论文信息 - Shortest path problems in planar graphs

Shortest path problems in planar graphs

Graph decomposition and data structures techniques are presented that make possible faster algorithms for shortest paths in planar graphs. Improved algorithms are presented for the single source problem, the all pairs problem, and the problem of finding a minimum cut in an undirected graph.

Greg N. Frederickson | G. Frederickson

[1] Frank Harary,et al. Graph Theory , 2016 .

[2] Robert E. Tarjan,et al. Applications of a planar separator theorem , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[3] Refael Hassin,et al. Maximum Flow in (s, t) Planar Networks , 1981, Inf. Process. Lett..

[4] D. Rose,et al. Generalized nested dissection , 1977 .

[5] Nils J. Nilsson,et al. Problem-solving methods in artificial intelligence , 1971, McGraw-Hill computer science series.

[6] Edsger W. Dijkstra,et al. A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[7] John H. Reif,et al. Minimum s-t Cut of a Planar Undirected Network in O(n log2(n)) Time , 1983, SIAM J. Comput..

[8] R. Tarjan,et al. A Separator Theorem for Planar Graphs , 1977 .

[9] Donald B. Johnson,et al. Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[10] Greg N. Frederickson,et al. Data structures for on-line updating of minimum spanning trees , 1983, STOC.

[11] G. Nemhauser. A generalized permanent label setting algorithm for the shortest path between specified nodes , 1972 .

[12] Alon Itai,et al. Maximum Flow in Planar Networks , 1979, SIAM J. Comput..

[13] Richard M. Karp,et al. Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[14] John H. Reif,et al. Minimum S-T Cut of a Planar Undirected Network in O(n log²(n)) Time , 1981, ICALP.