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Constant-Time Reachability in DAGs Using Multidimensional Dominance Drawings

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Abstract

Answering reachability queries in directed acyclic graphs is an operation required by many applications. In this paper, we present efficient algorithms to construct and search a space-efficient data structure in the k-dimensional space that is based on Graph Dominance Drawing. Our algorithms construct this data structure in O(km) time, while it can be stored in O(kn) space. Any reachability query is answered in constant time, since no “falsely implied paths (fips)” are introduced. We also present experimental results that show that the number of dimensions, k, in the solutions produced by our techniques is low. Additionally, we present a new method for constructing random DAGs with prespecified structure and density. The analysis of our experimental results reveals an interesting interplay between density and structure.

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Authors and Affiliations

  1. Computer Science Department, University of Crete, Voutes Campus, 700 13, Heraklion Crete, Greece

    Panagiotis Lionakis & Ioannis G. Tollis

  2. University of Perugia, Perugia, Italy

    Giacomo Ortali

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  1. Panagiotis Lionakis
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  2. Giacomo Ortali
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  3. Ioannis G. Tollis
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Correspondence to Panagiotis Lionakis.

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Lionakis, P., Ortali, G. & Tollis, I.G. Constant-Time Reachability in DAGs Using Multidimensional Dominance Drawings. SN COMPUT. SCI. 2, 320 (2021). https://doi.org/10.1007/s42979-021-00713-6

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