Single source distance oracle for planar digraphs avoiding a failed node or link

Authors:
Surender Baswana;Utkarsh Lath;Anuradha S. Mehta
Affiliations:
I.I.T. Kanpur, India;I.I.T. Kanpur, India;I.I.T. Kanpur, India
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

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Abstract

Let G = (V, E) be a directed planar graph on n = |V| vertices, and let s ε V be any fixed source vertex. We show that G can be preprocessed in O(n polylog n) time to build a data structure of O(n polylog n) size which can answer the following query in O(log n) time for any u, v ε V: report distance from s to v in the graph G\{u} We also address the all-pairs version of this problem and present a data structure with O(n√n polylog n) preprocessing time and space which guarantees O(√n polylog n) query time.