Praxisbegleitung – ein Konzept für die Führungskräfteentwicklung

Colleagues’ monitoring – a concept for executive development. The article presents the concept of Colleagues’ monitoring that combines the following formats: coaching, organisational and professional development. The program which is structured in a compact and modular way, has been for years successfully applied by the management consultancy relations. Methodically the following three elements are essential: to work on concrete personal management topics, the structured consultation with colleagues and to become acquainted with the concepts of organisational development, management and consultancy. The program is an on-going learning-process in a fixed group for six meetings during one year on a regular basis.     

Braucht Coaching eine philosophisch begründete Ethik?

Does coaching need a philosphically substantiated ethics? On the foundation of a systemic value oriented imperative for coachingThe general claim that coaches have to take responsibility for their clients is in contrast to the low interest in scientific discussion about ethics in coaching. One of the reasons for that seems to be the fact that this discussion is dominated by systemic thinking and its conviction that ethical aspects should be discussed as matter of contingency. From a philosophical point of view we can realize that this statement contains many ethical implications. Concerning a further development of coaching theory the author discusses these implications with regard to philosophical concepts of Kant, Habermas, Prange, Heidegger, Bauman and the Dalai Lama leading to the suggestion that systemic thinking should be more based on value orientation. On this theoretical grounds an ethical coaching imperative can be formulated with regard to the “categorical imperative” of Kant.     

Die „4-Level-Evaluation“: Messen der Ergebnis- und Prozessqualität im Coaching

“4-Level-Evaluation”: Measuring coaching success. Introducing a general and valid evaluation methodology, the “4-level-evaluation”, which will secure measuring coaching success and coaching process –without any limitation in terms of special tools or methods – and which every client will understand and appreciate. How to create a realistic evaluation bottom line, how to manage expectations to avoid perhaps disappointments, how to define possible coaching goals and how to eventually evaluate grades of achievement are explained and applied to a practical coaching case.     

Die Bedeutung von Familienkonstellationen im Coaching

Family Constellation Theory. The approach and its use in coaching The author shows the approach of Walter Toman, psychoanalyst and scientist of psychology, in the most important aspects and in its use in coaching. As a psychoanalytic theory of socialization it is used for the analysis of biographic dates. In opposit to traditional approaches of psychoanalysts Toman emphasizes relationships between siblings in a sense of ranking and gender.     

Approximating <Emphasis Type="Italic">k</Emphasis>-generalized connectivity via collapsing HSTs

An instance of the k -generalized connectivity problem consists of an undirected graph G=(V,E), whose edges are associated with non-negative costs, and a collection \({\mathcal{D}}=\{(S_{1},T_{1}),\ldots,(S_{d},T_{d})\}\) of distinct demands, each of which comprises a pair of disjoint vertex sets. We say that a subgraph ??G connects a demand (S _i ,T _i ) when it contains a path with one endpoint in S _i and the other in T _i . Given an integer parameter k, the goal is to identify a minimum cost subgraph that connects at least k demands in \({\mathcal{D}}\).Alon, Awerbuch, Azar, Buchbinder and Naor (SODA ’04) seem to have been the first to consider the generalized connectivity paradigm as a unified machinery for incorporating multiple-choice decisions into network formation settings. Their main contribution in this context was to devise a multiplicative-update online algorithm for computing log-competitive fractional solutions, and to propose provably-good rounding procedures for important special cases. Nevertheless, approximating the generalized connectivity problem in its unconfined form, where one makes no structural assumptions about the underlying graph and collection of demands, has remained an open question up until a recent O(log?² nlog?² d) approximation due to Chekuri, Even, Gupta and Segev (SODA ’08). Unfortunately, the latter result does not extend to connecting a pre-specified number of demands. Furthermore, even the simpler case of singleton demands has been established as a challenging computational task, when Hajiaghayi and Jain (SODA ’06) related its inapproximability to that of dense k -subgraph.In this paper, we present the first non-trivial approximation algorithm for k-generalized connectivity, which is derived by synthesizing several techniques originating in probabilistic embeddings of finite metrics, network design, and randomization. Specifically, our algorithm constructs, with constant probability, a feasible subgraph whose cost is within a factor of O(n ^2/3?polylog(n,k)) of optimal. We believe that the fundamental approach illustrated in the current writing is of independent interest, and may be applicable in other settings as well.     

Cha n nel assig nme n t problem a nd n-fold t-separa ted $$L(j_1,j_2,\ldo ts,j_m)$$-labeli ng of graphs

This paper considers the channel assignment problem in mobile communications systems. Suppose there are many base stations in an area, each of which demands a number of channels to transmit signals. The channels assigned to the same base station must be separated in some extension, and two channels assigned to two different stations that are within a distance must be separated in some other extension according to the distance between the two stations. The aim is to assign channels to stations so that the interference is controlled within an acceptable level and the spectrum of channels used is minimized. This channel assignment problem can be modeled as the multiple t-separated \(L(j_1,j_2,\ldots ,j_m)\)-labeling of the interference graph. In this paper, we consider the case when all base stations demand the same number of channels. This case is referred as n-fold t-separated \(L(j_1,j_2,\ldots ,j_m)\)-labeling of a graph. This paper first investigates the basic properties of n-fold t-separated \(L(j_1,j_2,\ldots ,j_m)\)-labelings of graphs. And then it focuses on the special case when \(m=1\). The optimal n-fold t-separated L(j)-labelings of all complete graphs and almost all cycles are constructed. As a consequence, the optimal n-fold t-separated \(L(j_1,j_2,\ldots ,j_m)\)-labelings of the triangular lattice and the square lattice are obtained for the case \(j_1=j_2=\cdots =j_m\). This provides an optimal solution to the corresponding channel assignment problems with interference graphs being the triangular lattice and the square lattice, in which each base station demands a set of n channels that are t-separated and channels from two different stations at distance at most m must be \(j_1\)-separated. We also study a variation of n-fold t-separated \(L(j_1,j_2,\ldots ,j_m)\)-labeling, namely, n-fold t-separated consecutive \(L(j_1,j_2,\ldots ,j_m)\)-labeling. And present the optimal n-fold t-separated consecutive L(j)-labelings of all complete graphs and cycles.     

Resource-sharing systems and hypergraph colorings

A resource-sharing system is modeled by a hypergraph H in which a vertex represents a process and an edge represents a resource consisting of all vertices (processes) that have access to it. A schedule of H=(V,E) is a mapping f:?→2 ^V , where f(i) is an independent set of H which consists of processes that operate at round i. The rate of f is defined as \({\rm rate}(f)=\limsup_{n\to\infty}\sum_{i=1}^{n}|f(i)|/(n|V|)\), which is the average fraction of operating processes at each round. The purpose of this paper is to study optimal rates for various classes of schedules under different fairness conditions. In particular, we give relations between these optimal rates and fractional/circular chromatic numbers. For the special case of the hypergraph is a connected graph, a new derivation for the previous result by Yeh and Zhu is also given.     

Some extremal results on the colorful monochromatic vertex-connectivity of a graph

A path in a vertex-colored graph is called a vertex-monochromatic path if its internal vertices have the same color. A vertex-coloring of a graph is a monochromatic vertex-connection coloring (MVC-coloring for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph G, the monochromatic vertex-connection number, denoted by mvc(G), is defined to be the maximum number of colors used in an MVC-coloring of G. These concepts of vertex-version are natural generalizations of the colorful monochromatic connectivity of edge-version, introduced by Caro and Yuster (Discrete Math 311:1786–1792, 2011). In this paper, we mainly investigate the Erd?s–Gallai-type problems for the monochromatic vertex-connection number mvc(G) and completely determine the exact value. Moreover, the Nordhaus–Gaddum-type inequality for mvc(G) is also given.     

A sufficient condition for planar graphs to be (3, 1)-choosable

A (k, d)-list assignment L of a graph is a function that assigns to each vertex v a list L(v) of at least k colors satisfying \(|L(x)\cap L(y)|\le d\) for each edge xy. An L-coloring is a vertex coloring \(\pi \) such that \(\pi (v) \in L(v)\) for each vertex v and \(\pi (x) \ne \pi (y)\) for each edge xy. A graph G is (k, d)-choosable if there exists an L-coloring of G for every (k, d)-list assignment L. This concept is known as choosability with separation. In this paper, we will use Thomassen list coloring extension method to prove that planar graphs with neither 6-cycles nor adjacent 4- and 5-cycles are (3, 1)-choosable. This is a strengthening of a result obtained by using Discharging method which says that planar graphs without 5- and 6-cycles are (3, 1)-choosable.     

Ausbildungssupervision per E-Mail — Möglichkeiten und Grenzen

Internet-based supervision for trainees — possibilities and limitations This paper presents an internet-based supervision concept for trainees in development aid projects, that has been designed at the KFH NW / University of Applied Sciences in Aachen (Germany). Based on a phase model, the article highlights requirements of email supervision in content and method. Furthermore, it reports results from a study with former participants of email supervision. Possibilities and limitations of internet-based supervision are discussed. Conclusion: Although email-supervision cannot be considered as an equivalent alternative to face-to-face consultation, it could be a useful methodical variation of supervision and coaching.     

Kann denn Coaching Führung sein?

May coaching be leadership? An analysis of literature on the term coaching. An analysis of the German-speaking literature about coaching shows for what the term Coaching or rather the title coach is used in actual publications dealing with the leading manager as a coach. It becomes apparent, that coaching is not seen as a specialized advisory profession. Instead the term is used as an alternative expression for leadership vocabulary as management style or managerial functions. The elaboration of terms and concepts concludes, that semantically it is meant leadership when it comes to the concept of the coaching manager. To be an exception, the management by systemic approach forms a brand-new perspective about organizations. However, to give respects to the German-speaking coaching community there should be a difference between leadership and coaching as well as notions and titles should be used more accurate among professional management coaches.     

Coupon coloring of some special graphs

Let G be a graph without isolated vertices. A k-coupon coloring of G is a k-coloring of G such that the neighborhood of every vertex of G contains vertices of all colors from \([k] =\{1, 2, \ldots , k\}\), which was recently introduced by Chen, Kim, Tait and Verstraete. The coupon coloring number \(\chi _c(G)\) of G is the maximum k for which a k-coupon coloring exists. In this paper, we mainly study the coupon coloring of some special classes of graphs. We determine the coupon coloring numbers of complete graphs, complete k-partite graphs, wheels, cycles, unicyclic graphs, bicyclic graphs and generalised \(\Theta \)-graphs.     

Estimating hybrid frequency moments of data streams

We consider the problem of estimating hybrid frequency moments of two dimensional data streams. In this model, data is viewed to be organized in a matrix form (A _i,j )_1≤i,j,≤n . The entries A _i,j are updated coordinate-wise, in arbitrary order and possibly multiple times. The updates include both increments and decrements to the current value of A _i,j . The hybrid frequency moment F _p,q (A) is defined as \(\sum_{j=1}^{n}(\sum_{i=1}^{n}{A_{i,j}}^{p})^{q}\) and is a generalization of the frequency moment of one-dimensional data streams.We present the first \(\tilde{O}(1)\) space algorithm for the problem of estimating F _p,q for p∈[0,2] and q∈[0,1] to within an approximation factor of 1±ε. The \(\tilde{O}\) notation hides poly-logarithmic factors in the size of the stream m, the matrix size n and polynomial factors of ε ^?1. We also present the first \(\tilde{O}(n^{1-1/q})\) space algorithm for estimating F _p,q for p∈[0,2] and q∈(1,2].     

Approximation and hardness results for label cut and related problems

We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t. We give the first non-trivial approximation and hardness results for the Label Cut problem. Firstly, we present an \(O(\sqrt{m})\)-approximation algorithm for the Label Cut problem, where m is the number of edges in the input graph. Secondly, we show that it is NP-hard to approximate Label Cut within \(2^{\log ^{1-1/\log\log^{c}n}n}\) for any constant c<1/2, where n is the input length of the problem. Thirdly, our techniques can be applied to other previously considered optimization problems. In particular we show that the Minimum Label Path problem has the same approximation hardness as that of Label Cut, simultaneously improving and unifying two known hardness results for this problem which were previously the best (but incomparable due to different complexity assumptions).     

On list <Emphasis Type="Italic">r</Emphasis>-hued coloring of planar graphs

A list assignment of G is a function L that assigns to each vertex \(v\in V(G)\) a list L(v) of available colors. Let r be a positive integer. For a given list assignment L of G, an (L, r)-coloring of G is a proper coloring \(\phi \) such that for any vertex v with degree d(v), \(\phi (v)\in L(v)\) and v is adjacent to at least \( min\{d(v),r\}\) different colors. The list r-hued chromatic number of G, \(\chi _{L,r}(G)\), is the least integer k such that for every list assignment L with \(|L(v)|=k\), \(v\in V(G)\), G has an (L, r)-coloring. We show that if \(r\ge 32\) and G is a planar graph without 4-cycles, then \(\chi _{L,r}(G)\le r+8\). This result implies that for a planar graph with maximum degree \(\varDelta \ge 26\) and without 4-cycles, Wagner’s conjecture in [Graphs with given diameter and coloring problem, Technical Report, University of Dortmund, Germany, 1977] holds.     

A note on (<Emphasis Type="Italic">s</Emphasis>, <Emphasis Type="Italic">t</Emphasis>)-relaxed <Emphasis Type="Italic">L</Emphasis>(2, 1)-labeling of graphs

Let \(G=(V, E)\) be a graph. For two vertices u and v in G, we denote \(d_G(u, v)\) the distance between u and v. A vertex v is called an i-neighbor of u if \(d_G(u,v)=i\). Let s, t and k be nonnegative integers. An (s, t)-relaxed k-L(2, 1)-labeling of a graph G is an assignment of labels from \(\{0, 1, \ldots , k\}\) to the vertices of G if the following three conditions are met: (1) adjacent vertices get different labels; (2) for any vertex u of G, there are at most s 1-neighbors of u receiving labels from \(\{f(u)-1,f(u)+1\}\); (3) for any vertex u of G, the number of 2-neighbors of u assigned the label f(u) is at most t. The (s, t)-relaxed L(2, 1)-labeling number \(\lambda _{2,1}^{s,t}(G)\) of G is the minimum k such that G admits an (s, t)-relaxed k-L(2, 1)-labeling. In this article, we refute Conjecture 4 and Conjecture 5 stated in (Lin in J Comb Optim. doi: 10.1007/s10878-014-9746-9, 2013).     

A PTAS for minimum weighted connected vertex cover $$P_3$$ problem in 3-dimensional wireless sensor networks

Given a connected and weighted graph \(G=(V, E)\) with each vertex v having a nonnegative weight w(v), the minimum weighted connected vertex cover \(P_{3}\) problem \((MWCVCP_{3})\) is required to find a subset C of vertices of the graph with minimum total weight, such that each path with length 2 has at least one vertex in C, and moreover, the induced subgraph G[C] is connected. This kind of problem has many applications concerning wireless sensor networks and ad hoc networks. When homogeneous sensors are deployed into a three-dimensional space instead of a plane, the mathematical model for the sensor network is a unit ball graph instead of a unit disk graph. In this paper, we propose a new concept called weak c-local and give the first polynomial time approximation scheme (PTAS) for \(MWCVCP_{3}\) in unit ball graphs when the weight is smooth and weak c-local.     

Is there any polynomial upper bound for the universal labeling of graphs?

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem.     

Maximizing target-temporal coverage of mission-driven camera sensor networks

In camera sensor networks (CSNs), the target coverage problem is of special importance since a sensor with different viewing directions captures distinct views for the same target. Furthermore, mission-driven monitoring applications in CSNs usually have special network lifetime requirements in which the limited battery lifetime of sensors probably can not sustain for full coverage. In this paper, based on effective-sensing model, we address three new coverage problems in mission-driven camera sensor networks, namely the target-temporal effective-sensing coverage with non-adjustable cameras (TEC-NC) problem, the target-temporal effective-sensing coverage with adjustable cameras (TEC-AC) problem, and the target-temporal effective-sensing coverage with fully-adjustable cameras (TEC-FAC) problem. Given a mission period, the common objective of the problems is to find a sleep-wakeup schedule such that the overall target-temporal coverage is maximized. For TEC-NC, we propose a 2-approximation algorithm and two new heuristics. We also design two greedy strategies, each of which can be combined with our solutions for TEC-NC to deal with TEC-AC and TEC-FAC, respectively. We finally conduct extensive experiments to evaluate the performance of the proposed algorithms, whose results indicate the proposed algorithms outperform the existing alternatives as well as are close to the theoretical optimum on average under certain conditions.     

Covering directed graphs by in-trees

Given a directed graph D=(V,A) with a set of d specified vertices S={s ₁,…,s _d }?V and a function f : S→? where ? denotes the set of positive integers, we consider the problem which asks whether there exist ∑ _i=1 ^d f(s _i ) in-trees denoted by \(T_{i,1},T_{i,2},\ldots,T_{i,f(s_{i})}\) for every i=1,…,d such that \(T_{i,1},\ldots,T_{i,f(s_{i})}\) are rooted at s _i , each T _i,j spans vertices from which s _i is reachable and the union of all arc sets of T _i,j for i=1,…,d and j=1,…,f(s _i ) covers A. In this paper, we prove that such set of in-trees covering A can be found by using an algorithm for the weighted matroid intersection problem in time bounded by a polynomial in ∑ _i=1 ^d f(s _i ) and the size of D. Furthermore, for the case where D is acyclic, we present another characterization of the existence of in-trees covering A, and then we prove that in-trees covering A can be computed more efficiently than the general case by finding maximum matchings in a series of bipartite graphs.