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Advanced Consistency Checking in Constraint Satisfaction Problems: An Overview

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This document explores the advancements in consistency checking within Constraint Satisfaction Problems (CSPs). Traditionally, consistency checking has been a passive approach to verifying the satisfaction of constraints. We delve into the binary structure of CSPs, represented as graphs where nodes denote variables and edges represent constraints. The concepts of arc consistency are introduced, along with algorithms such as AC-1, AC-2, and AC-3. Additionally, practical examples, including hotel room scheduling and solving puzzles like Sudoku, illustrate the application of these concepts and heuristics like Minimum Remaining Values (MRV) and Least Constraining Value (LCV).

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Advanced Consistency Checking in Constraint Satisfaction Problems: An Overview

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  1. Constraint Satisfaction Problems/Programming ZUI 2012/2013

  2. Consistency checking in CSP • until now – passive checking whether the constraints are satisfied • Where? When? Remember the scheme of the algorithm?

  3. Consistency checking in CSP • until now – passive checking whether the constraints are satisfied • Where? When? Remember the scheme of the algorithm?

  4. Binary CSP • unified structure of CSP instances • all constraints are binary • can we formalize all CSP problems with binary variables? • constraints can be represented as a graph • nodes – variables • edges – constraints between variables

  5. Consistency • nodes • edges / arcs

  6. Consistency • nodes • unary constraints are reflected in the domain of the variable • every value in the domain satisfies all unary constraints • edges / arcs • directed vi → vj • for every x from vi domain there exists a value y from vjdomain that satisfies all constraints between vi and vj

  7. Arc Consistency • make each edge in the graph of constraints consistent • do we have some guarantees? • What algorithm can we use? • AC-1 • AC-2 • AC-3 • …

  8. Example • scheduling requests to hotel rooms • list of requests (# of people, from, to) • set of rooms (# of beds) • heuristics? • MRV, LCV, …

  9. Example (2) • crosswords, sudoku, … • representation? • heuristics?

  10. Homework assignment 2

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