Resolving a Question about Randomized Fibonacci Heaps in the Negative
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چکیده
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 a special potential function where s is the number of operations on the heap requested so far. We first match this bound using an (apparently) different proof that reduces the analysis to the non-randomized case with high probability via a union bound. We then prove that randomized Fibonacci heaps, as originally defined, perform worse asymptotically then standard Fibonacci heaps. Specifically, while they match the amortized time bounds for every operation except delete-min, they can take O( √ n) amortized time for a single delete-min operation if an exponentially large (in n) number of heap operations are requested. A small modification can be used to bypass this issue, but we then show that even this modification fails by giving a request sequence for randomized Fibonacci heaps with ω(log s) expected average cost per delete-min.
منابع مشابه
Replacing Mark Bits with Randomness in Fibonacci Heaps
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...
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تاریخ انتشار 2013