Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A dissociation set in a graph   G=(V,E)     G  =  (  V  ,  E  )        is a vertex subset  D    such that the subgraph   G[D]     G  [  D  ]        induced on  D  has vertex degree at most 1. A 3-path vertex cover in a graph is a vertex subset  C  such that every path of three vertices contains at least one vertex from  C . A vertex set  D    is a dissociation set if and only if   V∖D     V  ∖  D        is a 3-path vertex cover. There are many applications for dissociation sets and 3-path vertex covers. Hover, it is NP-hard to compute a dissociation set of maximum size or a 3-path vertex cover of minimum size in graphs. Several exact algorithms have been proposed for these two problems and they can be solved in   O ⁎ (1.4658 n )       O    ⁎    (    1.4658    n    )        time in  n   -vertex graphs. ,  reveal some interesting structural properties of the two problems, which allow us to solve them in   O ⁎ (1.4656 n )       O    ⁎    (    1.4656    n    )        time and polynomial space or   O ⁎ (1.3659 n )       O    ⁎    (    1.3659    n    )        time and exponential space.
['Mingyu Xiao', 'Shaowei Kou']
I am writing a research paper on a idea Exact algorithms for the maximum dissociation set and minimum 3-path vertex cover problems
[{"from": "human", "value": "I am writing a research paper on a idea Exact algorithms for the maximum dissociation set and minimum 3-path vertex cover problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A dissociation set in a graph   G=(V,E)     G  =  (  V  ,  E  )        is a vertex subset  D \u00a0  such that the subgraph   G[D]     G  [  D  ]        induced on  D  has vertex degree at most 1. A 3-path vertex cover in a graph is a vertex subset  C  such that every path of three vertices contains at least one vertex from  C . A vertex set  D \u00a0  is a dissociation set if and only if   V\u2216D     V  \u2216  D        is a 3-path vertex cover. There are many applications for dissociation sets and 3-path vertex covers. Hover, it is NP-hard to compute a dissociation set of maximum size or a 3-path vertex cover of minimum size in graphs. Several exact algorithms have been proposed for these two problems and they can be solved in   O \u204e (1.4658 n )       O    \u204e    (    1.4658    n    )        time in  n \u00a0 -vertex graphs. ,  reveal some interesting structural properties of the two problems, which allow us to solve them in   O \u204e (1.4656 n )       O    \u204e    (    1.4656    n    )        time and polynomial space or   O \u204e (1.3659 n )       O    \u204e    (    1.3659    n    )        time and exponential space."}]