scholarly journals Submodular Flow Problem with a Nonseparable Cost Function

COMBINATORICA ◽  
1999 ◽  
Vol 19 (1) ◽  
pp. 87-109 ◽  
Author(s):  
Kazuo Murota
Keyword(s):  
Cost Function ◽  
Flow Problem ◽  
Submodular Flow

scholarly journals Competitive Equilibrium and Trading Networks: A Network Flow Approach

2020 ◽  
Author(s):  
Ozan Candogan ◽  
Markos Epitropou ◽  
Rakesh V. Vohra
Keyword(s):  
Network Flow ◽  
Competitive Equilibrium ◽  
Flow Problem ◽  
Comparative Statics ◽  
Bilateral Contracts ◽  
Submodular Flow ◽  
Competitive Equilibria ◽  
Trading Networks ◽  
The Impact ◽  
Shed Light

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

scholarly journals A combinatorial arc tolerance analysis for network flow problems

2005 ◽  
Vol 2005 (2) ◽  
pp. 83-94 ◽  
Author(s):  
P. T. Sokkalingam ◽  
Prabha Sharma
Keyword(s):  
Cost Function ◽  
Network Flow ◽  
Flow Problem ◽  
Tolerance Analysis ◽  
Network Flow Problems ◽  
Total Cost ◽  
Flow Problems ◽  
Optimal Flow ◽  
The Given ◽  
Total Cost Function

For the separable convex cost flow problem, we consider the problem of determining tolerance set for each arc cost function. For a given optimal flow x, a valid perturbation of cij(x) is a convex function that can be substituted for cij(x) in the total cost function without violating the optimality of x. Tolerance set for an arc(i,j) is the collection of all valid perturbations of cij(x). We characterize the tolerance set for each arc(i,j) in terms of nonsingleton shortest distances between nodes i and j. We also give an efficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in O(n3) time where n denotes the number of nodes in the given graph.

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