Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While it is known that the d-dimensional Steiner minimum tree problem in Hamming metric is NP-complete if d is part of the input, it is an open question whether this also holds for fixed dimensions. , this question is ansred by showing that the Steiner minimum tree problem in Hamming metric is already NP-complete in 3 dimensions. Furthermore,  show that, the minimum spanning tree gives a 2-2d approximation on the Steiner minimum tree for d>=2. Using this result,  analyse the so-called k-LCA and A"k approximation algorithms and show improved approximation guarantees for low dimensions.
['Ernst Althaus', 'Joschka Kupilas', 'Rouven Naujoks']
I am writing a research paper on a idea On the low-dimensional Steiner minimum tree problem in Hamming metric
[{"from": "human", "value": "I am writing a research paper on a idea On the low-dimensional Steiner minimum tree problem in Hamming metric"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While it is known that the d-dimensional Steiner minimum tree problem in Hamming metric is NP-complete if d is part of the input, it is an open question whether this also holds for fixed dimensions. , this question is ansred by showing that the Steiner minimum tree problem in Hamming metric is already NP-complete in 3 dimensions. Furthermore,  show that, the minimum spanning tree gives a 2-2d approximation on the Steiner minimum tree for d>=2. Using this result,  analyse the so-called k-LCA and A\"k approximation algorithms and show improved approximation guarantees for low dimensions."}]