A SELECTION-BASED SORTING
ALGORITHM
Here is one way to sort a list of size n via divide and
conquer. First identify the k 1
elements that would occupy positions n/k, 2n/k, 3n/k, . . . ,
(k 1)n/k in th
WHAT IS A SORTING NETWORK
A sorting network is a circuit that receives n inputs, , and
permutes
them to produce n outputs, , such that the outputs satisfy
y0 y 1
y2 . . . yn1. For brevity, we often r
CONVEX HULL OF A 2D POINT SET
The 2D convex hull algorithm presented in this section is a
representative example of
geometric problems that are encountered in image
processing and computer vision appl
ALTERNATIVE SORTING
ALGORITHMS
Much of the complexity of the parallel sorting algorithm
described in Section 6.3 is
related to our insistence that the k subproblems resulting
at the end be exactly of
FIGURES OF MERIT FOR SORTING
NETWORKS
Is the sorting network shown in Fig. 7.4 the best possible
4-sorter? To answer this
question, we need to specify what we mean by the best nsorter. Two figures of
DESIGN OF SORTING NETWORKS
There are many ways to design sorting networks, leading
to different results with respect
to the figures of merit defined in Section 7.2. For example,
Fig. 7.7 shows a 6-sor
SEARCHING AND DICTIONARY
OPERATIONS
Searching is one of the most important operations on
digital computers and consumes
a great deal of resources. A primary reason for sorting, an
activity that has be
SELECTION NETWORKS
If we need the kth smallest value among n inputs, then
using a sorting network would
be an overkill in that an n-sorter does more than what is
required to solve our (n, k) selection
CLASSES OF SORTING NETWORKS
A class of sorting networks that possess the same
asymptotic (log2 n) delay and (n
log2 n) cost as Batcher sorting networks, but that offer
some advantages, are the periodi
BATCHER SORTING NETWORKS
Batchers ingenious constructions date back to the early
1960s (published a few years
later) and constitute some of the earliest examples of
parallel algorithms. It is remarkab