Matching 2-lattice polyhedra: finding a maximum vector
Discrete Mathematics
Two-lattice polyhedra: duality and extreme points
Discrete Mathematics
Approximation algorithms
Journal of Combinatorial Theory Series B
A linear programming formulation of Mader's edge-disjoint paths problem
Journal of Combinatorial Theory Series B
Packing Non-Zero A-Paths In Group-Labelled Graphs
Combinatorica
Packing Non-Returning A-Paths*
Combinatorica
A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Min-cost multiflows in node-capacitated undirected networks
Journal of Combinatorial Optimization
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In this paper we propose a (semi-strongly) polynomial time algorithm to find a maximum packing subject to node-capacities, and thus we obtain a generalization of Keijsper, Pendavingh and Stougie algorithm concerning edge-capacities. Our method is based on Gerards' strongly polynomial time algorithm to find a maximum b-matching in a graph, which is based on a so-called Proximity Lemma. Our node-capacitated A-path packing algorithm first constructs a maximum fractional packing by using an ellipsoid method subroutine, then takes its integer part to obtain a near-optimal integral packing, and finally we construct a maximum integer packing by a short sequence of augmentations. This short sequence of augmentations is constructed by applying the version of Gerards' Proximity Lemma, specially formulated for the node-capacitated A-path packing problem. In addition, we also state some related results on the fractional packing problem. We prove the primal- and dual integrality of the corresponding linear program. We mention that the fractional packing problem reduces to the matroid fractional matching problem.