Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem

We present a factor 2 approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorithm first solves the linear relaxation of this problem, and then iteratively rounds off the solution. The key idea in rounding off is that in a basic solution of the LP relaxation, at least one edge gets included at least to the extent of half. We include this edge into our integral solution and solve the residual problem.

Authors

• Kamal Jain

Keywords

• Approximation algorithms
• Educational institutions
• Computer networks
• Cost function
• Electrical capacitance tomography
• Steiner trees
• Factor 2
• Estimation Algorithm
• Basic Solution
• Integral Solution
• Residual Problems
• Linear Programming Relaxation
• End Point
• Linear Programming
• Feasible Solution
• Part Of The Solution
• Feasible Set
• Leaf Node
• Family Settings
• Iterative Rounds
• Loop Iteration
• Binary Search
• Polytope
• Cost Of Solution
• Edge Values
• Vertex Cover
• Incident Edges
• Smallest Set
• Fractional Solution
• Multigraph