This thesis consists of four technical chapters. The first two chapters deal with filtering algorithms for global constraints. Namley, we show improved algorithms for the well known Global Cardinality Constraint. Then we define a new constraint, UseBy and its special case Same, and show efficient filtering algorithms for both. All of the filtering algorithms follow the same approach: model the constraint as a flow problem. The next two chapters deal with dynamic algoritms. That is, algorithms that maintain information about a directed acyclic graph (DAG) while the graph changes. The third chapter deals with the problem of maintaining the topological order of the nodes of a DAG upon deals with the problem of maintaining the topological order of the nodes of a DAG upon a sequence of edge insertions. The fourth chapter deals with the problem of maintaining the longest paths in a directed acyclic graph upon edge insertions and deletions
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