Exact Exponential Algorithms - Fedor Fomin & Dieter Kratsch {Springer} [Seduction28]

For a long time computer scientists have distinguished between fast and slow algorithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms.

There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable.

Every combinatorial problem is solvable in finite time by enumerating all possible solutions, i. e. by brute force search. But is brute force search always unavoidable? Definitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved significantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

The book is intended for advanced students and researchers in computer science, operations research, optimization and combinatorics.

About the Authors

The authors are highly regarded academics and educators in theoretical computer science, and in algorithmics in particular.