Efficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic Geometry
- A standard approach to accelerating shortest path algorithms on networks is the bidirectional search, which explores the graph from the start and the destination, simultaneously. In practice this strategy performs particularly well on scale-free real-world networks. Such networks typically have a heterogeneous degree distribution (e.g., a power-law distribution) and high clustering (i.e., vertices with a common neighbor are likely to be connected themselves). These two properties can be obtained by assuming an underlying hyperbolic geometry. <br /> To explain the observed behavior of the bidirectional search, we analyze its running time on hyperbolic random graphs and prove that it is (O) over tilde (n(2-1/alpha) + n(1/(2 alpha)) + delta(max)) with high probability, where alpha is an element of (1/2, 1) controls the power-law exponent of the degree distribution, and dmax is the maximum degree. This bound is sublinear, improving the obvious worst-case linear bound. Although our analysis depends on the underlying geometry, the algorithmA standard approach to accelerating shortest path algorithms on networks is the bidirectional search, which explores the graph from the start and the destination, simultaneously. In practice this strategy performs particularly well on scale-free real-world networks. Such networks typically have a heterogeneous degree distribution (e.g., a power-law distribution) and high clustering (i.e., vertices with a common neighbor are likely to be connected themselves). These two properties can be obtained by assuming an underlying hyperbolic geometry. <br /> To explain the observed behavior of the bidirectional search, we analyze its running time on hyperbolic random graphs and prove that it is (O) over tilde (n(2-1/alpha) + n(1/(2 alpha)) + delta(max)) with high probability, where alpha is an element of (1/2, 1) controls the power-law exponent of the degree distribution, and dmax is the maximum degree. This bound is sublinear, improving the obvious worst-case linear bound. Although our analysis depends on the underlying geometry, the algorithm itself is oblivious to it.…
Author details: | Thomas BläsiusORCiDGND, Cedric Freiberger, Tobias FriedrichORCiDGND, Maximilian KatzmannORCiDGND, Felix Montenegro-Retana, Marianne Thieffry |
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DOI: | https://doi.org/10.1145/3516483 |
ISSN: | 1549-6325 |
ISSN: | 1549-6333 |
Title of parent work (English): | ACM Transactions on Algorithms |
Publisher: | Association for Computing Machinery |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/03/30 |
Publication year: | 2022 |
Release date: | 2024/01/03 |
Tag: | Random graphs; bidirectional shortest path; hyperbolic geometry; scale-free networks |
Volume: | 18 |
Issue: | 2 |
Article number: | 19 |
Number of pages: | 32 |
First page: | 1 |
Last Page: | 32 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG, German Research Foundation); [390859508] |
Organizational units: | An-Institute / Hasso-Plattner-Institut für Digital Engineering gGmbH |
DDC classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 000 Informatik, Informationswissenschaft, allgemeine Werke |
Peer review: | Referiert |