Exact Distance Oracles for Planar Graphs with Failing Vertices

We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex u , target v and set X k failed vertices, such an oracle returns length shortest -to- path that avoids all vertices . propose can handle any number failures. show several tradeoffs between space, query time, preprocessing time. In particular, graph with n constant we Õ( )-size, Õ(√ )-query-time oracle. 1 then present space vs. time tradeoff: q ε [ 1,√ ], size k+1+o(1) / 2k answers queries ) For single failures ( = 1), our 2+o(1) 2 -size, improves over previously best known tradeoff Baswana et al. SODA 2012 by polynomial factors ≥ t ∈ (0,1/2]. multiple failures, no planarity exploiting results were known.