Signal Processing Structures for Solving Conservative Constraint Satisfaction Problems

TL;DR

This paper introduces verifiable conditions for using conservative signal processing structures to solve constraint satisfaction problems efficiently, with proven convergence and robustness in asynchronous and uncertain environments.

Contribution

It provides a set of practical, verifiable conditions for applying conservative signal processing structures to constraint satisfaction problems, including analysis of convergence and robustness.

Findings

Structures have desirable convergence properties

Robustness to communication and processing delays

Connections to optimization theory established

Abstract

This primary purpose of this paper is to succinctly state a number of verifiable and tractable sufficient conditions under which a particular class of conservative signal processing structures may be readily used to solve a companion class of constraint satisfaction problems using both synchronous and asynchronous implementation protocols. In particular, the mentioned class of structures is shown to have desirable convergence and robustness properties with respect to various uncertainties involving communication and processing delays. Essential ingredients to the arguments herein involve blending together functional composition methods, conservation principles, asynchronous signal processing implementation protocols, and methods of homotopy. Numerical experiments complement the theoretical presentation and connections to optimization theory are made.