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Graph Fill-In, Elimination Ordering, Nested Dissection and Contraction Hierarchies

  • Ben Strasser
  • Dorothea WagnerEmail author
Chapter

Abstract

Graph fill-in, elimination ordering, separators, nested dissection orders and tree-width are only some examples of classical graph concepts that are related in manifold ways. This essay shows how contraction hierarchies, a successful approach to speed up Dijkstra’s algorithm for shortest paths, fits into this series of graph concepts. A theoretical consequence of this insight is a guarantee for the size of the search space required by Dijkstra’s algorithm combined with contraction hierarchies. On the other hand, the use of nested dissection leads to a very practicable variant of contraction hierarchies that can be applied in scenarios where edge lengths often change.

Keywords

Search Space Chordal Graph Auxiliary Data Route Planning Elimination Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut für Theoretische InformatikKarlsruher Institut für TechnologieKarlsruheGermany

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