Rūsiņš
Freivalds
Duan
Ran
Peleg
David
equilibrium
length
model
adjustment
2013-01-01
price adjustment
425-436
allocation of money
https://scigraph.springernature.com/explorer/license/
combinatorial polynomial-time algorithm
linear Arrow–Debreu market
Arrow-Debreu markets
market
A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market
previous polynomial-time algorithms
time algorithm
utility
interior point method
Arrow-Debreu market model
https://doi.org/10.1007/978-3-642-39206-1_36
program
polynomial algorithm
exact solution
true
balanced flow
new method
polynomial time algorithm
We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities. Our algorithm views the allocation of money as flows and iteratively improves the balanced flow as in [Devanur et al. 2008] for Fisher’s model. We develop new methods to carefully deal with the flows and surpluses during price adjustments. In our algorithm, we need O(n6log(nU)) maximum flow computations, where n is the number of persons and U is the maximum integer utility, and the length of the numbers is at most O(nlog(nU)) to guarantee an exact solution. The previous polynomial time algorithms [Nenakov and Primak 1983, Jain 2007, Ye 2007] for this problem are based on solving convex programs using the ellipsoid algorithm or interior-point method.
flow computations
surplus
chapter
convex program
first combinatorial polynomial-time algorithm
2013
computation
problem
combinatorial polynomial algorithm
method
money
allocation
chapters
flow
solution
ellipsoid algorithm
market model
number
number of persons
persons
maximum flow computations
algorithm
Fisher model
2022-11-24T21:19
linear utility
pub.1034211474
dimensions_id
Max-Planck-Institut für Informatik, Saarbrücken, Germany
Max-Planck-Institut für Informatik, Saarbrücken, Germany
978-3-642-39206-1
978-3-642-39205-4
Automata, Languages, and Programming
Kurt
Mehlhorn
Marta
Kwiatkowska
Springer Nature - SN SciGraph project
Springer Nature
Information and Computing Sciences
Computation Theory and Mathematics
Fomin
Fedor V.
10.1007/978-3-642-39206-1_36
doi