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Integer Equal Flows

Journal Article · · Operations Research Letters
The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R{sub 1}, ..., R{sub {ell}} must carry equal flow. We show this problem is effectively inapproximable, even if the cardinality of each set R{sub k} is two. When {ell} is fixed, it is solvable in polynomial time.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA
Sponsoring Organization:
USDOE
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
964100
Report Number(s):
LLNL-JRNL-410584
Journal Information:
Operations Research Letters, Journal Name: Operations Research Letters Vol. 37; ISSN ORLED5; ISSN 0167-6377
Country of Publication:
United States
Language:
English

References (12)

A Lagrangean Relaxation Algorithm for the Two Duty Period Scheduling Problem journal March 1980
A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure journal April 2000
On the Complexity of Timetable and Multicommodity Flow Problems journal December 1976
Computationally Related Problems journal December 1974
Algorithms for the Simple Equal Flow Problem journal October 1999
Balanced network flows. I. A unifying framework for design and analysis of matching algorithms journal January 1999
Network models for vehicle and crew scheduling journal May 1984
Integer Programming with a Fixed Number of Variables journal November 1983
Network simplex algorithm for the general equal flow problem journal November 2003
On the Limits of Proper Learnability of Subclasses of DNF Formulas journal January 1996
The equal flow problem journal July 1988
A Lagrangean Relaxation Scheme for Structured Linear Programs With Application To Multicommodity Network Flows journal January 1997

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