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On the Complexity of Partitioning Graphs for Arc-Flags

Authors Reinhard Bauer, Moritz Baum, Ignaz Rutter, Dorothea Wagner



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Reinhard Bauer
Moritz Baum
Ignaz Rutter
Dorothea Wagner

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Reinhard Bauer, Moritz Baum, Ignaz Rutter, and Dorothea Wagner. On the Complexity of Partitioning Graphs for Arc-Flags. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 71-82, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/OASIcs.ATMOS.2012.71

Abstract

Precomputation of auxiliary data in an additional off-line step is a common approach towards improving the performance of shortest-path queries in large-scale networks. One such technique is the arc-flags algorithm, where the preprocessing involves computing a partition of the input graph. The quality of this partition significantly affects the speed-up observed in the query phase. It is evaluated by considering the search-space size of subsequent shortest-path queries, in particular its maximum or its average over all queries. In this paper, we substantially strengthen existing hardness results of Bauer et al. and show that optimally filling this degree of freedom is NP-hard for trees with unit-length edges, even if we bound the height or the degree. On the other hand, we show that optimal partitions for paths can be computed efficiently and give approximation algorithms for cycles and trees.
Keywords
  • shortest paths
  • arc-flags
  • search space
  • preprocessing
  • complexity

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