相关论文: Algorithms for Greechie Diagrams

In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We also include a computational comparison of several existing…

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…

The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…

The graph programming language GP 2 allows to apply sets of rule schemata (or "attributed" rules) non-deterministically. To analyse conflicts of programs statically, graphs labelled with expressions are overlayed to construct critical pairs…

Many critical decision-making tasks are now delegated to machine-learned models, and it is imperative that their decisions are trustworthy and reliable, and their outputs are consistent across similar inputs. We identify a new source of…

We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…

A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…

We train a small message-passing graph neural network to predict Hamiltonian cycles on Erd\H{o}s-R\'enyi random graphs in a critical regime. It outperforms existing hand-crafted heuristics after about 2.5 hours of training on a single GPU.…

For any integer $n\geq 1$ a middle levels Gray code is a cyclic listing of all $n$-element and $(n+1)$-element subsets of $\{1,2,\ldots,2n+1\}$ such that any two consecutive subsets differ in adding or removing a single element. The…

Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a…

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based…

Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…

Implementing graph algorithms efficiently in a rule-based language is challenging because graph pattern matching is expensive. In this paper, we present a number of linear-time implementations of graph algorithms in GP 2, an experimental…

Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…

Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…

The concept of a configuration graph associated to a primitive, aperiodic substitution is introduced in [1] as a convenient graphical representation of the infinite indeterminism of the shift space of the substitution. The main result of…

We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…

We present a deterministic linear-time algorithm for finding an odd cycle through two specified vertices in an undirected graph. This is shown in a generalized form as follows: Let $\Gamma$ be any group in which every element is of order at…

Although the applications of Non-Homogeneous Poisson Processes to model and study the threshold overshoots of interest in different time series of measurements have proven to provide good results, they needed to be complemented with an…

We describe algorithms for drawing media, systems of states, tokens and actions that have state transition graphs in the form of partial cubes. Our algorithms are based on two principles: embedding the state transition graph in a…