On the Board
Homework due today
Reading — Chapters 5 & 6
Important Properties of Algorithms
In Chapter 4, we saw a number of approaches to algorithm design — graph
traversals, divide and conquer, greedy, dynamic planning. Speaking in
broad terms, two properties of an algorithm should be critical concerns (in
this order)
• Correctness — The algorithm should solve the problem and produce a
correct answer. Correctness is the focus of Chapter 5.
For some problems, such as phonebook lookup, the correctness criterion
is simple and well defined: “Joe” is in the phonebook or he is not.
Sorting (as in bubblesort, mergesort, and insertion sort) is equally well
defined. For other problems, the criterion may not be well defined:
navigating from Rice to the Galleria, the greedy algorithm will make
locally optimal decisions that may lead to globally suboptimal solutions.
Is the suboptimal solution wrong? It leads to the Galleria. It is faster than
some of the paths. The greedy algorithm approximates the minimal-cost
path with a lower cost algorithm.
With an algorithm that produces approximate solutions, it is critical that
the designer and user both understand what results the algorithm
produces—in particular, whether the solution is exact or approximate. (In
some cases, we can bound the distance between the approximation and
the optimal solution!)
• Efficiency — How quickly can we solve the problem? Efficiency is the
focus of Chapter 6.
Going back to the first lecture, the parallel sort by first name was faster
(in clock time) than the insertion sort. To achieve that speed, it used all of
your brains in parallel. (Looking at total resource utilization, it may have
required more resources than the insertion sort.)
COMP 200: Elements of Computer Science
Fall 2004
Lecture 20: October 14, 2004
Introduction to Algorithmic Complexity
