Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. Hover, for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding (O(n 2 ) messages). A recently proposed algorithm called geographic gossip improves gossip efficiency by a √n factor, by exploiting geographic information to enable multihop long-distance communications.  proves that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional √n factor, and is order optimal (O(n) messages) for grids and random geometric graphs with high probability.  develop a general technique (travel agency method) based on Markov chain mixing time inequalities which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies.
['Florence Benezit', 'Alexandros G. Dimakis', 'Patrick Thiran', 'Martin Vetterli']
I am writing a research paper on a idea Order-Optimal Consensus Through Randomized Path Averaging
[{"from": "human", "value": "I am writing a research paper on a idea Order-Optimal Consensus Through Randomized Path Averaging"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. Hover, for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding (O(n 2 ) messages). A recently proposed algorithm called geographic gossip improves gossip efficiency by a \u221an factor, by exploiting geographic information to enable multihop long-distance communications.  proves that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional \u221an factor, and is order optimal (O(n) messages) for grids and random geometric graphs with high probability.  develop a general technique (travel agency method) based on Markov chain mixing time inequalities which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies."}]