An (α, β)-spanner of an n-vertex graph G = (V,E) is a subgraph H of G satisfying that dist(u, v,H) ≤ α ·dist(u, v,G)+β for every pair (u, v) ∈ V × V , where dist(u, v,G′) denotes the distance between u and v in G′ ⊆ G. It is known that for every integer k ≥ 1, every graph G has a polynomially constructible (2k − 1, 0)-spanner of size O(n). This size-stretch bound is essentially optimal by the g...

This paper describes a technique for efficiently searching metabolic pathways similar to a given query pathway, from a pathway database. Metabolic pathways can be converted into labeled directed graphs where the nodes represent chemical compounds. Similarity between two graphs can be computed using a metric based on Maximal Common Subgraph (MCS). By maintaining an inverted file that indexes all...

The Wythoff construction takes a d-dimensional polytope P , a subset S of {0, . . . , d} and returns another d-dimensional polytope P (S). If P is a regular polytope, then P (S) is vertex-transitive. This construction builds a large part of the Archimedean polytopes and tilings in dimension 3 and 4. We want to determine, which of those Wythoffians P (S) with regular P have their skeleton or dua...

Many educators and researchers are trying to define statistical literacy for the 21st century. Kimura, a Japanese science educator, has suggested that a key task of statistical literacy is the ability to extract qualitative information from quantitative information, and/or to create new information from qualitative and quantitative information. This article presents research that offers a theor...

All symmetric designs are determined for which the automorphism group is 2-transitive on the set of points. This note contains a proof of the following result. Theorem. Let D be a symmetric design with v > 2k such that Aut D is 2-transitive on points. Then D is one o f the following: (i) a projective space; (ii) the unique Hadamard design with v = I 1 and k = 5; (iii) a unique design with v = 1...

Graph-based semi-supervised learning (SSL) methods usually consist of two stages: in the first stage, a graph is constructed from the set of input instances; and in the second stage, the available label information along with the constructed graph is used to assign labels to the unlabeled instances. Most of the previously proposed graph construction methods are unsupervised in nature, as they i...

The new approach of distributed graphs and graph transformation as developed in this article allows to use structured graph transformation on two abstraction levels, the network and the local level. The network level contains the description of the topological structures of a system. The local level covers the description of states and their transitions in local systems. Local state transitions...

Monoidal categories of acyclic graphs capture the notion of multihole context, pervasive in syntax and semantics. Milner’s bigraphs is a recent example. We give a method for generalising such categories to monoidal closed categories of acyclic graphs. The method combines the Int-construction, lifting traced monoidal categories to compact closed ones; the recent formulation of sortings for react...

A 1-factorization of a graph is a decomposition of the graph into edge disjoint perfect matchings. There is a well-known method, which we call the K-construction, for building a 1-factorization of Kn;n from a 1-factorization of Knþ1. The 1-factorization of Kn;n can be written as a latin square of order n. The K-construction has been used, among other things, to make perfect 1-factorizations, su...

The Program Dependence Graph was introduced by Ottenstein and Ottenstein in 1984. It was suggested to be a suitable internal program representation for monolithic programs, for the purpose of carrying out certain software engineering operations such as slicing and the computation of program metrics. Since then, Horwitz et al. have introduced the multi-procedural equivalent System Dependence Gra...