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In this paper we consider the Capacitated Arc Routing Problem, in which a fleet of K vehicles, all of them based on a specific vertex (the depot) and with a known capacity Q, must service a subset of the edges of the graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity.A heuristic algorithm for this problem is proposed consisting of: the selection of K centers, the construction of K connected graphs with associated loads not exceeding the vehicle...
We show that the problem of deciding if there is a schedule
of length three for the multiprocessor scheduling problem on identical
machines and unit execution time tasks in -complete even for bipartite
graphs, i.e. for precedence graphs of depth one. This complexity result
extends a classical result of Lenstra and Rinnoy Kan [5].
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 problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.
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