Computers and intractability a guide to the theory of np completeness. You can help by expanding it with reliably sourced entries. In 1972, richard karp wrote a paper showing many of the key problems in operations research to be np complete. Decision problems for which there is a polytime algorithm. I given a new problem x, a general strategy for proving it np complete is 1. Convert the matrix into lower triangular matrix by row transformations, then we know that principal. These are just my personal ideas and are not meant to be rigorous. This is the book to have if you are looking at p v np problems, and np completeness. It also provides adequate preliminaries regarding computational problems and computational models. Demonstrating np complete reductions other than garey and. If y is np complete and x 2npsuch that y p x, then x is np complete. Np complete problems are the hardest problems in np set. As there are hundreds of such problems known, this list is in no way. Most of the problems in this list are taken from garey and johnsons seminal book.
In computational complexity theory, a problem is npcomplete when it can be solved by a. What are the best self contained books that mainly serve the purpose of. Freeman, 1979 david johnson also runs a column in the journal journal of algorithms in the hcl. This is an online textbook on heuristic algorithms. The book features an appendix providing a thorough compendium of np complete problems which was updated in later printings of the book. Catalog of npcomplete problems, more uptodate than. It is made freely available by its author and publisher.
If x is an npcomplete problem, and y is a problem in np with the property. This list is in no way comprehensive there are more than 3000 known np complete problems. This is a list of some of the more commonly known problems that are np complete when expressed as decision problems. This graph has multiple edges between two verticesa feature we have not been allowing so far in this book, but one that is meaningful for this particular problem. This is a dynamic list and may never be able to satisfy particular standards for completeness. The focus on search problems and promise problems in this book is to be appreciated since many books neglect these topics. The focus of this book is the pversus np question and the theory of np completeness. Strategy 3sat sequencing problemspartitioning problemsother problems proving other problems np complete i claim. It covers the theory, and then provides a list of a problems that are np complete, broken down into sections, with details of how the problem has been proved to be np complete, i. This is a rough guide to the meaning of np complete. List of np complete problems from wikipedia, the free encyclopedia here are some of the more commonly known problems that are np complete when expressed as decision problems.
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