The.Algorithm.Design.Manual.Springer-Verlag.1998

Priority Queues
This arises, for example, in shortest path computations whenever we discover a shorter route to a
vertex v than we had previously established. Thus v has a higher priority of being accessed next.
Properly implemented and used, they lead to better performance on very large computations. Still,
they are sufficiently complicated that you shouldn't mess with them unless you really know what
you are doing.
Implementations: LEDA (see Section ) provides a complete collection of priority queues in C++,
including Fibonacci heaps, pairing heaps, Emde-Boas trees, and bounded height priority queues.
Fibonacci heaps are their default implementation.
SimPack/Sim++ is a library of routines for implementing discrete event simulations, built by Robert
Cubert and Paul Fishwick, of the University of Florida. Priority queues are integral to such
simulations, and Sim++ contains implementations of linked, binary, leftist, and calendar heaps [Bro88].
If you need a priority queue to control a simulation, check out http://www.cis.ufl.edu/
fishwick/simpack/simpack.html. An associated book [Fis95] describes model design using SimPack.
Bare bones implementations in C and Pascal of the basic priority queue data structures appear in
[GBY91]. Most notable is the inclusion of implementations of exotic priority queues such as P-trees and
pagodas. See Section for further details.
XTango (see Section ) is an algorithm animation system for UNIX and X-windows, that includes
animations of such advanced priority queue data structures as binomial and Fibonacci heaps, as well as a
spiffy animation of heapsort.
Many textbooks provide implementations of simple priority queues, including [MS91] (see Section ).
Algorithm 561 [Kah80] of the Collected Algorithms of the ACM is a Fortran implementation of a heap
(see Section ).
Notes: Good expositions on efficient heap construction algorithms include [Baa88, Ben86, CLR90,
Man89, MT90b]. See [GBY91] for a description of several exotic priority queues. Empirical
comparisons between priority queue data structures include [Jon86].
Bounded height priority queues are useful data structures in practice, but they do not have good worstcase
performance bounds when arbitrary insertions and deletions are permitted. However, von Emde
Boas priority queues [vEBKZ77] support insertion, deletion, search, max, and min operations
where each key is an element from 1 to n.
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