An integer programming proof of Cook’s theorem of NP-completeness
نویسنده
چکیده
The theory of NP-completeness has its roots in a foundational result by Cook, who showed that Boolean satisfiability (SAT) is NP-complete and thus unlikely to admit an efficient solution. We prove an analogous result using binary integer programming in the place of SAT. The proof gives deeper insight into the theory of NP-completeness to operations researchers for whom the language of integer programming is more natural than that of Boolean logic.
منابع مشابه
What is Cook's theorem?
In this paper, we make a preliminary interpretation of Cook’s theorem presented in [1]. This interpretation reveals cognitive biases in the proof of Cook’s theorem that arise from the attempt of constructing a formula in CNF to represent a computation of a nondeterministic Turing machine. Such cognitive biases are due to the lack of understanding about the essence of nondeterminism, and lead to...
متن کاملOn Linear Arithmetic with Stars
We consider an extension of integer linear arithmetic with a star operator that takes closure under vector addition of the set of solutions of linear arithmetic subformula. We show that the satisfiability problem for this language is in NP (and therefore NP-complete). Our proof uses a generalization of a recent result on sparse solutions of integer linear programming problems. We present two co...
متن کاملLinear Arithmetic with Stars
We consider an extension of integer linear arithmetic with a “star” operator takes closure under vector addition of the solution set of a linear arithmetic subformula. We show that the satisfiability problem for this extended language remains in NP (and therefore NP-complete). Our proof uses semilinear set characterization of solutions of integer linear arithmetic formulas, as well as a general...
متن کاملSimulated annealing
Metaheuristics are general problem solving algorithms which abstract from the actual problem description. Therefore they can be easily applied to many optimization problems. Simulated annealing is a simple and fast metaheuristic with an analogy to metal processing. As metal particles generate a solid and regular structure when cooling slowing simulated annealing seeks a low-energy solution avoi...
متن کاملA note on the complexity of task scheduling with communication contention
Considering the contention for communication resources in task scheduling is discussed in [3]. Theorem 1 of [3] states the NP-completeness of the associated decision problem and the corresponding proof shows NP-completeness in the weak sense [2]. Here, a new proof is presented for Theorem 1 of [3] that shows NP-completeness in the strong sense. The proof is based on a reduction from the well-kn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014