Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and differ...

A chordal graph is the intersection graph of a family of subtrees of a tree, or, equivalently, it is the (edge-)intersection graph of leaf-generated subtrees of a full binary tree. In this paper, a generalization of chordal graphs from this viewpoint is studied: a graph G=(V; E) is representable if there is a family of subtrees {Sv}v∈V of a binary tree, such that uv ∈ E if and only if |Su ∩ Sv|...

A number of papers present algorithms to construct isosurfaces with sharp edges and corners from hermite data, i.e. the exact surface normals at the exact intersection of the surface and grid edges. We discuss some fundamental problems with the previous algorithms and describe a new approach, based on merging grid cubes near sharp edges, that produces significantly better results. Our algorithm...

Uniform random intersection graphs have received much interest and been used in diverse applications. A uniform random intersection graph with n nodes is constructed as follows: each node selects a set of Kn different items uniformly at random from the same pool of Pn distinct items, and two nodes establish an undirected edge in between if and only if they share at least one item. For such grap...

We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube Qd to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their intersection is non-empty. Our motivation for considering such graphs is to model ‘random compatibility’ between vertices in a large network. For both of the model...

The station location problem consists of placing new stations along the railway tracks of an existing network in order to increase the number of users. In this paper we consider the problem for a railway network consisting of two intersecting lines forming an angle α. An approach for solving the problem in polynomial time for sufficiently large angles α is presented.

This paper examines a point of intersection between the work of the late Robert de Marrais and Vedic Physics. Specifically, de Marrais discussed the concept of Lissajous Figures in relation to Sedenions and his 42 Assessors, in his first paper about Box Kites. Later, John Baez took up a related subject, the problem of epicycloids, apparently without having read the work of de Marrais. This pape...

Let H(n,N), where k ≥ 2, be a random hypergraph on the vertex set [n] = {1, 2, . . . , n} with N edges drawn independently with replacement from all subsets of [n] of size k. For d̄ = kN/n and any ε > 0 we show that if k = o(ln(d̄/ lnn)) and k = o(ln(n/ ln d̄)), then with probability 1−o(1) a random greedy algorithm produces a proper edge-colouring of H(n,N) with at most d̄(1+ε) colours. This yield...

In this paper, the authors splice together an image which has been split up on a piece of paper by using duplication detection. The nearest pieces are connected using edge searching and matching and the pieces that have graphics or textures are matched using the edge shape and intersection between the two near pieces. Thus, the initial step is to mark the direction of each piece and put the pie...