文章基本信息

标题：On the Complexity of Partitioning Graphs for Arc-Flags
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作者：Bauer, Reinhard ; Baum, Moritz ; Rutter, Ignaz 等
期刊名称：OASIcs : OpenAccess Series in Informatics
电子版ISSN：2190-6807
出版年度：2012
卷号：25
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：shortest paths; arc-flags; search space; preprocessing; complexity