On the complexity of column generation in survivable network design with path-based survivability mechanisms

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.

• Author: Sebastian Orlowski; Michal Pioro
• Department/s: Department of Electrical and Information Technology
• Publishing year: 2008
• Language: English
• Publication/Series: ZIB-Report
• Document type: Report
• Publisher: Warsaw University of Technology
• Topic: Electrical Engineering, Electronic Engineering, Information Engineering
• Status: Published
• Report number: 08-51
• Research group: Networking
• ISBN/ISSN/Other: ISSN: 1438-0064