Related papers: A Simple Algorithm for Computing a Cycle Separator
The divisor theory of graphs views a finite connected graph $G$ as a discrete version of a Riemann surface. Divisors on $G$ are formal integral combinations of the vertices of $G$, and linear equivalence of divisors is determined by the…
The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size. Recently, Hager and Hungerford [1] developed a…
For many applications, we are unable to take full advantage of the potential massive parallelisation offered by supercomputers or cloud computing because it is too hard to work out how to divide up the computation task between processors in…
A separating system of a graph $G$ is a family $\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\mathcal{S}$ that contains $e$ but not $f$. Recently, it…
Wiring diagrams are given for a quantum algorithm processor in CMOS to compute, in parallel, all divisors of an n-bit integer. Lines required in a wiring diagram are proportional to n. Execution time is proportional to the square of n.
Binary linear classification has been explored since the very early days of the machine learning literature. Perhaps the most classical algorithm is the Perceptron, where a weight vector used to classify examples is maintained, and additive…
A balanced separator of a graph $G$ is a set of vertices whose removal disconnects the graph into connected components that are a constant factor smaller than $G$. Lipton and Tarjan [FOCS'77] famously proved that every planar graph admits a…
Given a family F of subsets of a ground set V, its orthogonal is defined to be the family of subsets that do not overlap any element of F. Using this tool we revisit the problem of designing a simple linear time algorithm for undirected…
Linear optical circuits with single-photon sources offer a promising platform for quantum chemistry and machine learning. However, current applications are all based on support vector machines or gradient-free optimization methods. This…
How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications…
We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
We call a graph $G$ separable if a balanced separator can be computed for $G$ of size $O(n^c)$ with $c<1$. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…