Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a k-connected graph G=(V,E) and V ??V, k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find S?V?V ? with minimum cardinality such that the subgraph induced by V ??S is k-connected. ,  study the hardness of k-VCSAP in undirect graphs.  first prove k-VCSAP is APX-hard. Then,  improve the lor bound in two ways by relying on different assumptions. That is,  prove no algorithm for k-VCSAP has a PR better than O(log?(log?n)) unless P=NP and O(log?n) unless NP?DTIME(n O(log?log?n)), where n is the size of an input graph.
['Changcun Ma', 'Dong-Hyun Kim', 'Yuexuan Wang', 'Wei Wang', 'Nassim Sohaee', 'Weili Wu']
I am writing a research paper on a idea Hardness of k-Vertex-Connected Subgraph Augmentation Problem
[{"from": "human", "value": "I am writing a research paper on a idea Hardness of k-Vertex-Connected Subgraph Augmentation Problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a k-connected graph G=(V,E) and V ??V, k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find S?V?V ? with minimum cardinality such that the subgraph induced by V ??S is k-connected. ,  study the hardness of k-VCSAP in undirect graphs.  first prove k-VCSAP is APX-hard. Then,  improve the lor bound in two ways by relying on different assumptions. That is,  prove no algorithm for k-VCSAP has a PR better than O(log?(log?n)) unless P=NP and O(log?n) unless NP?DTIME(n O(log?log?n)), where n is the size of an input graph."}]