Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
Minimization of an M-convex function
Discrete Applied Mathematics
Mathematical Programming: Series A and B
M-Convex Function on Generalized Polymatroid
Mathematics of Operations Research
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
A Coordinatewise Domain Scaling Algorithm for M-convex Function Minimization
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Quasi M-convex and L-convex functions: quasiconvexity in discrete optimization
Discrete Applied Mathematics - Submodularity
Mathematics of Operations Research
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M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272; Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization.