Abstract
A connected road network with N nodes and L edges has \(K \le L\) edges identified as one-way roads. In a feasible direction, these one-way roads are assigned a direction each, so that every node can reach any other [Robbins ’39]. Using O(L) preprocessing time and space usage, it is shown that all feasible directions can be found in O(K) amortized time each. To do so, we give a new algorithm that lists all the strong orientations of an undirected connected graph with m edges in O(m) amortized time each, using O(m) space. The cost can be deamortized to obtain O(m) delay with \(O(m^2)\) preprocessing time and space.
Work partially supported by the Italian Ministry of Education, University, and Research (MIUR) under PRIN 2012C4E3KT national research project AMANDA—Algorithmics for MAssive and Networked DAta.
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Notes
- 1.
This is crucial, as the presence of unary nodes is the reason behind the \(O(m^2)\) cost of the approach based on [7], mentioned in the introduction.
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Conte, A., Grossi, R., Marino, A., Rizzi, R., Versari, L. (2016). Directing Road Networks by Listing Strong Orientations. In: Mäkinen, V., Puglisi, S., Salmela, L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science(), vol 9843. Springer, Cham. https://doi.org/10.1007/978-3-319-44543-4_7
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