The analysis of a nested dissection algorithm
Numerische Mathematik
Optimal node ranking of trees in linear time
Information Processing Letters
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
Using Multi-level Graphs for Timetable Information in Railway Systems
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Approximating Treewidth, Pathwidth, and Minimum Elimination Tree Height
WG '91 Proceedings of the 17th International Workshop
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Highway dimension, shortest paths, and provably efficient algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
VC-dimension and shortest path algorithms
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Preprocessing speed-up techniques is hard
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Exact Routing in Large Road Networks Using Contraction Hierarchies
Transportation Science
On optimal preprocessing for contraction hierarchies
Proceedings of the 5th ACM SIGSPATIAL International Workshop on Computational Transportation Science
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Contraction hierarchies are a speed-up technique to improve the performance of shortest-path computations, which works very well in practice. Despite convincing practical results, there is still a lack of theoretical explanation for this behavior. In this paper, we develop a theoretical framework for studying search space sizes in contraction hierarchies. We prove the first bounds on the size of search spaces that depend solely on structural parameters of the input graph, that is, they are independent of the edge lengths. To achieve this, we establish a connection with the well-studied elimination game. Our bounds apply to graphs with treewidth k, and to any minor-closed class of graphs that admits small separators. For trees, we show that the maximum search space size can be minimized efficiently, and the average size can be approximated efficiently within a factor of 2. We show that, under a worst-case assumption on the edge lengths, our bounds are comparable to the recent results of Abraham et al. [1], whose analysis depends also on the edge lengths. As a side result, we link their notion of highway dimension (a parameter that is conjectured to be small, but is unknown for all practical instances) with the notion of pathwidth. This is the first relation of highway dimension with a well-known graph parameter.