On the complexity of column generation in survivable network design with path-based survivability mechanisms
Författare
Summary, in English
This survey concerns optimization problems arising in the design
of survivable communication networks. It turns out that such
problems can be modeled in a natural way as non-compact linear
programming formulations based on multicommodity flow network
models. These non-compact formulations involve an exponential
number of path flow variables, and therefore require column
generation to be solved to optimality. We consider several
path-based survivability mechanisms and present results, both
known and new, on the complexity of the corresponding column
generation problems (called the pricing problems). We discuss
results for the case of the single link (or node) failures
scenarios, and extend the considerations to multiple link
failures. Further, we classify the design problems corresponding
to different survivability mechanisms according to the structure
of their pricing problem. Finally, we show that almost all
encountered pricing problems are hard to solve for scenarios
admitting multiple failures.
of survivable communication networks. It turns out that such
problems can be modeled in a natural way as non-compact linear
programming formulations based on multicommodity flow network
models. These non-compact formulations involve an exponential
number of path flow variables, and therefore require column
generation to be solved to optimality. We consider several
path-based survivability mechanisms and present results, both
known and new, on the complexity of the corresponding column
generation problems (called the pricing problems). We discuss
results for the case of the single link (or node) failures
scenarios, and extend the considerations to multiple link
failures. Further, we classify the design problems corresponding
to different survivability mechanisms according to the structure
of their pricing problem. Finally, we show that almost all
encountered pricing problems are hard to solve for scenarios
admitting multiple failures.
Publiceringsår
2008
Språk
Engelska
Publikation/Tidskrift/Serie
ZIB-Report
Dokumenttyp
Rapport
Förlag
Warsaw University of Technology
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Status
Published
Report number
08-51
Forskningsgrupp
- Networking
ISBN/ISSN/Övrigt
- ISSN: 1438-0064