Fast Fibonacci heaps with worst case extensions
Vladan Majerech

TL;DR
This paper introduces simplified, efficient Fibonacci heaps with worst-case guarantees, reducing overhead and maintaining optimal asymptotic times for key operations, suitable for practical implementation.
Contribution
It proposes a new approach to Fibonacci heaps that minimizes overhead and allows worst-case operation guarantees without complex violation list maintenance.
Findings
Achieved worst-case bounds for heap operations with reduced overhead
Implemented full DecreaseKey-Meld interface in the proposed heaps
Demonstrated practical implementation advantages using arrays over pointers
Abstract
We are concentrating on reducing overhead of heaps based on comparisons with optimal worstcase behaviour. The paper is inspired by Strict Fibonacci Heaps [1], where G. S. Brodal, G. Lagogiannis, and R. E. Tarjan implemented the heap with DecreaseKey and Meld interface in assymptotically optimal worst case times (based on key comparisons). In the paper [2], the ideas were elaborated and it was shown that the same asymptotical times could be achieved with a strategy loosing much less information from previous comparisons. There is big overhead with maintainance of violation lists in these heaps. We propose simple alternative reducing this overhead. It allows us to implement fast amortized Fibonacci heaps, where user could call some methods in variants guaranting worst case time. If he does so, the heaps are not guaranted to be Fibonacci until an amortized version of a method is called. Of…
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Taxonomy
TopicsSoftware Testing and Debugging Techniques · Complexity and Algorithms in Graphs · Parallel Computing and Optimization Techniques
