Related papers: Near-Optimal Heaps and Dijkstra on Pointer Machine…

In this paper we prove that Dijkstra's shortest-path algorithm, if implemented with a sufficiently efficient heap, is universally optimal in its running time, and with suitable small additions is also universally optimal in its number of…

Let G be a weighted (directed) graph with n vertices and m edges. Given a source vertex s, Dijkstra's algorithm computes the shortest path lengths from s to all other vertices in O(m + n log n) time. This bound is known to be worst-case…

Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap…

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…

A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Omega(log log n / log log log n) amortized time on the decrease-key operation (given O(log n) amortized-time…

The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…

Dynamic memory issues are hard to locate and may cost much of a development project's efforts and was repeatedly reported similarly afterwards independently by different persons. Verification as one formal method may proof a given program's…

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}…

The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

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…

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…

Hopsets and spanners are fundamental graph structures, playing a key role in shortest path computation, distributed communication, and more. A (near-exact) hopset for a given graph $G$ is a (small) subset of weighted edges $H$ that when…

We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…

In this paper, we review existing points-to Separation Logics for dynamic memory reasoning and we find that different usages of heap separation tend to be an obstacle. Hence, two total and strict spatial heap operations are proposed upon…

The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…

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…

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…

Emerging workloads, such as graph processing and machine learning are approximate because of the scale of data involved and the stochastic nature of the underlying algorithms. These algorithms are often distributed over multiple machines…

This paper explores the notion of approximate data structures, which return approximately correct answers to queries, but run faster than their exact counterparts. The paper describes approximate variants of the van Emde Boas data…