Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lor and the upper bounds. One of them is the ll studied continuous problem of the Rectilinear Steiner Arborescence$$\text{RSA}$$.  improve the lor bound and the upper bound on the competitive ratio for $$\text{RSA}$$ from $$O\log N$$ and $$\varOmega \sqrt{\log N}$$ to $$\varTheta \frac{\log N}{\log \log N}$$, where N is the number of Steiner points. This separates the competitive ratios of $$\text{RSA}$$ and the Symetric-$$\text{RSA}$$$$\text{SRSA}$$, two problems for which the bounds of Berman and Coulston is STOC 1997 re identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be vied as the discrete counterparts or a network counterpart of $$\text{RSA}$$. For this second problem  present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points the latter are similar to those  derived for $$\text{RSA}$$.
['Erez Kantor', 'Shay Kutten']
I am writing a research paper on a idea Optimal Competitiveness for the Rectilinear Steiner Arborescence Problem
[{"from": "human", "value": "I am writing a research paper on a idea Optimal Competitiveness for the Rectilinear Steiner Arborescence Problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lor and the upper bounds. One of them is the ll studied continuous problem of the Rectilinear Steiner Arborescence$$\\text{RSA}$$.  improve the lor bound and the upper bound on the competitive ratio for $$\\text{RSA}$$ from $$O\\log N$$ and $$\\varOmega \\sqrt{\\log N}$$ to $$\\varTheta \\frac{\\log N}{\\log \\log N}$$, where N is the number of Steiner points. This separates the competitive ratios of $$\\text{RSA}$$ and the Symetric-$$\\text{RSA}$$$$\\text{SRSA}$$, two problems for which the bounds of Berman and Coulston is STOC 1997 re identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be vied as the discrete counterparts or a network counterpart of $$\\text{RSA}$$. For this second problem  present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points the latter are similar to those  derived for $$\\text{RSA}$$."}]