Djidjev, Hristo N.2017-08-022017-08-022005-06-01Djidjev, Hristo N.. "On-Line and Dynamic Algorithms for Shortest Path Problems." (2005) https://hdl.handle.net/1911/96440.https://hdl.handle.net/1911/96440We describe algorithms for finding shortest paths and distances in aplanar 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. For outerplanar digraphs, for instance, the data structures can be updated after any such change in only O (log of n) time, where N is the number of vertices of the digraph. We also describe the first parallel algorithms for solving the dynamic version of the shortest path problem. Our results can be extended to hold for digraphs of genus o(n).20 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR94-224