Intuitive solution-doubling techniques for worst-case analysis of some survivable network design problems

Authors:
Anantaram Balakrishnan;Thomas L. Magnanti;Prakash Mirchandani
Affiliations:
Smeal College of Business Administration, Penn State University, University Park, PA, USA;School of Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA;Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, USA
Venue:
Operations Research Letters
Year:
2001

Citing 5
Cited 2

Minimum-weight two-connected spanning networks

Mathematical Programming: Series A and B
Survivable networks, linear programming relaxations and the parsimonious property

Mathematical Programming: Series A and B
Improved approximation algorithms for network design problems

SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Designing Hierarchical Survivable Networks

Operations Research
Connectivity–splitting models for survivable network design

Networks

Evolutionary algorithms and matroid optimization problems

Proceedings of the 9th annual conference on Genetic and evolutionary computation
The k-path tree matroid and its applications to survivable network design

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

An intuitive solution-doubling argument establishes well known results concerning the worst-case performance of spanning tree-based heuristics for the Steiner network problem and the traveling salesman problem. This note shows that the solution-doubling argument and its implications apply to certain more general Low Connectivity Steiner (LCS) problems that are important in the design of survivable telecommunication networks. We use the doubling strategy to establish worst-case upper bounds on the value of tree-based heuristics relative to the optimal value for some versions of the LCS problem, and also provide a tight lower bound based on solutions to matching problems.