cs345-8 - Searching for Solutions Careful Analysis of...

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1 Searching for Solutions Careful Analysis of Expansions The Bucket Algorithm
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2 Solutions and Expansions For every subgoal p(X,Y) of a query, each solution must have a subgoal (view) whose expansion allows a containment mapping to p(X,Y). “Bucket” for a subgoal = set of views that “cover” the subgoal. A solution must include > 1 view from each bucket.
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3 But … There’s much more to the story. A careful examination of how variables from the view definitions, query, solution, and expansion relate will eventually reveal additional constraints on the structure of the solutions.
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4 (Non)Distinguished Variables A variable that appears in the head of a CQ is said to be distinguished ; otherwise nondistinguished. p(X,Y) :- q(X,Z) & r(Z,Y) Distinguished Nondistinguished
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5 Local Variables of Expansions When we expand a view subgoal of a solution, the nondistinguished variables of the view definition become local . A local variable may not appear anywhere else in the expansion. Variables of the solution substitute for the distinguished variables of a view definition.
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6 Picture Correspond to dist- inguished of the view v(X,Y) :- p(X,Z) & q(Z,Y) sol(U,V) :- … & v(U,W) & … exp(U,V) :- … & p(U,Z1) & q(Z1,W) … Distinguished in solution; may appear elsewhere Nondistinguished in solution; may appear elsewhere Local from view; may not appear except as shown Exposed variables
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7 Exposed Variables Variables of the expansion that have substituted for distinguished variables of a view . These are the only variables that may appear in subgoals belonging to the expansion of two different solution subgoals.
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8 The Variables of the Query A query variable is
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