Fixed Point Computation Problems and Facets of Complexity (Invited Talk)

Author Mihalis Yannakakis

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Author Details

Mihalis Yannakakis
  • Department of Computer Science, Columbia University, 455 Computer Science Building, 1214 Amsterdam Avenue, New York, NY 10027, USA

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Mihalis Yannakakis. Fixed Point Computation Problems and Facets of Complexity (Invited Talk). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Many problems from a wide variety of areas can be formulated mathematically as the problem of computing a fixed point of a suitable given multivariate function. Examples include a variety of problems from game theory, economics, optimization, stochastic analysis, verification, and others. In some problems there is a unique fixed point (for example if the function is a contraction); in others there may be multiple fixed points and any one of them is an acceptable solution; while in other cases the desired object is a specific fixed point (for example the least fixed point or greatest fixed point of a monotone function). In this talk we will discuss several types of fixed point computation problems, their complexity, and some of the common themes that have emerged: classes of problems for which there are efficient algorithms, and other classes for which there seem to be serious obstacles.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Fixed Point
  • Polynomial Time Algorithm
  • Computational Complexity


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