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- W2068243119 abstract "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." @default.
- W2068243119 created "2016-06-24" @default.
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- W2068243119 date "2006-07-01" @default.
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- W2068243119 title "Oracles for bounded-length shortest paths in planar graphs" @default.
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- W2068243119 doi "https://doi.org/10.1145/1159892.1159895" @default.
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