Rainbow connectivity: hardness and tractability

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: 1) For every fixed k >= 3, it is NP-Complete to decide whether src(G) <= k even when the graph G is bipartite. 2) For every fixed odd k >= 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. (J. Comb. Opt., 2011) where they prove the hardness for the even case. 3) The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. 4) For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.

Economic measurement in public welfare economics : practical experiences on the regional level in Germany

Resumen: ¿Cuál es el precio justo para la asistencia social? Este artículo muestra que la medición económica efectuada en mercados basados en el valor de los servicios prestados podría responder esta pregunta. La medición económica puede hacer lo mismo en distintos campos del trabajo social aplicando diferentes métodos, tales como ofertas públicas o negociaciones calificadas. Después de dar un breve panorama teórico, se presentan y analizan en detalle dos proyectos alemanes. El artículo muestra cómo la introducción de mecanismos de negociación en la asistencia social expresados en términos de resultados pueden traer efectos positivos para las finanzas públicas, así como también para el bien común.

Effects of Carbon Dioxide Capture and Storage in Germany on European Electricity Exchange and Welfare

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Recent investigations on zooplankton in the Limnological Institute of the University of Freiburg, in Falkau (Germany). [Translation from: Acta cient.Venezolana 18, 94-97, 1967. ]

Histochemical experiments are conducted in order to study the interrenal cells of European brook lamprey (Lampetra planeri).

Development of trophic state and phytoplankton in an oligo-mesotrophic reservoir (Kleine Kinzig) in Black Forest, Germany

Since 1989, intensive studies have been made on a relatively new (1983-84) oligotrophic reservoir and its pre-reservoir in the Black Forest. This paper briefly reports on the hydrochemistry, especially annual variations in phosphorus loadings, and the seasonal development of phytoplankton in 1989 and 1990.

Design and path planning for a remote-brained service robot

This article introduced an effective design method of robot called remote-brain, which is made the brain and body separated. It leaves the brain in the mother environment, by which we mean the environment in which the brain's software is developed, and talks with its body by wireless links. It also presents a real robot TUT06-B based on this method which has human-machine interaction, vision systems, manipulator etc. Then it discussed the path planning method for the robot based on ant colony algorithm in details, especially the Ant-cycle model. And it also analyzed the parameter of the algorithm which can affect the convergence. Finally, it gives the program flow chat of this algorithm.

Application of ICA in on-line verification of the phase difference of the current sensor

The performance of the current sensor in power equipment may become worse affected by the environment. In this paper, based on ICA, we propose a method for on-line verification of the phase difference of the current sensor. However, not all source components are mutually independent in our application. In order to get an exact result, we have proposed a relative likelihood index to choose an optimal result from different runs. The index is based on the maximum likelihood evaluation theory and the independent subspace analysis. The feasibility of our method has been confirmed by experimental results.

Study on text-dependent speaker recognition based on Biomimetic Pattern Recognition

We studied the application of Biomimetic Pattern Recognition to speaker recognition. A speaker recognition neural network using network matching degree as criterion is proposed. It has been used in the system of text-dependent speaker recognition. Experimental results show that good effect could be obtained even with lesser samples. Furthermore, the misrecognition caused by untrained speakers occurring in testing could be controlled effectively. In addition, the basic idea "cognition" of Biomimetic Pattern Recognition results in no requirement of retraining the old system for enrolling new speakers.