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

Ben Strasser () and Dorothea Wagner ()
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Ben Strasser: Karlsruher Institut für Technologie, Institut für Theoretische Informatik
Dorothea Wagner: Karlsruher Institut für Technologie, Institut für Theoretische Informatik

A chapter in Gems of Combinatorial Optimization and Graph Algorithms, 2015, pp 69-82 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-24971-1_7

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DOI: 10.1007/978-3-319-24971-1_7

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