A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Introduction to algorithms
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Solving the Convex Cost Integer Dual Network Flow Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Geometric intersection problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
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We study here a convex optimization problem with variables subject to a given partial order. This problem is a generalization of the known maximum (or minimum) closure problem and the isotonic regression problem. The algorithm we devise has complexity O(mnlog n2/m + n log U), for U the largest interval of values associated with a variable. For the quadratic problem and for the closure problem the complexity of our algorithm is strongly polynomial, O(mnlog n2/m). For the isotonic regression problem the complexity is O(n log U).