Resolving begin and end time

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Hi,
   I am doing my thesis on developing an engine for SMIL boston version. And, I have a question on time resolving.  In the SMIL boston specification, the aim of the language is to construct a time graph which contains all time instant relation 
between two end points from different elements. Solving begin and end time of an element must deal with those end point from the others. Do you have any suggestion on the algorithm to do this? Do I have to know the concept of constaint propagation?

Thank you so much.