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Stable Networks and Product Graphs
Tomás Feder

Memoirs of the American Mathematical Society
1995; 223 pp; softcover
Volume: 116
ISBN-10: 0-8218-0347-6
ISBN-13: 978-0-8218-0347-9
List Price: US$54
Individual Members: US$32.40
Institutional Members: US$43.20
Order Code: MEMO/116/555
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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.


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
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