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External memory priority queues with decrease-key and applications to graph algorithms

par Iacono, John ;Jacob, Riko;Tsakalidis, Konstantinos
Référence Leibniz international proceedings in informatics, 144, 60
Publication Publié, 2019-09-01

Article révisé par les pairs

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Résumé :

We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in (Formula presented.) amortized I/Os and operations ExtractMin and Delete in (Formula presented.) amortized I/Os, for any real ε ∈ (0, 1), using (Formula presented.) blocks. Previous I/O-efficient priority queues either support these operations in (Formula presented.) amortized I/Os [Kumar and Schwabe, SPDP’96] or support only operations Insert, Delete and ExtractMin in optimal (Formula presented.) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS’99]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in (Formula presented.) I/Os and operation Extract on K extracted elements in (Formula presented.) amortized I/Os, using O (N/B ) blocks. Previous results achieve (Formula presented.) B I/Os and (Formula presented.) I/Os, respectively [Buchsbaum et al., SODA’00]. Our results imply improved (Formula presented.) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V, E) with E = Ω (V 1+ε) , ε > 0 and V = Ω (M), which is equal to the I/O-optimal bound for sorting E values in external memory.