Replacing Mark Bits with Randomness in Fibonacci Heaps
نویسندگان
چکیده
A Fibonacci heap is a deterministic data structure implementing a priority queue with optimal amortized asymptotic operation costs. An unaesthetic aspect of Fibonacci heaps is that they must maintain a “mark bit” which serves only to ensure efficiency of heap operations, not their correctness. Karger proposed a simple randomized variant of Fibonacci heaps in which mark bits are replaced by coin flips. This modified data structure still has expected amortized cost O(1) for insert, decrease-key, and merge. Karger conjectured that this data structure has expected amortized cost O(log s) for delete-min, where s is the number of heap operations. In this paper, we give a tight analysis of randomized Fibonacci heaps, resolving Karger’s conjecture. Specifically, we obtain matching upper and lower bounds of Θ(log s/ log log s) for the runtime of delete-min. We also prove a tight lower bound of Ω( √ n) on delete-min in terms of the number of heap elements n. Finally, we give a simple additional modification to these heaps which yields a tight runtime O(log n/ log log n) for delete-min. ∗[email protected] †[email protected] 1 ar X iv :1 40 7. 25 69 v2 [ cs .D S] 1 1 Ju l 2 01 4
منابع مشابه
Resolving a Question about Randomized Fibonacci Heaps in the Negative
In this project, we study a randomized variant of Fibonacci heaps where instead of using mark bits, one flips coins in order to determine whether to cascade bringing nodes into the root list. Although it seems intuitive that such heaps should have the same expected performance as standard Fibonacci heaps—and Karger has conjectured as such—the only previous work was an O(log s) upper bound using...
متن کاملPairing Heaps are Sub - optimalbyMichael
Pairing heaps were introduced as a self-adjusting alternative to Fibonacci heaps. They provably enjoy log n amortized costs for the standard heap operations. Although it has not been veri ed that pairing heaps perform the decrease key operation in constant amortized time, this has been conjectured and extensive experimental evidence supports this conjecture. Moreover, pairing heaps have been ob...
متن کاملRelaxed Fibonacci heaps: An alternative to Fibonacci heaps with worst case rather than amortized time bounds
متن کامل
Relaxed Fibonacci heaps : An alternative to Fibonacci heaps with worst case rather than amortized time bounds ∗ Chandrasekhar
We present a new data structure called relaxed Fibonacci heaps for implementing priority queues on a RAM. Relaxed Fibonacci heaps support the operations find minimum, insert, decrease key and meld, each in O(1) worst case time and delete and delete min in O(log n) worst case time. Introduction The implementation of priority queues is a classical problem in data structures. Priority queues find ...
متن کاملImproved Upper Bounds for Pairing Heaps
Pairing heaps are shown to have constant amortized time Insert and Meld, thus showing that pairing heaps have the same amortized runtimes as Fibonacci heaps for all operations but Decrease-Key.
متن کامل