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12. Implementation Methods

This article explores the implementation methods for evaluating and manipulating gap-graphs, which visually represent conjunctions of difference constraints. It discusses techniques such as shortcuts, merging, relation algebra, and matrix representation. Additionally, it addresses questions regarding satisfiability testing, vertex shortcutting, graph merging, datalog query evaluation, finding complement and difference, set-graphs, and optimization of relational algebra.

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12. Implementation Methods

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  1. 12. Implementation Methods Evaluation with gap-graphs Gap-graphs – visually represents a conjunctions of difference constraints

  2. Shortcut – u a+b v if u a x and x b v

  3. Merge – union vertices and edges from both input gap-order graphs. If some edge occurs but different labels, then keep larger label. Relation algebra on set of gap-graphs – can be defined based on shortcut and merge.

  4. Evaluation with matricesMatrix representation of first gap-graph: Question: how can we test satisfiability of a gap- graph ?

  5. Question: how can we shortcut a vertex ? Question: how can we merge two gap-graph ?

  6. Question: how do we evaluate datalog queries ? Question: how do we find complement and difference ?

  7. Boolean constraints • Set-graphs – represent conjunction of subset constraints

  8. Pairs of matrices for each set-graph Question: how do we test satisfiability ?

  9. Optimization of relational algebra • Perform selection and projection as early as possible by applying algebraic rewrite rules.

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