Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Interior point algorithms for network flow problems
Advances in linear and integer programming
Bundle-based relaxation methods for multicommodity capacitated fixed charge network design
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Spectral Analysis of (Sequences of) Graph Matrices
SIAM Journal on Matrix Analysis and Applications
A Specialized Interior-Point Algorithm for Multicommodity Network Flows
SIAM Journal on Optimization
A Study of Preconditioners for Network Interior Point Methods
Computational Optimization and Applications
A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems
INFORMS Journal on Computing
New Preconditioners for KKT Systems of Network Flow Problems
SIAM Journal on Optimization
A Computational Study of Cost Reoptimization for Min-Cost Flow Problems
INFORMS Journal on Computing
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Support-graph preconditioners have been shown to be a valuable tool for the iterative solution, via a Preconditioned Conjugate Gradient method, of the KKT systems that must be solved at each iteration of an Interior Point algorithm for the solution of Min Cost Flow problems. These preconditioners extract a proper triangulated subgraph, with "large" weight, of the original graph: in practice, trees and Brother-Connected Trees (BCTs) of depth two have been shown to be the most computationally efficient families of subgraphs. In the literature, approximate versions of the Kruskal algorithm for maximum-weight spanning trees have most often been used for choosing the subgraphs; Prim-based approaches have been used for trees, but no comparison have ever been reported. We propose Prim-based heuristics for BCTs, which require nontrivial modifications w.r.t. the previously proposed Kruskal-based approaches, and present a computational comparison of the different approaches, which shows that Prim-based heuristics are most often preferable to Kruskal-based ones.