The Branch and Bound algorithms which are refereed to as B & B are
commonly used to solve NP - hard combinatorial optimization problems.
Although these algorithms were efficient, the size of problems which can solved
and proved the optimality of s
olution by these algorithms was limited, because
of the limitation of computers capabilities although of it’s highly development.
When the parallel programming 46
and Multiprocessors computers were appeared, the researcher thought to
use the capabilities of these techniques and machines to increase the size of
solved problems. Three main anomalies may occur when the parallelism is
used.
This research aimed to design a new model of Branch and Bound
algorithms in order to analyze the performance. This model based on a new
rule to choose the best node among the equal evaluation node. Tight bounds of
each rules were computed and proved the ability to achieve it. Sufficient and
necessary condition anomalous are given regarding the predisposition for each
of the three classes of behavior.
In this research, we discussed and compared the results of further
relaxations on the assumptions used in branch and bound algorithms. We
suggested using the asynchronous models to have the utmost benefit of the
capabilities of parallel programming.
The study is researching the fault tolerance in the large distributed
environments such as grid computing and clusters of computers in
order to find the most effective ways to deal with the errors
associated with the crash one of the devices in th
e environment or
network disconnection to ensure the continuity of the application in
the presence of the faults.In this paper we study a model of the
distributed environment and the parallel applications within it. Then
we provide a checkpoint mechanism that will enable us to ensure
continuity of the work used by a virtual representation of the
application (macro dataflow) and suitable for the applications
which uses work stealing algorithm to distribute the tasks which
are implemented in heterogeneous and dynamic environment.
This mechanism will add a simple cost to the cost of parallel
execution as a result of keeping part of the work during fault-free
execution. The study also provides a mathematical model to
calculate the time complexity i.e. the cost of this proposed
mechanism.
