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Journal Article

Maximum Network Flow with Floating Point Arithmetic

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44003

Althaus,  Ernst
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Althaus, E., & Mehlhorn, K. (1998). Maximum Network Flow with Floating Point Arithmetic. Information Processing Letters, 66, 109-113.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-372C-D
Abstract
We discuss the implementation of network flow algorithms in floating point arithmetic. We give an example to illustrate the difficulties that may arise when floating point arithmetic is used without care. We describe an iterative improvement scheme that can be put around any network flow algorithm for integer capacities. The scheme carefully scales the capacities such that all integers arising can be handled exactly using floating point arithmetic. Let n and m be the number of nodes and edges of the network, respectively. For m 109 and with double precision floating point arithmetic, the number of iterations is always bounded by three, and the relative error in the flow value is at most 2−19. For m 106 and with double precision arithmetic, the relative error after the first iteration is bounded by 10−3.