Abstract
Up to now, we designed algorithms only for those optimization problems which allow an efficient (that is, polynomial) solution. This chapter is devoted to NP-complete problems; we use the Travelling Salesman Problem introduced in Chapter 1 and shown to be NP-complete in Chapter 2 as the standard example. We saw in Chapter 2 that NP-complete problems are a class of problems for which no good algorithms are known and it is quite likely even that no such algorithms exist. Now we consider the question how such ‘hard’ problems might be handled. Possible approaches include approximation techniques, heuristics, relaxations, post-optimization, local optimums, complete enumeration and several more. We explain all the techniques by using the TSP which can serve as a paradigm for a difficult problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jungnickel, D. (1999). A Hard Problem: The TSP. In: Graphs, Networks and Algorithms. Algorithms and Computation in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03822-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-662-03822-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03824-6
Online ISBN: 978-3-662-03822-2
eBook Packages: Springer Book Archive