TY - GEN

T1 - On dynamic approximate shortest paths for planar graphs with worst-case costs

AU - Abraham, Ittai

AU - Chechik, Shiri

AU - Delling, Daniel

AU - Goldberg, Andrew V.

AU - Werneck, Renato F.

PY - 2016

Y1 - 2016

N2 - Given a base weighted planar graph Ginput on n nodes and parameters M, ∈ we present a dynamic distance oracle with 1 + ∈ stretch and worst case update and query costs of ∈-3M4· poly-log(n). We allow arbitrary edge weight updates as long as the shortest path metric induced by the updated graph has stretch of at most M relative to the shortest path metric of the base graph Ginput. For example, on a planar road network, we can support fast queries and dynamic traffic updates as long as the shortest path from any source to any target (including using arbitrary detours) is between, say, 80 and 3 miles-per-hour. As a warm-up we also prove that graphs of bounded treewidth have exact distance oracles in the dynamic edge model. To the best of our knowledge, this is the first dynamic distance oracle for a non-trivial family of dynamic changes to planar graphs with worst case costs of o(n1-2) both for query and for update operations.

AB - Given a base weighted planar graph Ginput on n nodes and parameters M, ∈ we present a dynamic distance oracle with 1 + ∈ stretch and worst case update and query costs of ∈-3M4· poly-log(n). We allow arbitrary edge weight updates as long as the shortest path metric induced by the updated graph has stretch of at most M relative to the shortest path metric of the base graph Ginput. For example, on a planar road network, we can support fast queries and dynamic traffic updates as long as the shortest path from any source to any target (including using arbitrary detours) is between, say, 80 and 3 miles-per-hour. As a warm-up we also prove that graphs of bounded treewidth have exact distance oracles in the dynamic edge model. To the best of our knowledge, this is the first dynamic distance oracle for a non-trivial family of dynamic changes to planar graphs with worst case costs of o(n1-2) both for query and for update operations.

UR - http://www.scopus.com/inward/record.url?scp=84963636063&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974331.ch53

DO - 10.1137/1.9781611974331.ch53

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AN - SCOPUS:84963636063

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 740

EP - 753

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

A2 - Krauthgamer, Robert

PB - Association for Computing Machinery

T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

Y2 - 10 January 2016 through 12 January 2016

ER -