Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   deal with a directed graph G = (V, E) with non-negative integer edge costs where the edge costs are bounded by c and |V| = n and m = |E|.  show the all pairs shortest path (APSP) problem can be solved in O(mn + n2 log(c/n))) time with the data structure of cascading bucket system. The idea for speed-up is to share a single priority queue among n single source shortest path (SSSP) problems that are solved for APSP.  use the traditional computational model such that comparison-addition operations on distance data and random access with O(log n) bits can be done in O(1) time. Also the graph is not separated, meaning m ≥ n. Our complexity is best for a relatively large bound on edge cost, c, such that c = o(n log n).
['Tadao Takaoka']
I am writing a research paper on a idea Efficient algorithms for the all pairs shortest path problem with limited edge costs
[{"from": "human", "value": "I am writing a research paper on a idea Efficient algorithms for the all pairs shortest path problem with limited edge costs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   deal with a directed graph G = (V, E) with non-negative integer edge costs where the edge costs are bounded by c and |V| = n and m = |E|.  show the all pairs shortest path (APSP) problem can be solved in O(mn + n2 log(c/n))) time with the data structure of cascading bucket system. The idea for speed-up is to share a single priority queue among n single source shortest path (SSSP) problems that are solved for APSP.  use the traditional computational model such that comparison-addition operations on distance data and random access with O(log n) bits can be done in O(1) time. Also the graph is not separated, meaning m \u2265 n. Our complexity is best for a relatively large bound on edge cost, c, such that c = o(n log n)."}]