Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study graph augmentation under the dilation criterion. In our case,  consider a plane geometric graph G = (V, E) and a set C of edges.  aim to add to G a minimal number of nonintersecting edges from C to bound the ratio beten the graph-based distance and the Euclidean distance for all pairs of vertices described by C. Motivated by the problem of decomposing a polygon into natural subregions,  present an optimal linear-time algorithm for the case that P is a simple polygon and C models an internal triangulation of P. The algorithm admits some straightforward extensions. Most importantly, in pseudopolynomial time, it can approximate a solution of minimum total length or, if C is ighted, compute a solution of minimum total ight.  show that minimizing the total length or the total ight is akly NP-hard. Finally,  show how our algorithm can be used for two ll-known problems in GIS: generating variable-scale maps and area aggregation.
['Jan-Henrik Haunert', 'Wouter Meulemans']
I am writing a research paper on a idea Partitioning Polygons via Graph Augmentation
[{"from": "human", "value": "I am writing a research paper on a idea Partitioning Polygons via Graph Augmentation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study graph augmentation under the dilation criterion. In our case,  consider a plane geometric graph G = (V, E) and a set C of edges.  aim to add to G a minimal number of nonintersecting edges from C to bound the ratio beten the graph-based distance and the Euclidean distance for all pairs of vertices described by C. Motivated by the problem of decomposing a polygon into natural subregions,  present an optimal linear-time algorithm for the case that P is a simple polygon and C models an internal triangulation of P. The algorithm admits some straightforward extensions. Most importantly, in pseudopolynomial time, it can approximate a solution of minimum total length or, if C is ighted, compute a solution of minimum total ight.  show that minimizing the total length or the total ight is akly NP-hard. Finally,  show how our algorithm can be used for two ll-known problems in GIS: generating variable-scale maps and area aggregation."}]