CSPs and Connectedness: P/NP Dichotomy for Idempotent, Right Quasigroups

Author

McGrail, Robert W. ; Belk, James ; Garber, Solomon ; Wood, Japheth ; Fish, Benjamin

Author_Institution

Reem Kayden Center for Sci. & Comput. Bard Coll., Annandle-on-Hudson, NY, USA

fYear

2014

fDate

22-25 Sept. 2014

Firstpage

367

Lastpage

374

Abstract

In the 1990´s, Jeavons showed that every finite algebra corresponds to a class of constraint satisfaction problems. Vardi later conjectured that idempotent algebras exhibit P/NP dichotomy: Every non NP-complete algebra in this class must be tractable. Here we discuss how tractability corresponds to connectivity in Cayley graphs. In particular, we show that dichotomy in finite idempotent, right quasi groups follows from a very strong notion of connectivity. Moreover, P/NP membership is first-order axiomatizable in involutory quandles.

Keywords

algebra; computational complexity; constraint satisfaction problems; graph theory; CSPs; Cayley graph connectivity; NP-complete algebra; P/NP membership; P/NP-complete dichotomy; constraint satisfaction problems; finite idempotent quasigroup dichotomy; first-order axiomatization; idempotent algebras; involutory quandles; right quasigroups; Algebra; Educational institutions; Marine animals; Polynomials; Roads; Scientific computing; Involutory Quandles; Malcev Term; P/NP Dichotomy; Right Quasigroups;

fLanguage

English

Publisher

ieee

Conference_Titel

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on

Conference_Location

Timisoara

Print_ISBN

978-1-4799-8447-3

Type

conf

DOI

10.1109/SYNASC.2014.56

Filename

7034706