Related papers: Why some heaps support constant-amortized-time dec…

We improve the lower bound on the amortized cost of the decrease-key operation in the pure heap model and show that any pure-heap-model heap (that has a \bigoh{\log n} amortized-time extract-min operation) must spend \bigom{\log\log n}…

Since the invention of the pairing heap by Fredman, Sedgewick, Sleator, and Tarjan, it has been an open question whether this or any other simple "self-adjusting" heap supports decrease-key operations in $O(\log\log n)$ time, where $n$ is…

We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find-min requires O(1) worst-case time, insert, meld and decrease-key require O(1) amortized time, and delete-min requires $O(\log n)$ amortized…

The pairing heap is a simple "self-adjusting" implementation of a heap (priority queue). Inserting an item into a pairing heap or decreasing the key of an item takes O(1) time worst-case, as does melding two heaps. But deleting an item of…

The smooth heap and the closely related slim heap are recently invented self-adjusting implementations of the heap (priority queue) data structure. We analyze the efficiency of these data structures. We obtain the following amortized bounds…

The Fibonacci heap is a classic data structure that supports deletions in logarithmic amortized time and all other heap operations in O(1) amortized time. We explore the design space of this data structure. We propose a version with the…

A Fibonacci heap is a deterministic data structure implementing a priority queue with optimal amortized operation costs. An unfortunate aspect of Fibonacci heaps is that they must maintain a "mark bit" which serves only to ensure efficiency…

Improving the structure and analysis in \cite{elm0}, we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an $O(\log \log{n})$ in \cite{elm0}) and the same amortized bounds for all other operations.…

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…

We show the $O(\log n)$ time extract minimum function of efficient priority queues can be generalized to the extraction of the $k$ smallest elements in $O(k \log(n/k))$ time (we define $\log(x)$ as $\max(\log_2(x), 1)$.), which we prove…

We introduce a new family of priority-queue data structures: partition-based simple heaps. The structures consist of $O(\log n)$ doubly-linked lists; order is enforced among data in different lists, but the individual lists are unordered.…

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.

Naively storing a counter up to value $n$ would require $\Omega(\log n)$ bits of memory. Nelson and Yu [NY22], following work of [Morris78], showed that if the query answers need only be $(1+\epsilon)$-approximate with probability at least…

Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an…

We revisit multipass pairing heaps and path-balanced binary search trees (BSTs), two classical algorithms for data structure maintenance. The pairing heap is a simple and efficient "self-adjusting" heap, introduced in 1986 by Fredman,…

A heap is a dynamic data structure that stores a set of labeled values under the following operations: pop returns the minimum value of the heap, Push($x_i$) pushes a new value $x_i$ onto the heap, and DecreaseKey($i$, $v$) decreases the…

We introduce the hollow heap, a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and delete-min take $O(1)$ time, worst case as well as amortized; delete and…

The smooth heap is a recently introduced self-adjusting heap [Kozma, Saranurak, 2018] similar to the pairing heap [Fredman, Sedgewick, Sleator, Tarjan, 1986]. The smooth heap was obtained as a heap-counterpart of Greedy BST, a binary search…

We investigate the limits of one of the fundamental ideas in data structures: fractional cascading. This is an important data structure technique to speed up repeated searches for the same key in multiple lists and it has numerous…

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…