The all-to-all alternative route problem
The formation of a tree leaf
In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...
The maximum capacity shortest path problem : generation of efficient solution sets
Individual items of flow in a telecommunications or a transportation network may need to be separated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destination will depend on the size of the convoy. The Quickest Path problem seeks a path to minimise this convoy travel time. A closely related bicriterion problem is the Maximum Capacity Shortest...
The Maximum Capacity Shortest Path Problem: Generation of Efficient Solution Sets
Individual items of flow in a telecommunications or a transportation network may need to be separated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destination will depend on the size of the convoy. The Quickest Path problem seeks a path to minimise this convoy travel time. A closely related bicriterion problem is the Maximum Capacity...
Time-delay polynomial networks and rates of approximation.
Two open problems in communication in edge-disjoint paths modes