Abstract
We introduce an improved structure of distance sensitivity oracle (DSO). The task is to pre-process a non-negatively weighted graph so that a data structure can quickly answer replacement path length for every triple of source, terminal and failed vertex. The previous best algorithm [Bernstein and Karger, 2009] constructs in time (\(\tilde{O}(\cdot )\) suppresses poly-logarithmic factors.) \(\tilde{O}(mn)\) a distance sensitivity oracle of size \(O(n^2\log n)\) that processes queries in O(1) time. As an improvement, our oracle takes up \(O(n^2)\) space, while preserving O(1) query efficiency and \(\tilde{O}(mn)\) preprocessing time. One should notice that space complexity and query time of our novel data structure are asymptotically optimal.
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Duan, R., Zhang, T. (2017). Improved Distance Sensitivity Oracles via Tree Partitioning. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_30
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DOI: https://doi.org/10.1007/978-3-319-62127-2_30
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