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Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector
  • S. Fujishige
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1 May 1980
TLDR
The algorithms proposed in the present paper efficiently solve the problem of finding a lexicographically optimal flow in a network with multiple sources and sinks, which is a special case of the problem considered here. Expand
A combinatorial strongly polynomial algorithm for minimizing submodular functions
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employsExpand
A Note on Kelso and Crawford's Gross Substitutes Condition
TLDR
It is proved that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is anM?-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999). Expand
Polymatroidal Dependence Structure of a Set of Random Variables
  • S. Fujishige
  • Computer Science, Mathematics
  • Inf. Control.
  • 1 October 1978
TLDR
The present paper points out that the entropy function h is a β -function, i.e., a monotone non-decreasing and submodular function with h(O) = 0 and that the pair ( E, h ) is a polymatroid. Expand
A Submodular Function Minimization Algorithm Based on the Minimum-Norm Base ⁄
We consider an application of the minimum-norm-point algorithm to submodular function minimization. Although combinatorial polynomial algorithms for submodular function minimization (SFM) haveExpand
Structures of polyhedra determined by submodular functions on crossing families
  • S. Fujishige
  • Mathematics, Computer Science
  • Math. Program.
  • 1 June 1984
The present paper shows that for any submodular functionf on a crossing family with, if the polyhedron is nonempty, then there exist a unique distributive lattice with and a unique submodularExpand
Theory of submodular programs: A fenchel-type min-max theorem and subgradients of submodular functions
  • S. Fujishige
  • Mathematics, Computer Science
  • Math. Program.
  • 1 June 1984
TLDR
A convex (or concave) conjugate function of a submodular (or supermodular) function is defined and a Fenchel-type min-max theorem for sub modular and super modular functions is shown. Expand
ALGORITHMS FOR SOLVING THE INDEPENDENT-FLOW PROBLEMS
Given a capacitated network with the entrance· vertex set VI and the exit-vertex set V2 on which polymatroids are defmed, an independent flow is a flow in the network such that a vector correspondingExpand
An O(n log2n) algorithm for the optimal sink location problem in dynamic tree networks
TLDR
This paper presents an O(nlog2n) time algorithm for the sink location problem, in a dynamic network of tree structure where n is the number of vertices in the network, and shows that the quickest transshipment problem can be solved in O( nlog2 n) time if a given network is a tree and has a single sink. Expand
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