相关论文: Algorithms for Greechie Diagrams

This article describes haggies, a program for the generation of optimised programs for the efficient numerical evaluation of mathematical expressions. It uses a multivariate Horner-scheme and Common Subexpression Elimination to reduce the…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring…

The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…

(I) We revisit the algorithmic problem of finding all triangles in a graph $G=(V,E)$ with $n$ vertices and $m$ edges. According to a result of Chiba and Nishizeki (1985), this task can be achieved by a combinatorial algorithm running in…

We present a novel way to manipulate ultra-cold atoms where four atomic levels are trapped by appropriately tuned optical lattices. When employed to perform quantum computation via global control, this unique structure dramatically reduces…

We present an improved orderly algorithm for constructing all unlabelled lattices up to a given size, that is, an algorithm that constructs the minimal element of each isomorphism class relative to some total order. Our algorithm employs a…

I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…

We extend our previous algorithm that generates all labeled graphs with a given graphical degree sequence to generate all labeled triangle-free graphs with a given graphical degree sequence. The algorithm uses various pruning techniques to…

A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we consider several problems of graph theory and developed optimal algorithms to solve such problems on cactus graphs. The running time of…

A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…

Graph neural networks (GNN) have shown promising results for several domains such as materials science, chemistry, and the social sciences. GNN models often contain millions of parameters, and like other neural network (NN) models, are…

We present an algorithm to enumerate isometry classes of integral quadratic lattices of a given rank and determinant, and analyze its running time by giving bounds on the number of genus symbols for a fixed rank and determinant. We build on…

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…

We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in…

The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…

This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…

In the Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems the input is a split graph $G$ and an integer $k$, and the goal is to decide whether there is a set $S$ of at most $k$ vertices such that $G-S$ is a block…