Optimal message routing without complete routing tables
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Journal of the ACM (JACM)
Implicit Data Structures for the Dictionary Problem
Journal of the ACM (JACM)
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Space-Efficient and Fault-Tolerant Message Routing in Outerplanar Networks
IEEE Transactions on Computers
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
IEEE Transactions on Parallel and Distributed Systems
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
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An algorithm is presented for generating a succinct encoding of all pairs shortest path information in a directed planar graph G with real-valued edge costs but no negative cycles. The algorithm runs in &Ogr;(pn) time, where n is the number of vertices in G, and p is the minimum cardinality of a subset of the faces that cover all vertices, taken over all planar embeddings of G. Linear-time algorithms are presented for various subproblems including that of finding an appropriate embedding of G and a corresponding face-on-vertex covering of cardinality &Ogr;(p), and of generating all pairs shortest path information in a directed outerplanar graph.