Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 2-Disjoint Connected Subgraphs problem, given a graph along with two disjoint sets of terminals Z1, Z2, asks whether it is possible to find disjoint sets A1, A2, such that Z1⊆A1, Z2⊆A2 and A1, A2 induce connected subgraphs. While the naive algorithm runs in O(2nnO(1)) time, solutions with complexity of form O((2−e)n) have been found only for special graph classes [15, 19].   present an O(1.933n) algorithm for 2-Disjoint Connected Subgraphs in general case, thus breaking the 2n barrier. As a counterpoise of this result  show that if  parameterize the problem by the number of non-terminal vertices, it is hard both to speed up the brute-force approach and to find a polynomial kernel.
['Marek Cygan', 'Marcin Pilipczuk', 'Michał Pilipczuk', 'Jakub Onufry Wojtaszczyk']
I am writing a research paper on a idea Solving the 2-disjoint connected subgraphs problem faster than 2 n
[{"from": "human", "value": "I am writing a research paper on a idea Solving the 2-disjoint connected subgraphs problem faster than 2 n"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 2-Disjoint Connected Subgraphs problem, given a graph along with two disjoint sets of terminals Z1, Z2, asks whether it is possible to find disjoint sets A1, A2, such that Z1\u2286A1, Z2\u2286A2 and A1, A2 induce connected subgraphs. While the naive algorithm runs in O(2nnO(1)) time, solutions with complexity of form O((2\u2212e)n) have been found only for special graph classes [15, 19].   present an O(1.933n) algorithm for 2-Disjoint Connected Subgraphs in general case, thus breaking the 2n barrier. As a counterpoise of this result  show that if  parameterize the problem by the number of non-terminal vertices, it is hard both to speed up the brute-force approach and to find a polynomial kernel."}]