Contents 1 Average - Case Computational Complexity Theory 1

The Lattice Reduction Algorithm of Gauss: An Average Case Analysis

The lattice reduction algorithm of Gauss is shown to have an average case complexity which is asymptotic to a constant. Introduction. The “reduction” algorithm of Gauss plays an important r6le in several areas of computational number theory, principally in matters related to the reduction of integer lattice bases. It is also intimately connected with extensions to complex numbers of the Euclide...

Texts in Computational Complexity: Average-Case Complexity

Computational Complexity Theory

Being NP complete has been widely interpreted as being computationally intractable But NP completeness is a worst case concept Some NP complete problems are easy on average but some may not be How is one to know whether an NP complete problem is di cult on average The theory of average case computational complexity initiated by Levin about ten years ago is devoted to studying this problem This ...

Facility Location: Discrete Models and Local Search Methods

Discrete location theory is one of the most dynamic areas of operations research. We present the basic mathematical models used in this field, as well as their properties and relationship with pseudo-Boolean functions. We also investigate the theory of PLS-complete problems, average and worst case computational complexity of the local search algorithms, and approximate local search. Finally, we...

The University of Chicago Hierarchy Theorems and Resource Tradeoffs for Semantic Classes a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Computer Science By

Computational complexity theory studies the minimum resources (time, space, randomness etc.) to solve computational problems. Two fundamental questions in this area are: 1. Can more problems be solved given more of a given resource? A positive answer to this question is known as a hierarchy theorem. 2. Can one resource be traded off with another when solving a given problem? Such a result is kn...