Approximate spanning cactus

• No approximation algorithms are known for computing minimum spanning cactus and bottleneck spanning cactus.
• For minimum spanning cactus approximation algorithm with relative error τ is presented.
• For Bottleneck spanning cactus approximation algorithm with relative error 2τ−12τ−1 is presented.

We study minimum spanning cactus and bottleneck spanning cactus problems with τ-triangle inequality. Both problems are NP-Complete. No approximation algorithms are known for these problems. We present τ   approximation algorithm for the first and 2τ−12τ−1 approximation algorithm for the second problem.