# On a dual network exterior point simplex type algorithm and its computational behavior∗

George Geranis; Konstantinos Paparrizos; Angelo Sifaleras

RAIRO - Operations Research (2012)

- Volume: 46, Issue: 3, page 211-234
- ISSN: 0399-0559

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topGeranis, George, Paparrizos, Konstantinos, and Sifaleras, Angelo. "On a dual network exterior point simplex type algorithm and its computational behavior∗." RAIRO - Operations Research 46.3 (2012): 211-234. <http://eudml.org/doc/222508>.

@article{Geranis2012,

abstract = {The minimum cost network flow problem, (MCNFP) constitutes a wide category of network
flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for
the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex
type” category. Similar to the classical dual network simplex algorithm (DNSA), this
algorithm starts with a dual feasible tree-solution and after a number of iterations, it
produces a solution that is both primal and dual feasible, i.e. it is
optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual
feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual
problem and at the same time infeasible for the primal problem. In this paper, we present
for the first time, the mathematical proof of correctness of DNEPSA, a detailed
comparative computational study of DNEPSA and DNSA on sparse and dense random problem
instances, a statistical analysis of the experimental results, and finally some new
results on the empirical complexity of DNEPSA. The analysis proves the superiority of
DNEPSA compared to DNSA in terms of cpu time and iterations.},

author = {Geranis, George, Paparrizos, Konstantinos, Sifaleras, Angelo},

journal = {RAIRO - Operations Research},

keywords = {Network flows; minimum cost network flow problem; dual network exterior point simplex algorithm; network flows},

language = {eng},

month = {9},

number = {3},

pages = {211-234},

publisher = {EDP Sciences},

title = {On a dual network exterior point simplex type algorithm and its computational behavior∗},

url = {http://eudml.org/doc/222508},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Geranis, George

AU - Paparrizos, Konstantinos

AU - Sifaleras, Angelo

TI - On a dual network exterior point simplex type algorithm and its computational behavior∗

JO - RAIRO - Operations Research

DA - 2012/9//

PB - EDP Sciences

VL - 46

IS - 3

SP - 211

EP - 234

AB - The minimum cost network flow problem, (MCNFP) constitutes a wide category of network
flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for
the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex
type” category. Similar to the classical dual network simplex algorithm (DNSA), this
algorithm starts with a dual feasible tree-solution and after a number of iterations, it
produces a solution that is both primal and dual feasible, i.e. it is
optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual
feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual
problem and at the same time infeasible for the primal problem. In this paper, we present
for the first time, the mathematical proof of correctness of DNEPSA, a detailed
comparative computational study of DNEPSA and DNSA on sparse and dense random problem
instances, a statistical analysis of the experimental results, and finally some new
results on the empirical complexity of DNEPSA. The analysis proves the superiority of
DNEPSA compared to DNSA in terms of cpu time and iterations.

LA - eng

KW - Network flows; minimum cost network flow problem; dual network exterior point simplex algorithm; network flows

UR - http://eudml.org/doc/222508

ER -

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