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Lecture Notes in Computer Science
Thorup and Zwick, in the seminal paper [Journal of ACM, 52(1), 2005, pp 1-24], showed that a weighted undirected graph on n vertices can be preprocessed in subcubic time to design a data structure which occupies only subquadratic space, and yet, for any pair of vertices, can answer distance query approximately in constant time. The data structure is termed as approximate distance oracle. Subsequently, there has been improvement in their preprocessing time, and presently the best knowndoi:10.1007/978-3-540-70575-8_50 fatcat:erqtijtkmzfxzj5othkv73zuz4