Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the I nterval  C ompletion  problem  are given an n-vertex graph  G  and an integer  k , and the task is to transform  G  by making use of at most  k  edge additions into an interval graph. This is a fundamental graph modification problem with applications in sparse matrix multiplication and molecular biology. The question about fixed-parameter tractability of I nterval  C ompletion  was asked by Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999] and was ansred affirmatively more than a decade later by Villanger at el. [STOC 2007; SIAM J. Comput. 2009], who presented an algorithm with running time  O ( k  2 k   n  3  m ).  give the first subexponential parameterized algorithm solving I nterval  C ompletion  in time  k   O ([EQUATION])  n   O (1) . This adds I nterval  C ompletion  to a very small list of parameterized graph modification problems solvable in subexponential time.
['Ivan Bliznets', 'Fedor V. Fomin', 'Marcin Pilipczuk', 'Michał Pilipczuk']
I am writing a research paper on a idea Subexponential parameterized algorithm for interval completion
[{"from": "human", "value": "I am writing a research paper on a idea Subexponential parameterized algorithm for interval completion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the I nterval  C ompletion  problem  are given an n-vertex graph  G  and an integer  k , and the task is to transform  G  by making use of at most  k  edge additions into an interval graph. This is a fundamental graph modification problem with applications in sparse matrix multiplication and molecular biology. The question about fixed-parameter tractability of I nterval  C ompletion  was asked by Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999] and was ansred affirmatively more than a decade later by Villanger at el. [STOC 2007; SIAM J. Comput. 2009], who presented an algorithm with running time  O ( k  2 k   n  3  m ).  give the first subexponential parameterized algorithm solving I nterval  C ompletion  in time  k   O ([EQUATION])  n   O (1) . This adds I nterval  C ompletion  to a very small list of parameterized graph modification problems solvable in subexponential time."}]