Relevant and irredundant anchor sets

An important issue that arises in the calculation of start times is the cascading effect of anchors. Let A(v ) and T(v,) be the anchor set and start time of a vertex Vi, where T(w ) is given as  

In general, there may be disjoint paths to a vertex from every anchor a g A(t ,). Therefore, the corresponding offsets ro(v ), Va g A(ui) are necessary in the computation of the start time T(v,). 

we improve significantly the efficiency of the scheduling algorithm (Section 6.3.5) by focusing on a smaller number of anchors. Second, we can achieve a smaller and faster control implementation of a relative schedule because the start time depends on fewer offsets, and hence on fewer synchronizations. 

We identify the anchors of a vertex v,- that may directly affect the start time T vi) by introducing the concept of the relevant anchor set of a vertex. We present first the following definitions. 

Definition 6.2.8 The relevant anchor set of a vertex v,- in a constraint graph G V, E) is the set of anchors R vi) = r r A such that there exists a defining path / (r,v,).  

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