Related papers: Notes on color reductions and $\gamma$ traces
Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…
With the long term perspective of using quantum computers and tensor networks for lattice gauge theory simulations, an efficient method of digitizing gauge group elements is needed. We thus present our results for a handful of…
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Let $2\le k\in\mathbb{Z}$. A total coloring of a$k$-regular simple graph via $k+1$ colors is an efficient total coloring if each color yields an efficient dominating set, where the efficient domination condition applies to the restriction…
We present here a new method for evaluating determinants -- the reduction method. Firstly, in the section 2, we apply it to third-order determinants and after, in the section 3, we generalize it to higher-order determinants. In the section…
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An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…
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The selection of $\eta$ mesons with a high efficiency and a high purity can be important in the formation of statistically significant invariant mass spectra in the reconstruction of short-lived particles such as $\eta' \rightarrow \pi^{+}…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…