# The Algorithm Design Manual

# The Algorithm Design Manual

Language: English

Pages: 730

ISBN: 1848000693

Format: PDF / Kindle (mobi) / ePub

Most professional programmers that I’ve encountered are not well prepared to tackle algorithm design problems. This is a pity, because the techniques of algorithm design form one of the core practical technologies of computer science. Designing correct, efficient, and implementable algorithms for real-world problems requires access to two distinct bodies of knowledge: • Techniques – Good algorithm designers understand several fundamental algorithm design techniques, including data structures, dynamic programming, depth first search, backtracking, and heuristics. Perhaps the single most important design technique is modeling, the art of abstracting a messy real-world application into a clean problem suitable for algorithmic attack. • Resources – Good algorithm designers stand on the shoulders of giants. Rather than laboring from scratch to produce a new algorithm for every task, they can figure out what is known about a particular problem. Rather than re-implementing popular algorithms from scratch, they seek existing implementations to serve as a starting point. They are familiar with many classic algorithmic problems, which provide sufficient source material to model most any application. This book is intended as a manual on algorithm design, providing access to combinatorial algorithm technology for both students and computer professionals.

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problems in this book for which we couldn’t find any efficient algorithm. The theory of NP-completeness provides the tools needed to show that all these problems are on some level really the same problem. The key idea to demonstrating the hardness of a problem is that of a reduction, or translation, between two problems. The following allegory of NP-completeness may help explain the idea. A bunch of kids take turns fighting each other in the schoolyard to prove how “tough” they are. Adam beats

specify which edge should be selected next. It might seem reasonable to next select the edge whose endpoints have the highest degree. However, this does not improve the worst-case bound and just makes it more difficult to analyze. A postprocessing cleanup step can’t hurt – The flip side of designing simple heuristics is that they can often be modified to yield better-in-practice solutions without weakening the approximation bound. For example, a postprocessing step that deletes any unnecessary

similar to [CP90]. dmclique.c uses a “semi-exhaustive greedy” scheme for finding large independent sets from [JAMS91]. Kreher and Stinson [KS99] provide branch-and-bound programs in C for finding the maximum clique using a variety of lower-bounds, available at http://www.math.mtu.edu/~kreher/cages/Src.html. GOBLIN (http://www.math.uni-augsburg.de/~fremuth/goblin.html) implements branch-and-bound algorithms for finding large cliques. They claim to be able to work with graphs as large as 150 to

objects such as line segments, polygons, and polyhedra. Books with chapters discussing such problems include [dBvKOS00, CLRS01, PS85]. Preparata and Shamos [PS85] provide a good exposition on the special case of finding intersections and unions of axis-oriented rectangles—a problem that arises often in VLSI design. An optimal O(n lg n + k) algorithm for computing line segment intersections is due to Chazelle and Edelsbrunner [CE92]. Simpler, randomized algorithms achieving the same time bound

compare different algorithms for raw speed. Finding good test data can be surprisingly difficult. Here are some pointers: TSPLIB – This well-respected library of test instances for the traveling salesman problem [Rei91] provides the standard collection of hard instances of TSPs. TSPLIB instances are large, real-world graphs, derived from applications such as circuit boards and networks. TSPLIB is available from http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/. Somewhat older