We present a new heuristic point-to-point routing algorithm based on contraction hierarchies (CH). Given an ε ≥ 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. CH is based on node contraction: removing nodes from a network and adding shortcut edges to preserve shortest path distances. Our algorithm tries t...

In many clustering systems (hierarchies, pyramids and more generally weak hierarchies) clusters are generated by two elements only. This paper is devoted to such clustering systems (called binary clustering systems). It provides some basic properties, links with (closed) weak hierarchies and some qualitative versions of bijection theorems that occur in Numerical Taxonomy. Moreover, a way to ass...

There is a long tradition of community ecologists using interspecific dominance hierarchies as a way to explain species coexistence and community structure. However, there is considerable variation in the methods used to construct these hierarchies, how they are quantified, and how they are interpreted. In the study of ant communities, hierarchies are typically based on the outcome of aggressiv...

Large organizations are typically modelled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this article is to study the validity of these approximations. I show that modelling hierarchies with a continuum of tiers is not a good approximation. I also show, for a particular model of balanced hierarchies, that ig...

Lars Kirkegaard B kdal Bent Bruun Kristensen The Maersk Mc-Kinney Moller Institute for Production Technology University of Southern Denmark/Odense University, DK-5230 Odense M, Denmark e-mail: flkb, [email protected] Abstract A whole is aggregated from parts, where a part can be aggregated itself or be atomic. The structure forms an aggregation (or part-whole) hierarchy. The whole can be...

Paragon: A Language Using Type Hierarchies for the Specification, Implementation, and Selection of Abstract Data Types (Lecture Notes in Computer Science) . Abstraction hierarchies : a model of. HathiTrust Digital Library Paragon A Language Using Type Hierarchies for the Specification, Implementation, and Selection of Abstract Data Types (Electronic book text) / Author: Mark . Kindle free e boo...

Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with ∂̄-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite codimension in the space of independent variables. For higher ∂̄-index these hierarchies represent themselves families of multidimensional equations with multidimensiona...

Using Projection to accelerate Ray Tracing Anastasia Bezerianos M.Sc. Graduate Department of Computer Science University of Toronto 2001 The high cost of Ray Tracing image rendering has driven many researchers to devise acceleration techniques like bounding volume hierarchies. This thesis introduces new ways of building bounding volume hierarchies. We modify existing algorithms to use bounding ...

Difference hierarchies were originally introduced by Hausdorff and they play an important role in descriptive set theory. In this survey paper, we study difference hierarchies of regular languages. The first sections describe standard techniques on difference hierarchies, mostly due to Hausdorff. We illustrate these techniques by giving decidability results on the difference hierarchies based o...

Internet marketplaces are now faced with new challenges that arise from the need to seamlessly integrate enormous number of product catalogs from different sources. In order to help users find products efficiently, Internet shops provide hierarchies of product catalogs (called category hierarchies). However, the absence of robust models (and well understood semantics) for product catalogs and t...