Friday, 16:15 - 16:40 h, Room: H 3008

 

Laszlo VĂ©gh
Concave generalized flows with applications to market equilibria

 

Abstract:
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an ε-approximate solution in O(m(m+log n)log(MUm/ε)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters.
This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant
of the Fat-Path algorithm by Goldberg, Plotkin and Tardos, not using any cycle cancellations.
We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately extends these market models to more general settings. We also obtain a combinatorial algorithm for nonsymmetric Arrow-Debreu Nash bargaining, settling an open question by Vazirani.

 

Talk 3 of the invited session Fri.3.H 3008
"Faster algorithms for network flow problems" [...]
Cluster 2
"Combinatorial optimization" [...]

 

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