It is known that given a directed graph E and a subset X of vertices, the sum Σ v∈X P v of vertex projections in the C *-algebra of E converges strictly in the multiplier algebra to a projection P X. Here we give a construction which, in certain cases, produces a directed graph F such that C * (F) is isomorphic to the corner P X C * (E)P X. Corners of this type arise naturally as the fixed poin...

The Planar Graph Metric Compression Problem is to compactly encode the distances among k nodes in a planar graph of size n. Two naïve solutions are to store the graph using Opnq bits, or to explicitly store the distance matrix with Opk log nq bits. The only lower bounds are from the seminal work of Gavoille, Peleg, Prennes, and Raz [SODA’01], who rule out compressions into a polynomially smalle...

We propose a new algorithm called DPC+ to enforce partial path consistency (PPC) on qualitative constraint networks. PPC restricts path consistency (PC) to a triangulation of the underlying constraint graph of a network. As PPC retains the sparseness of a constraint graph, it can make reasoning tasks such as consistency checking and minimal labelling of large qualitative constraint networks muc...

To minimize the access cost in large disk arrays (RAID) Cohen et al. [5–7] introduced (d, f)-cluttered orderings of various set systems, d, f ∈ N. In case of a graph this amounts to an ordering of the edge set such that the number of points contained in any d consecutive edges is bounded by the number f . For the complete graph, Cohen et al. gave some optimal solution for small parameters d [5]...

A (d, 1)-total labelling of a graph G assigns integers to the vertices and edges of G such that adjacent vertices receive distinct labels, adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least d. The span of a (d, 1)-total labelling is the maximum difference between two labels. The (d, 1)-total number, denoted λTd (G...

In this work we consider a generalization of graph flows. A flow is, in its simplest formulation, labelling the directed edges with real numbers subject to various constraints. common constraint is conservation vertex, meaning that sum labels on incoming vertex equals those outgoing edges. One easy fact if conserving all but one then it also remaining one. our do not label numbers, elements fro...

The problems of object class segmentation [2], which assigns an object label such as road or building to every pixel in the image and dense stereo reconstruction, in which every pixel within an image is labelled with a disparity [1], are well suited for being solved jointly. Both approaches formulate the problem of providing a correct labelling of an image as one of Maximum a Posteriori (MAP) e...

The (p,1)-total number λp (G) of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two incident edges have the same label and the difference between the labels of a vertex and its incident edges is at least p. In this paper we consider the list version. Let L(x) be a list of ...

Let h ≥ 1 be an integer. An L(h, 1, 1)-labelling of a (finite or infinite) graph is an assignment of nonnegative integers (labels) to its vertices such that adjacent vertices receive labels with difference at least h, and vertices distance 2 or 3 apart receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over a...