Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
Shortest path queries in planar graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Preprocessing an undirected planar network to enable fast approximate distance queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Oracles for distances avoiding a link-failure
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded Incremental Computation
Bounded Incremental Computation
Concrete Math
On-Line Algorithms for Shortest Path Problems on Planar Digraphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Compact Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Adjacency queries in dynamic sparse graphs
Information Processing Letters
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Three-coloring triangle-free planar graphs in linear time
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Three-coloring triangle-free planar graphs in linear time
ACM Transactions on Algorithms (TALG)
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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We present a new approach for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G = (V, E), one can build in O(|V|) time a data structure, which allows to check in O(1) time whether two given vertices are at distance at most k in G and if so a shortest path between them is returned. Graph G can be undirected as well as directed.Our data structure works in fully dynamic environment. It can be updated in O(1) time after removing an edge or a vertex while updating after an edge insertion takes polylogarithmic amortized time. Besides deleting elements one can also disable ones for some time. It is motivated by a practical situation where nodes or links of a network may be temporarily out of service.Our results can be easily generalized to other wide classes of graphs---for instance we can take any minor-closed family of graphs.