Monotone Operations and Monotone Groups∗
نویسندگان
چکیده
We survey an algebraic approach to proving impossibility results in distributed computing. The approach is emerging around monotone groups, a new class of algebraic groups we define here as a tight suit to monotone Read&Modify&Write (or RMW) operations in a distributed system. The yields of this approach have been the first impossibility results for implementations of monotone RMW operations that are based on switching networks, a class of concurrent, low-contention data structures in distributed computing. ∗This work has been partially supported by the Future and Emerging Technologies program of the European Union under EU contracts 001907 (DELIS) and 015964 (AEOLUS), and by research funds from Rensselaer Polytechnic Institute and University of Cyprus. †Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180. Email: [email protected] ‡Department of Computer Science, University of Cyprus, Nicosia CY-1678, Cyprus. Email: [email protected] §Department of Computer Engineering and Informatics, University of Patras, 265 00 Patras, Greece, & Research and Academic Computer Technology Institute, 261 10 Patras, Greece. Email: [email protected]
منابع مشابه
A SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...
متن کاملSome results on $L$-complete lattices
The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...
متن کاملThe Cost of Concurrent, Low-Contention Read-Modify-Write
In this work, we embark on a study of the possibility (or impossibility), and the corresponding costs, of devising concurrent, low-contention implementations of atomic Read-Modify-Write operations (abbreviated as RMW), in a distributed system. We consider a natural class of RMW operations which give rise to a certain class of algebraic groups that we introduce here and call monotone groups. Our...
متن کاملWeak differentiability of solutions to SDEs with semi-monotone drifts
In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift. To prove this formula, we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded.
متن کاملA Hybrid Proximal Point Algorithm for Resolvent operator in Banach Spaces
Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...
متن کامل