Minimal join graph set synthesis self-managing cliques algorithm
The goal of this work is to offer improvements for the existing minimal join graph set designing algorithm and to actualize them in an improved algorithm. Algebraic Bayesian network global structure theory in common and join graphs clique classification in particular are overviewed. Minimal join graph set designing algorithm basic scheme is given. Maximal join graph should be built over a given vertex set. A clique graph should be built by that graph. Every clique should be collated to the set of vertexes that belong to the clique. Cliques order should be specified. With the order all the cliques should be sorted out. All homages should be sorted out for every clique by the means of the Pruefer algorithm, because an homage is a tree. Than all sinews should be sorted out for every homage. So that, all the sinews would be sorted out for each clique. All such sinews should be reordered to sinew array for the clique. According to the minimal join graph set theorem, it's enough to design all branches in the purpose to design all minimal join graphs. It can be done by sorting out all sinew combinations chosen one for each clique and uniting them into the one graph. On the base of observed classification three basic algorithm improvements that base some cliques specifies, are suggested. The first improvement is to use only the cliques (e.g. only the maximal join graph subgraphs), the weight of which equals to weigh of any maximal join graph edge. The second improvement is to use only the cliques that have more than one connection components having lost all the edges of the same weight. (e.g. the cliques that has more than one possession).The third improvement is to use cliques that have only two vertices not in designing sinews, but to add their only edge to a special graph - necessary edges graph. Minimal join graph set designing algorithm that actualizes the improvements is suggested. The further algebraic Bayesian network global structure analysis might be useful in the purpose to create new efficient minimal join graph set designing algorithms.