Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the survivable network design problem (SNDP) for vertex connectivity. Given a graph G(V,E) with costs on edges, the goal of SNDP is to find a minimum cost subset of edges that ensures a given set of pairwise  vertex connectivity  requirements. When all connectivity requirements are beten a special vertex, called the  source , and vertices in a subset T ⊆ V, called  terminals , the problem is called the  single-source  SNDP. Our main result is a randomized k O(k 2 )  log 4 n-approximation algorithm for single-source SNDP where k denotes the largest connectivity requirement for any source-terminal pair. In particular,  get a poly-logarithmic approximation for any constant k. Prior to our work, no non-trivial approximation guarantees re known for this problem for any k ≥ 3.  also show that SNDP is k Ω(1) -hard to approximate and provide an elementary construction that shows that the ll-studied set-pair linear programming relaxation for this problem has an Ω(k 1/3 ) integrality gap.
['Tanmoy Chakraborty', 'Julia Chuzhoy', 'Sanjeev Khanna']
I am writing a research paper on a idea Network design for vertex connectivity
[{"from": "human", "value": "I am writing a research paper on a idea Network design for vertex connectivity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the survivable network design problem (SNDP) for vertex connectivity. Given a graph G(V,E) with costs on edges, the goal of SNDP is to find a minimum cost subset of edges that ensures a given set of pairwise  vertex connectivity  requirements. When all connectivity requirements are beten a special vertex, called the  source , and vertices in a subset T \u2286 V, called  terminals , the problem is called the  single-source  SNDP. Our main result is a randomized k O(k 2 )  log 4 n-approximation algorithm for single-source SNDP where k denotes the largest connectivity requirement for any source-terminal pair. In particular,  get a poly-logarithmic approximation for any constant k. Prior to our work, no non-trivial approximation guarantees re known for this problem for any k \u2265 3.  also show that SNDP is k \u03a9(1) -hard to approximate and provide an elementary construction that shows that the ll-studied set-pair linear programming relaxation for this problem has an \u03a9(k 1/3 ) integrality gap."}]