Journal of Complexity
Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
An ellipsoid algorithm for the computation of fixed points
Journal of Complexity - Festschrift for Joseph F. Traub, Part 1
Computational complexity of fixed points and intersection points
Journal of Complexity
Approximating fixed points of weakly contracting mappings
Journal of Complexity
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A two-dimensional bisection envelope algorithm for fixed points
Journal of Complexity
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Profit-maximizing multicast pricing by approximating fixed points [Extended Abstract]
Proceedings of the 4th ACM conference on Electronic commerce
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Algorithm 825: A deep-cut bisection envelope algorithm for fixed points
ACM Transactions on Mathematical Software (TOMS)
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A duality model of TCP and queue management algorithms
IEEE/ACM Transactions on Networking (TON)
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
A recursive algorithm for the infinity-norm fixed point problem
Journal of Complexity
The spending constraint model for market equilibrium: algorithmic, existence and uniqueness results
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Paths Beyond Local Search: A Tight Bound for Randomized Fixed-Point Computation
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On graph-theoretic lemmata and complexity classes
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Quantum Separation of Local Search and Fixed Point Computation
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
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We prove a new discrete fixed point theorem for direction-preserving functions defined on integer points, based on a novel characterization of boundary conditions for the existence of fixed points. The theorem allows us to derive an improved algorithm for finding such a fixed point. We also develop a new lower bound proof technique. Together, they allow us to derive an asymptotic matching bound for the problem of finding a fixed point in a hypercube of any constantly bounded finite dimension. Exploring a linkage with the approximation version of the continuous fixed point problem, we obtain asymptotic matching bounds for the complexity of the approximate Brouwer fixed point problem in the continuous case for Lipschitz functions. It settles a fifteen-years-old open problem of Hirsch, Papadimitriou, and Vavasis by improving both the upper and lower bounds. Our characterization for the existence of a fixed point is also applicable to functions defined on nonconvex domains, which makes it a potentially useful tool for the design and analysis of algorithms for fixed points in general domains.