Utilizing Shelve Slots: Sufficiency Conditions for Some Easy Instances of Hard Problems

Distinguishing Easy and Hard Instances

Biased random satisfiability problems: from easy to hard instances.

In this paper we study biased random K -satisfiability ( K -SAT) problems in which each logical variable is negated with probability p . This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K -SAT problems. The exact solution of 1-SAT case is given. The critical point of K -SAT problems and results...

Hard Instances of Hard Problems

This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time many one reductions It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity It follows that every weakly hard problem has a dense set of such maximally hard instances This extends the theorem ...

Sparse instances of hard problems

In this thesis, we use and refine methods of computational complexity theory to analyze the complexity of sparse instances, such as graphs with few edges or formulas with few constraints of bounded width. Two natural questions arise in this context: • Is there an efficient algorithm that reduces arbitrary instances of an NP-hard problem to equivalent, sparse instances? • Is there an algorithm t...

Random constraint satisfaction: Easy generation of hard (satisfiable) instances

In this paper, we try to further demonstrate that the models of random CSP instances proposed by Xu and Li are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features. First, it is quite easy to generate random instances of any arity since no particular structure has to be integrated, or property enforced, in such instances. Then, the existen...