Abstract
We describe algorithms for finding shortest paths and distances in a planar digraph which exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. Our data structures can be updated after any such change in only polylogarithmic time, while a single-pair query is answered in sublinear time. We also describe the first parallel algorithms for solving the dynamic version of the shortest path problem.
This work was partially supported by the EC ESPRIT Basic Research Action No. 7141 (ALCOM II), by the EC Cooperative Action IC-1000 (project ALTEC) and by the NSF grants No. CDA-9211155 and No. CCR-9409191.
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Djidjev, H.N., Pantziou, G.E., Zaroliagis, C.D. (1995). On-line and dynamic algorithms for shortest path problems. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_73
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