We consider the subgraph isomorphism problem where, given two graphs G (source graph) and F (pattern graph), one is to decide whether there is a (not necessarily induced) subgraph of G isomorphic to F. While many practical heuristic algorithms have been developed for the problem, as pointed out by [JAIR 2018], for each of them there are rather small instances which they cannot cope. Therefore, developing an alternative approach that could possibly cope with these hard instances would be of interest. A seminal paper by Alon, Yuster and Zwick [J. ACM 1995] introduced the color coding approach to solve the problem, where the main part is a dynamic programming over color subsets and partial mappings. As with many exponential-time dynamic programming algorithms, the memory requirements constitute the main limiting factor for its usage. Because these requirements grow exponentially with the treewidth of the pattern graph, all existing implementations based on the color coding principle restrict themselves to specific pattern graphs, e.g., paths or trees. In contrast, we provide an efficient implementation of the algorithm significantly reducing its memory requirements so that it can be used for pattern graphs of larger treewidth. Moreover, our implementation not only decides the existence of an isomorphic subgraph, but it also enumerates all such subgraphs (or given number of them). We provide an extensive experimental comparison of our implementation to other available solvers for the problem.
Our aim is to make step towards competitive implementation of color coding based algorithm for , in order to see, where this approach can be potentially beneficial against the existing algorithms. To this end, we extend the comparisons of algorithms @cite_21 @cite_3 @cite_26 to color coding based algorithms, including the one proposed in this paper.
@cite_21 @cite_3 @cite_26
1977400967 2021501646 2019234714 1485830228
We introduce an algorithm for automatic selection of semantically-resonant colors to represent data (e.g., using blue for data about "oceans", or pink for "love"). Given a set of categorical values and a target color palette, our algorithm matches each data value with a unique color. Values are mapped to colors by collecting representative images, analyzing image color distributions to determine value-color affinity scores, and choosing an optimal assignment. Our affinity score balances the probability of a color with how well it discriminates among data values. A controlled study shows that expert-chosen semantically-resonant colors improve speed on chart reading tasks compared to a standard palette, and that our algorithm selects colors that lead to similar gains. A second study verifies that our algorithm effectively selects colors across a variety of data categories. Color equalization algorithms exhibit a variety of behaviors described in two differing types of models: Gray World and White Patch. These two models are considered alternatives to each other in methods of color correction. They are the basis for two human visual adaptation mechanisms: Lightness Constancy and Color Constancy. The Gray World approach is typical of the Lightness Constancy adaptation because it centers the histogram dynamic, working the same way as the exposure control on a camera. Alternatively, the White Patch approach is typical of the Color Constancy adaptation, searching for the lightest patch to use as a white reference similar to how the human visual system does. The Retinex algorithm basically belongs to the White Patch family due to its reset mechanism. Searching for a way to merge these two approaches, we have developed a new chromatic correction algorithm, called Automatic Color Equalization (ACE), which is able to perform Color Constancy even if based on Gray World approach. It maintains the main Retinex idea that the color sensation derives from the comparison of the spectral lightness values across the image. We tested different performance measures on ACE, Retinex and other equalization algorithms. The results of this comparison are presented.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. This paper provides a fast algorithm to order in a meaningful, strict way the integer gray values in digital (quantized) images. It can be used in any exact histogram specification-based application. Our algorithm relies on the ordering procedure based on the specialized variational approach. This variational method was shown to be superior to all other state-of-the art ordering algorithms in terms of faithful total strict ordering but not in speed. Indeed, the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions. In this paper, we propose a simple and fast fixed point algorithm to minimize these functionals. The fast convergence of our algorithm results from known analytical properties of the model. Our algorithm is equivalent to an iterative nonlinear filtering. Furthermore, we show that a particular form of the variational model gives rise to much faster convergence than other alternative forms. We demonstrate that only a few iterations of this filter yield almost the same pixel ordering as the minimizer. Thus, we apply only few iteration steps to obtain images, whose pixels can be ordered in a strict and faithful way. Numerical experiments confirm that our algorithm outperforms by far its main competitors. This paper reports on a simple, decentralized, anytime, stochastic, soft graph-colouring algorithm. The algorithm is designed to quickly reduce the number of colour conflicts in large, sparse graphs in a scalable, robust, low-cost manner. The algorithm is experimentally evaluated in a framework motivated by its application to resource coordination in large, distributed networks.