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.     

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.     

FPT-algorithms for some problems related to integer programming

This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem, where one of the centers must be in P, and we solve it in \(O(n^2\log n)\) time. Second, we consider the mixed k-center problem, where m of the centers are in P, and we solve it in \(O(n^{m+O(\sqrt{k-m})})\) time. Motivated by two practical constraints, we propose two variations of the problem. Third, we present a 2-approximation algorithm and three heuristics solving the mixed k-center problem (\(k>2\)).     

A characterization of linearizable instances of the quadratic minimum spanning tree problem

We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph \(G=(V,E)\) that can be solved as a linear minimum spanning tree problem. We give a characterization of such problems when G is a complete graph, which is the standard case in the QMSTP literature. We extend our characterization to a larger class of graphs that include complete bipartite graphs and cactuses, among others. Our characterization can be verified in \(O(|E|^2)\) time. In the case of complete graphs and when the cost matrix is given in factored form, we show that our characterization can be verified in O(|E|) time. Related open problems are also indicated.     

On computing a minimum secure dominating set in block graphs

In a graph \(G=(V,E)\), a set \(D \subseteq V\) is said to be a dominating set of G if for every vertex \(u\in V{\setminus }D\), there exists a vertex \(v\in D\) such that \(uv\in E\). A secure dominating set of the graph G is a dominating set D of G such that for every \(u\in V{\setminus }D\), there exists a vertex \(v\in D\) such that \(uv\in E\) and \((D{\setminus }\{v\})\cup \{u\}\) is a dominating set of G. Given a graph G and a positive integer k, the secure domination problem is to decide whether G has a secure dominating set of cardinality at most k. The secure domination problem has been shown to be NP-complete for chordal graphs via split graphs and for bipartite graphs. In Liu et al. (in: Proceedings of 27th workshop on combinatorial mathematics and computation theory, 2010), it is asked to find a polynomial time algorithm for computing a minimum secure dominating set in a block graph. In this paper, we answer this by presenting a linear time algorithm to compute a minimum secure dominating set in block graphs. We then strengthen the known NP-completeness of the secure domination problem by showing that the secure domination problem is NP-complete for undirected path graphs and chordal bipartite graphs.     

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.     

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.