Optimal root choice for parallel processing of tree decompositions. (24th February 2010) - Li, Yueping; Nie, Zhe; Lu, Yunting
This paper deals with the root choice strategy for tree decomposition when multiple agents (processors) are deployed. Tree decomposition is one of the most important decompositions in graph theory. It not only plays a role in theoretical investigations but also has widely practical applications. The reason is that many hard problems can be divided into sub-problems within the nodes in tree decomposition. When solving problems in tree decomposition, the precedence constraints graph takes the form of a tree. The first step is to choose a root since tree decomposition does not define any root. In addition, the root choice affects the time complexity when parallel processing is employed. The main findings of this paper are: a) an algorithm for determining the root which makes the latest completion time minimum; b) some results of the allocation of the optimal root; c) an improved version algorithm using branch-and-bound strategy based on the results. In addition, remarks and future works are presented.