This paper uses a Rokeach Value Survey methodology to again ask the question, now in the mid 1990s, whether business student ethics are different from non-business student ethics. Additionally, the paper addresses the question of whether a course can alter or change student ethics and values during a semester. Thirdly, this paper attempts to operationalize and empirically test and measure the new ethical concepts of moral management and moral maximization.