A network is a collection of gates, each with many inputs and many outputs, where links join individual outputs to individual inputs of gates; the unlinked inputs and outputs of gates are viewed as inputs and outputs of the network. A stable configuration assigns values to inputs, outputs, and links in a network, to ensure that the gate equations are satisfied. The problem of finding stable configurations in a network is computationally hard. In this work, Feder restricts attention to gates that satisfy a nonexpansiveness condition requiring small perturbations at the inputs of a gate to have only a small effect at the outputs of the gate. The stability question on the class of networks satisfying this local nonexpansiveness condition contains stable matching as a main example, and defines the boundary between tractable and intractable versions of network stability.

Readership

Research mathematicians.

Table of Contents

• Abstract
• Acknowledgements
• Introduction
• Preliminaries
• Stability in nonexpansive networks
• Optimization and enumeration
• Stable matching
• Metric networks and product graphs
• Bibliography
• Index