The matching extension problem in general graphs is co-NP-complete

A simple connected graph G with 2n vertices is said to be k-extendable for an integer k with \(0<k<n\) if G contains a perfect matching and every matching of cardinality k in G is a subset of some perfect matching. Lakhal and Litzler (Inf Process Lett 65(1):11–16, 1998) discovered a polynomial algorithm that decides whether a bipartite graph is k-extendable. For general graphs, however, it has been an open problem whether there exists a polynomial algorithm. The new result presented in this paper is that the extendability problem is co-NP-complete.     

Reliability evaluation of a multicast over coded packet networks

Network coding is a generalization of conventional routing methods that allows a network node to code information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, theoretical results usually do not consider the stochastic nature in information processing and transmission, especially when the capacity of each arc becomes stochastic due to failure, attacks, or maintenance. Hence, the reliability measurement of network coding becomes an important issue to evaluate the performance of the network under various system settings. In this paper, we present analytical expressions to measure the reliability of multicast communications in coded networks, where network coding is most promising. We define the probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric. To do this, we first introduce an exact mathematical formulation to construct multicast connections over coded packet networks under a limited transmission cost. We then propose an algorithm based on minimal paths to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Our results show that the reliability of multicast routing with network coding improved significantly compared to the case of multicast routing without network coding.     

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.     

On the <Emphasis Type="Italic">m</Emphasis>-clique free interval subgraphs polytope: polyhedral analysis and applications

In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results.     

New lower bounds for the second variable Zagreb index

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randi?, the second Zagreb and the modified Zagreb indices.     

Can Private Donations Help Public Universities Build Bridges Over Troubled Waters?: Practical Lessons for Administrators and Donors

With decreasing appropriations, some public organizations seek donations, often from large donors who may want to generate a return on investment by transforming the institution. As such, an interesting question emerges about institutions’ ability to meet donors’ expectations. Long fundraising histories, combined with a political and decentralized nature, make state universities an interesting venue to study the use of donations to create institutional change. Based on two single-state case studies, this research argues that real and perceived organizational barriers must be overcome. It concludes with implications for both administrator and donors.     

Ausbildung zum Ausbildungssupervisor für Verhaltenstherapie

Psychotherapy requires a high qualification which is gained mainly in practical training. Own treatments of mentally ill patients during training requires close-meshed supervision. This also has to meet the highest standards, which require a systematic training as a training supervisor. This article discusses the various aspects that have to be taken into consideration in behavior therapy. Beyond adherence to therapy manuals, extremely complex interaction processes have to be taken into account that cannot be substantiated by the classical behavior therapy. To this extent, supervision appears as a bridge between science and the art of psychotherapy.     

International coopetition for innovation: Are the benefits worth the challenges?

International coopetition has rarely been studied in relation to innovation. Further exploration of effects of international coopetition, i.e. the pursuit of simultaneous cooperation and competition, on a firm’s innovation performance is especially important as such a relationship is challenging with a high propensity to fail. This observation formed the point of departure for this study, which aims to increase the understanding of the effects of international coopetition on firm innovativeness and how these effects are conditioned on the magnitude of the organizational adjustments a firm introduces. We use an unbalanced panel of 9839 firms that participated in four waves of the Swedish Community Innovation Survey between 2008 and 2014 as our empirical base. We illustrate that firms that cooperate with competitors internationally are more likely to exhibit higher propensity to introduce radical innovations, yet this effect is conditioned upon the magnitude of organizational adjustments. Overall, our study contributes to the understanding of the implications of international coopetition and what a firm needs to benefit from it.     

Coopetition in coworking-spaces: value creation and appropriation tensions in an entrepreneurial space

Coopetition has the potential to improve entrepreneurship and innovation. It will be prevalent in coworking-spaces building a growing field for individual and corporate entrepreneurship. The individuals’ physical closeness in the professional and social space of the coworking-space eases multifaceted transfers of explicit and implicit knowledge, stimulating creation, transfer, overhaul, and implementation of entrepreneurial ideas. While entrepreneurs in these coworking-spaces collaborate on sharing knowledge and resources and on finding creative ideas from which can breed new venture concepts, they simultaneously compete on the appropriation of values. Thus, entrepreneurs in coworking-spaces face coopetitive tensions of creating and appropriating the values. Based  on  interview data and secondary sources, this paper explains four different prototype institutions of coworking-spaces: the corporate coworking-space, the open corporate coworking-space, the consultancy coworking-space, and the independent coworking-space. Study explains different tensions of value creation and appropriation that occur within the coopetition in the different forms of coworking-spaces.     

Growing Wealth Gaps in Education

Prior research on trends in educational inequality has focused chiefly on changing gaps in educational attainment by family income or parental occupation. In contrast, this contribution provides the first assessment of trends in educational attainment by family wealth and suggests that we should be at least as concerned about growing wealth gaps in education. Despite overall growth in educational attainment and some signs of decreasing wealth gaps in high school attainment and college access, I find a large and rapidly increasing wealth gap in college attainment between cohorts born in the 1970s and 1980s, respectively. This growing wealth gap in higher educational attainment co-occurred with a rise in inequality in children’s wealth backgrounds, although the analyses also suggest that the latter does not fully account for the former. Nevertheless, the results reported here raise concerns about the distribution of educational opportunity among today’s children who grow up in a context of particularly extreme wealth inequality.