Priority queues and double-ended priority queues are fundamental data types in Computer Science, and various data structures have been proposed to implement them. In particular, diamond deques, interval heaps, min-max-pair heaps, and twin-heaps provide implicit structures for double-ended priority queues. Although these heap-like structures are essentially the same when they are presented in an...

A priority queue transforms an input permutation cr of some set of size n into an output permutation z. It is shown that the number of such pairs (a, z) is (n + 1)"1 Some related enumerative and algorithmic questions are also considered.

Machines whose sole function is to re-order their input data are considered. Every such machine defines a set of allowable input-output pairs of permutations. These sets are studied in terms of the minimal disallowed pairs (the basis). Some allowable sets with small bases are considered including the one defined by a priority queue machine. For more complex machines defined by two or more prior...

We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and pq, for prime numbers p, q with q|p − 1. We also show that certain twisting deformation of the symmetric group is simple as a Hopf algebra. On the other hand, we p...

In this paper we show that the widely used normalization constraint ∑ n i=1 wi = 1 does not apply to the priority vectors associated with reciprocal relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalization may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalizatio...

In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N) space E77].

A k-bounded priority queue transforms an input sequence CT into an output sequence z which is a re-ordering of the sequence c while never storing more than k elements during the transformation. We consider the set of all such related pairs (a, 7) in both the case that cs is a binary sequence and the case that o is a permutation of 1,2,. , n. We derive properties of this relation and use it to d...

The heap-on-top (hot) priority queue data structure 6] improves on the best known times for Dijkstra's shortest path algorithm. It also has very good practical performance and is robust over a wide range of graph types. The heart of Dijkstra's algorithm is a monotone priority queue, that is, a priority queue where no element on the queue ever becomes smaller than the most recently extracted ele...