Abstract. In this paper we present a computationally efficient algorithm utilizing a fully or seminonlocal graph Laplacian for solving a wide range of learning problems in binary data classification and image processing. In their recent work [Multiscale Model. Simul., 10 (2012) 1. Introduction. This work develops a fast algorithm for a recent variational method in a graph setting. The method is inspired by diffuse interface models that have been used in a variety of problems, such as those in fluid dynamics and materials science. We consider data represented as nodes in a weighted graph, and each edge is assigned a numerical value describing the similarity between the nodes. In spectral graph theory, this approach is successfully used to perform various learning tasks in imaging and data clustering. The standard techniques of the theory are thoroughly described in [13,45], and the graph Laplacian, which is discussed in more detail in section 2.2, is introduced as one of the fundamental concepts. In imaging, spectral methods are often used in image segmentation applications, as shown in [54,33,14].We are particularly interested in nonlocal total variation methods, as they are a link between spectral graph theory and diffuse interface models and thus can be used as a motivation for our algorithm. These methods are used in numerous image processing applications. They were initially developed as methods for image denoising [9,29] but were successfully applied to many other image processing problems such as inpainting and reconstruction in [30,63,49], image deblurring in [40], and manifold processing in [18].Bertozzi and Flenner introduce a graph-based model based on the Ginzburg-Landau func-

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In this paper we present new evolutionary approach for solving the Routing and Carrier Selection Problem (RCSP). New encoding scheme is implemented with appropriate objective function. This approach in most cases keeps the feasibility of individuals by using specific representation and modified genetic operators. The numerical experiments were carried out on the standard data sets known from the literature and results were successful comparing to two other recent heuristic for solving RCSP.

Our goal is to estimate a probability density based on discrete point data via segmentation techniques. Since point data may represent certain activities, such as crime, our method can be successfully used for detecting regions of high activity. In this work we design a binary segmentation version of the well-known Maximum Penalized Likelihood Estimation (MPLE) model, as well as a minimization algorithm based on thresholding dynamics originally proposed by Merriman et al. (The Computational Crystal Growers, pp. 73-83, 1992). We also present some computational examples, including one with actual residential burglary data from the San Fernando Valley.

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