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The complexity of short schedules for uet bipartite graphs

Evripidis Bampis (2010)

RAIRO - Operations Research

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].

The formation of a tree leaf

Qinglan Xia (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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 inverse carrier problem

Grant B. Gustafson, Miroslav Laitoch (2002)

Czechoslovak Mathematical Journal

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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