prices of a general linear Arrow-Debreu market, where every agent can own

multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu

markets consider the case where each agent can own all of one good only. We

present an $\\tilde{\\mathcal{O}}((n+m)^7 \\log^3(UW))$ algorithm where $n$, $m$,

$U$ and $W$ refer to the number of agents, the number of goods, the maximal

integral utility and the maximum quantity of any good in the market

respectively. The algorithm refines the iterative algorithm of Duan, Garg and

Mehlhorn using several new ideas. We also identify the hard instances for

existing combinatorial algorithms for linear Arrow-Debreu markets. In

particular we find instances where the ratio of the maximum to the minimum

equilibrium price of a good is $U^{\\Omega(n)}$ and the number of iterations

required by the existing iterative combinatorial algorithms of Duan, and

Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the

two algorithms.

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