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

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Figure

Table 1: Asymptotic amortized I/O-bounds of cache-aware and cache-oblivious priority queueoperations (respectively, above and below the horizontal line) on N elements and real ε ∈ (0, 1).∗Expected I/Os.
Figure 1: Overview of an x-treap D on “key” × “partial order” space.Black/white dotsrepresent elements in the front/rear buffers, respectively
Figure 3: A new x-treap after operation Initialize.
Figure 4: The top and middle buffers and the top upper level buffers, (a) before operationFlush-Up, (b) after Step 5 and (c) after Step 6 .
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