Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a graph with the edge costs satisfying the β-sharpened triangle inequality: cost(u,v)≤β(cost(u,x)+cost(x,v)), for l/2≤β<1,  study the NP-hard problem of finding a minimum cost spanning subgraph which is k-vertex-connected, k≥2.  analyze an approximation quadratic-time algorithm whose performance ratio is . The main motivation of this study is to provide an algorithm with a good performance ratio and a practical worst case running time for significative subclasses of the metric Travelling Salesman Problem and the naturally related to it connectivity problems.
['Alessandro Ferrante', 'Mimmo Parente']
I am writing a research paper on a idea ON THE VERTEX-CONNECTIVITY PROBLEM FOR GRAPHS WITH SHARPENED TRIANGLE INEQUALITY
[{"from": "human", "value": "I am writing a research paper on a idea ON THE VERTEX-CONNECTIVITY PROBLEM FOR GRAPHS WITH SHARPENED TRIANGLE INEQUALITY"}, {"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 graph with the edge costs satisfying the \u03b2-sharpened triangle inequality: cost(u,v)\u2264\u03b2(cost(u,x)+cost(x,v)), for l/2\u2264\u03b2<1,  study the NP-hard problem of finding a minimum cost spanning subgraph which is k-vertex-connected, k\u22652.  analyze an approximation quadratic-time algorithm whose performance ratio is . The main motivation of this study is to provide an algorithm with a good performance ratio and a practical worst case running time for significative subclasses of the metric Travelling Salesman Problem and the naturally related to it connectivity problems."}]