Directing Road Networks by Listing Strong Orientations
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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.
- 6.Chartrand, G., Harary, F., Schultz, M., Wall, C.E.: Forced orientation number of a graph. Congressus Numerantium, pp. 183–192 (1994)Google Scholar
- 10.Conte, A., Grossi, R., Marino, A., Rizzi, R.: Listing acyclic orientations of graphs with single, multiple sources. In: Proceedings LATIN (2011) Observation of strains: Theoretical Informatics - 12th Latin American Symposium, Ensenada, 11-15 April 2016, pp. 319–333 (2016)Google Scholar
- 22.Roberts, F.S.: Graph theory and its applications to problems of society. NSF-CBSM Monograph No. 29. SIAM Publications (1978)Google Scholar
- 27.Uno, T.: Two general methods to reduce delay and change of enumeration algorithms: NII Technical report NII-2003-004E, Tokyo (2003)Google Scholar