constraint consistency n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Constraint Consistency PowerPoint Presentation
Download Presentation
Constraint Consistency

Loading in 2 Seconds...

play fullscreen
1 / 14

Constraint Consistency - PowerPoint PPT Presentation


  • 161 Views
  • Uploaded on

Constraint Consistency. Chapter 3. Section 3.3. Definition 3.3.2: Path Consistency, Two variables relative to a third non-binary, binary Three variables A network (note: R ij i j) Revise-3 updates binary constraints, not domains

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Constraint Consistency' - oriel


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
constraint consistency

Constraint Consistency

Chapter 3

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 3
Section 3.3
  • Definition 3.3.2: Path Consistency,
    • Two variables relative to a third
      • non-binary, binary
    • Three variables
    • A network (note: Rij ij)
  • Revise-3 updates binary constraints, not domains
  • PC-1, PC-3 (like AC-1, AC-3) update binary constraints, not domains
    • This is not the PC-3 algorithm of Mackworth!!

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 4
Section 3.4
  • i-consistency
    • A relation is i-consistent (Dy, y not specified in S!!)
    • A network is i-consistent (i not specified distinct )
  • Algorithms: Revise-i, i-consistency-1
    • Should variables be distinct?
    • Note: complexity

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 4 1
Section 3.4.1
  • for binary CSPs,

Path-consistency  3-consistency

  • with ternary CSPs, ternary constraints are accounted for

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 5 1
Section 3.5.1
  • Generalized arc-consistency
    • non-binary CSPs
    • checks value support in domain of variables
    • updates domains
    • complexity
  • Relational arc-consistency
    • non-binary CSPs
    • updates relations RS-{x}

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 5
Section 3.5
  • No transition between 3.5 and 3.5.1, it would be good to have one

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 5 2
Section 3.5.2
  • Global constraints:
    • non-binary constraints dictated by practical applications
    • scope is parametrized
  • Relational description is unrealistic, defined intentionally (error: implicit)
  • Specialized algorithms ensure generalized arc-consistency
  • Examples: alldifferent, sum, global cardinality (generalization of alldifferent), cumulative, cycle

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 5 3
Section 3.5.3
  • Bounds consistency, large ordered domains, not necessarily continuous
  • Bind domains by intervals
  • Ensure that interval endpoints are AC
  • Weaker notion of consistency, cost effective
  • Mechanism: tighten endpoints until AC.
  • Example: alldifferent in O(nlogn)

CSCE 990-06 Spring 2003 B.Y. Choueiry

historical note
Historical note
  • The concepts of global constraint and bound consistency were developed in the context of Constraint Programming.

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 6
Section 3.6
  • Constraints with specific semantics (non-random): e.g., numeric/algebraic, boolean
  • Implications on
    • Arc-consistency
    • Path-consistency
    • Generalized arc-consistency
    • Relational arc-consistency

CSCE 990-06 Spring 2003 B.Y. Choueiry

3 6 algebraic constraints
3.6 Algebraic constraints
  • Too general term, in fact linear inequalities
  • Constraint composition is linear elimination
  • Binary case: constraints of bounded difference
    • Arc-consistency filters domains
    • Path-consistency tightens/adds binary constraints
  • Non-binary case (non-negative integer domains, why?)
    • Generalized arc-consistency filters domains
    • Relational arc-consistency tightnes/adds constraints

CSCE 990-06 Spring 2003 B.Y. Choueiry

3 6 boolean constraints
3.6 Boolean Constraints
  • Domain filtering: unit clause
  • Binary clauses
    • Constraint composition is the resolution rule
    • Arc-consistency achieved adding unit clause (unary constraint)
    • Path consistency achieved adding a binary clause
  • Non-binary clauses
    • Generalized arc-consistency won’t yield new unit clauses
    • Relational arc-consistency adds new clauses by unit resolution tractability of unit propagation algorithm

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 7
Section 3.7
  • Arc-consistency, path-consistency are sometimes guaranteed to solve the CSP
  • Restricted classes
    • Topologic restrictions: tree-structured
      • Arc-consistency guarantees solvability
    • Domains restrictions: bi-values domains, CNF theories with clause length 1 or 2
      • Path-consistency guarantees solvability
    • Constraint semantic: Horn Clauses
      • Unit propagation/resolution (relational-arc consistency) guarantees solvability (see tractability of Horn Theories in CSE 876)

CSCE 990-06 Spring 2003 B.Y. Choueiry

section 3 8
Section 3.8
  • Notice how non-binary constraints are depicted in Figures 3.17, 3.18: contours instead of box nodes. This is inherited from DB literature.

CSCE 990-06 Spring 2003 B.Y. Choueiry