Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may ansr connectivity queries of the form 'Are vertices u and v connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n) time. This results improves over previously known O(n \log n) time algorithm.
['Jakub Lacki', 'Piotr Sankowski']
I am writing a research paper on a idea Optimal Decremental Connectivity in Planar Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Optimal Decremental Connectivity in Planar Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may ansr connectivity queries of the form 'Are vertices u and v connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n) time. This results improves over previously known O(n \\log n) time algorithm."}]