## In Some Curved Spaces, One Can Solve NP-Hard Problems in Polynomial Time

Citations: | 6 - 6 self |

### BibTeX

@MISC{Kreinovich_insome,

author = {Vladik Kreinovich and Maurice Margenstern and Université Paul and Verlaine Metz},

title = {In Some Curved Spaces, One Can Solve NP-Hard Problems in Polynomial Time},

year = {}

}

### OpenURL

### Abstract

In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NP-hard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NP-hard. It is well known that many important practical problems are NP-hard; see, e.g., [11, 14, 27]. Under the usual hypothesis that P̸=NP, NP-hardness has the following intuitive meaning: every algorithm which solves all instances of the corresponding problem requires, for