Bounds for the traveling salesman paths of two-dimensional modular lattices

We present tight upper and lower bounds for the traveling salesman path through the points of two-dimensional modular lattices. We use these results to bound the traveling salesman path of two-dimensional Kronecker point sets. Our results rely on earlier work on shortest vectors in lattices as well as on the strong convergence of Jacobi–Perron type algorithms.     

Placement characteristics and stability: a longitudinal analysis of Norwegian children in foster homes

This paper investigates how enhanced support for foster parents, such as covering fees and providing consultants and relief, may reduce the number of replacements experienced by children in foster care. It also investigates the extent to which replacements are associated with family (kin) vs. non‐family foster parents, or with legal characteristics of the placement (i.e. forced administrative decisions vs. relief measures agreed upon by the parents). Statistical analyses of administrative data from Norway investigated the longitudinal relationships between these characteristics and the number of replacements at two levels – children (N = 16 109) and municipalities (N = 418) – over 5 years (2007–2011). The results reveal modest associations between enhanced support and fewer replacements; for example, replacement rates are lower for children placed in homes of kin than in non‐family homes. Replacements also tend to be fewer when the placement is forced rather than consensual.     

Change is an Ongoing Ethical Event: Levinas,Bakhtin and the Dialogical Dynamics of Becoming

In this article, we use the intersubjective ethics of Bakhtin and Levinas and a case illustration to explore change in therapy as an ethical phenomenon. We follow Lakoff and Johnson in their emphasis on the way our conceptions of change seem permeated by metaphors. Bakhtin and Levinas both suggest through a language in which metaphors play a crucial role, that human existence—the consciousness and the subject—emerge within the dialogue of the encounter. They both describe the dynamics of human existence as ethical in their origin. Following this, we argue that change may be seen as an ongoing ethical event and that the dynamics of change are found in the ways we constantly become in this event. We investigate the ethical dynamics of this ongoing event through three themes illuminating the contributions of both Bakhtin and Levinas: (1) we become as responsible, (2) we become in speaking, (3) we become in answering the unknown. We explore these themes through a case illustration. Finally, we briefly point out some possible implications for mental health practice.     

Compact labelings for efficient first-order model-checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is nicely locally clique-width-decomposable. This notion generalizes that of a nicely locally tree-decomposable class. The graphs of such classes can be covered by graphs of bounded clique-width with limited overlaps. We also consider such labelings for bounded first-order formulas on graph classes of bounded expansion. Some of these results are extended to counting queries.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

On the distance paired domination of generalized Petersen graphs <Emphasis Type="Italic">P</Emphasis>(<Emphasis Type="Italic">n</Emphasis>,1) and <Emphasis Type="Italic">P</Emphasis>(<Emphasis Type="Italic">n</Emphasis>,2)

Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a k -distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a k-distance paired dominating set for graph G is the k -distance paired domination number, denoted by γ _p ^k (G). In this paper, we determine the exact k-distance paired domination number of generalized Petersen graphs P(n,1) and P(n,2) for all k≥1.     

Geometric rounding: a dependent randomized rounding scheme

We develop a new dependent randomized rounding method for approximation of a number of optimization problems with integral assignment constraints. The core of the method is a simple, intuitive, and computationally efficient geometric rounding that simultaneously rounds multiple points in a multi-dimensional simplex to its vertices. Using this method we obtain in a systematic way known as well as new results for the hub location, metric labeling, winner determination and consistent labeling problems. A comprehensive comparison to the dependent randomized rounding method developed by Kleinberg and Tardos (J. ACM 49(5):616–639, 2002) and its variants is also conducted. Overall, our geometric rounding provides a simple and effective alternative for rounding various integer optimization problems.     

A special combinatorial problem: pitch arrangement for pneumatic tires

In this paper, we introduce a combinatorial problem faced in the tire industry and then define it and optimize it by tabu search from the perspective of operational research. Such a problem is termed the pitch arrangement problem and involves both selecting and sequencing problems along with noninteger design variables. Pitch arrangement is an essential procedure for tires before their manufacture. Using this procedure, engineers have to choose an optimal groove distribution on tire treads for the purpose of manufacturing low-noise tires. Most research works on pitch arrangement are supported by tire companies, and their results are patented instead of being published. In this study, we define the abovementioned problem clearly and optimize it by tabu search. Two actual manufactured tires are chosen for the case studies. In addition, two patents and two types of pitch sequences optimized by genetic algorithms are also applied to these two tires for comparison. The pitch arrangement is optimized successfully and the performance of tabu search is found to be outstanding.     

The role,power and influence of company chairs

This paper develops an analytical framework to depict the heterogeneity that characterises the role of board chair and demonstrate the potential variability in how chairs operate boards and exercise power and influence on strategy, control and resource related tasks at board level. Theories of power and influence, as applied to top management teams and boards of directors, are explicated within the context of contemporary governance practices that are establishing the role of the board chair as distinct to that of the chief executive officer. Specifically, the paper maps sources of power and varying contemporary chair practices, including chair nomenclature (i.e. executive vs. non-executive chairs), chair origin (insider vs. outsider) and chair time (full-time vs. part-time). A number of theoretical chair-power models emerge from this analysis and are subject to empirical analysis using data collected from 160 chairs of 500 FTSE-listed companies. Theoretically and empirically, the paper complements structural approaches to studying boards with attention to behaviour on boards. By linking board structure, board process and the exercise of influence, the study reveals both differences amongst chairs in how they run the board, but also that chairs’ differ in the influence they exert on board-related tasks. Full-time executive chairs exert their greatest influence in strategy and resource dependence tasks whereas part-time, non-executive chairs seem to exert more influence over monitoring and control tasks.     

Board size and corporate performance: the missing role of board leadership structure

Different arguments have been introduced in the literature both for and against large and small board sizes. In this context, empirical evidence regarding the impact of board size on corporate performance is less conclusive, which means that further study is needed. Contrary to previous work, it is hypothesized in this study that the relationship between board size and corporate performance is more likely to be confounded by board leadership structure. Econometric analysis provided strong evidence for the applicability of this hypothesis and demonstrated that board size positively affects corporate performance in the presence of CEO non-duality (board leadership structure that is split between the roles of the CEO and the roles of the chairman). Furthermore, board size is shown to have a negative influence on corporate performance in the presence of CEO duality (board leadership structure that assigns the roles of both CEO and chairman to the same person). This conclusion is robust to the use of different measures of corporate performance, control variables and econometric models. Thus, these findings cast doubt on most of the existing evidence that posits that either large or small board size is always the best alternative to be followed in all organizations.