Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#In the article “Arc Tolerances in Shortest-Path and Network Flow Problems” by D. R. Shier and C. Witzgall, several methods re described to compute, relative to a given tree T, the “arc tolerance” of each arc in a graph G of n nodes and A arcs. One method, the “dead-end retraction” method was shown to take O(n2) time and O(n2) space, and another method, the “cycle-tracing” method was shown to take O(nA) time but only O(A) space. For the important case of large sparse graphs, these methods either require excessive time, or excessive space. In this note implementations of both of the above methods are described which require O(A) space and O(A) log n) time. In the cycle-tracing method this is a strict improvement even for the dense case.
['Dan Gusfield']
I am writing a research paper on a idea A note on Arc tolerances in sparse shortest-path and network flow problems
[{"from": "human", "value": "I am writing a research paper on a idea A note on Arc tolerances in sparse shortest-path and network flow problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#In the article \u201cArc Tolerances in Shortest-Path and Network Flow Problems\u201d by D. R. Shier and C. Witzgall, several methods re described to compute, relative to a given tree T, the \u201carc tolerance\u201d of each arc in a graph G of n nodes and A arcs. One method, the \u201cdead-end retraction\u201d method was shown to take O(n2) time and O(n2) space, and another method, the \u201ccycle-tracing\u201d method was shown to take O(nA) time but only O(A) space. For the important case of large sparse graphs, these methods either require excessive time, or excessive space. In this note implementations of both of the above methods are described which require O(A) space and O(A) log n) time. In the cycle-tracing method this is a strict improvement even for the dense case."}]