Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a linear distance relaxation of the n- team Traveling Tournament Problem (TTP), a simple yet porful heuristic that temporarily "assumes" the n teams are located on a straight line, thereby reducing the(n2) pairwise distance parameters to just n - 1 variables. The modified problem then becomes easier to analyze, from which  determine an approximate solution for the actual instance on n teams.  present combinatorial techniques to solve the Linear Distance TTP (LD-TTP) for n = 4 and n = 6, without any use of computing, generating the complete set of optimal distances regardless of where the n teams are located.#R##N##R##N# show that there are only 295 non-isomorphic schedules that can be a solution to the 6-team LD-TTP, and demonstrate that in all previously-solved benchmark TTP instances on 6 teams, the distance-optimal schedule appears in this list of 295, even when the six teams are arranged in a circle or located in three-dimensional space.  then extend the LD-TTP to multiple rounds, and apply our theory to produce a nearly-optimal regular-season schedule for the Nippon Pro Baseball league in Japan.  conclude the paper by generalizing our theory to the n-team LD-TTP, producing a feasible schedule whose total distance is guaranteed to be no worse than 4/3 times the optimal solution.
['Richard Hoshino', 'Ken-ichi Kawarabayashi']
I am writing a research paper on a idea The linear distance traveling tournament problem
[{"from": "human", "value": "I am writing a research paper on a idea The linear distance traveling tournament problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a linear distance relaxation of the n- team Traveling Tournament Problem (TTP), a simple yet porful heuristic that temporarily \"assumes\" the n teams are located on a straight line, thereby reducing the(n2) pairwise distance parameters to just n - 1 variables. The modified problem then becomes easier to analyze, from which  determine an approximate solution for the actual instance on n teams.  present combinatorial techniques to solve the Linear Distance TTP (LD-TTP) for n = 4 and n = 6, without any use of computing, generating the complete set of optimal distances regardless of where the n teams are located.#R##N##R##N# show that there are only 295 non-isomorphic schedules that can be a solution to the 6-team LD-TTP, and demonstrate that in all previously-solved benchmark TTP instances on 6 teams, the distance-optimal schedule appears in this list of 295, even when the six teams are arranged in a circle or located in three-dimensional space.  then extend the LD-TTP to multiple rounds, and apply our theory to produce a nearly-optimal regular-season schedule for the Nippon Pro Baseball league in Japan.  conclude the paper by generalizing our theory to the n-team LD-TTP, producing a feasible schedule whose total distance is guaranteed to be no worse than 4/3 times the optimal solution."}]