Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs.  investigate the viability of a similar idea within message passing – for integral solutions in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP),  propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a. community mining) using modularity optimization,  introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases  are able to derive simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP  are able to find near-optimal solutions in the time that empirically grows with N3, demonstrating that augmentation is practical and efficient.
['Siamak Ravanbakhsh', 'Reihaneh Rabbany', 'Russell Greiner']
I am writing a research paper on a idea Augmentative Message Passing for Traveling Salesman Problem and Graph Partitioning
[{"from": "human", "value": "I am writing a research paper on a idea Augmentative Message Passing for Traveling Salesman Problem and Graph Partitioning"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs.  investigate the viability of a similar idea within message passing \u2013 for integral solutions in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP),  propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a. community mining) using modularity optimization,  introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases  are able to derive simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP  are able to find near-optimal solutions in the time that empirically grows with N3, demonstrating that augmentation is practical and efficient."}]