Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs
We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous trade-offs between the preprocessing, query, and update times. Our data structure is based on a recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly chosen subset of vertices. We apply this result to construct improved shortest path algorithms for dynamic planar digraphs.
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- 1.H. Bondlaender, “Dynamic Algorithms for Graphs with Treewidth 2”, Proc. 19th WG'93, LNCS 790, pp.112–124, Springer-Verlag, 1994.Google Scholar
- 2.S. Chaudhuri and C. Zaroliagis, “Shortest Path Queries in Digraphs of Small Treewidth”, Proc. 22nd ICALP, LNCS, Springer-Verlag, 1995, to appear.Google Scholar
- 3.H. Djidjev, G. Pantziou and C. Zaroliagis, “On-line and Dynamic Algorithms for Shortest Path Problems”, Proc. 12th STACS, LNCS 900, pp.193–204, Springer-Verlag, 1995.Google Scholar
- 4.E. Feuerstein and A.M. Spaccamela, “Dynamic Algorithms for Shortest Paths in Planar Graphs”, Theor. Computer Science, 116 (1993), pp.359–371.Google Scholar
- 5.G.N. Frederickson, “Using Cellular Graph Embeddings in Solving All Pairs Shortest Path Problems”, Proc. 30th Annual IEEE Symp. on FOCS, 1989.Google Scholar
- 7.R. Hassin, “Maximum flow in (s,t)-planar networks”, Inform. Proc. Lett., 13(1981), p.107.Google Scholar
- 8.G. Miller and J. Naor, “Flows in planar graphs with multiple sources and sinks”, Proc. 30th IEEE Symp. on FOCS, 1989, pp.112–117.Google Scholar
- 9.B. Schieber and U. Vishkin, “On Finding Lowest Common Ancestors: Simplification and Parallelization”, SIAM J. Computing, 17(6), pp.1253–1262, 1988.Google Scholar