Local%20search%20characteristics%20of%20incomplete%20SAT%20procedures

1
Local search characteristics of incomplete SAT
procedures

• Tang Yi
• Based on 1

2
Local search methods

• Effective engineering methods for finding
  satisfying assignments
• Incomplete and cannot prove if the solution
  exists
• Systematic understanding remains elusive
• Analysis largely empirical and hard to predict
  the effects of a minor change

3
Measuring local search performance (1)

• Depth
• how many clauses remain unsatisfied as search
  proceeds
• by averaging depth over all search steps as an
  overall summary

4
Measuring local search performance(2)

• Mobility
• how rapidly a local search moves in search
  space (while it tries to simultaneously stay deep
  in the object)
• by calculating the Hamming distance between
  variable assignments that are k steps apart and
  average this quantity over the entire sequence

5
Measuring local search performance(3)

• Coverage
• how many systematically the search explores
  the entire space
• by computing the coverage rate to be (n max
  gap) / search steps where max gap is the maximum
  Hamming distance between unexplored assignment
  and the nearest evaluated assignment

6
SDF a new local search strategy

• Two main different components
• (1) steepest descent in more informative
  objective function
• (2) multiplicative clauses re-weighting to
  move out of local minima and travel to promising
  new regions
• Weighted-score function
• h(x, w)

7
SDF procedure

• SDF
• Flip the variable that leads to the greatest
  increase in weighted-score function
• Re-weight
• re-weight the unsatisfied clauses and
  re-normalize the clause weights so that the
  resulting largest difference is
• flatten the weight profile of the satisfied
  clauses by shrinking of the distance
  towards their common mean

8
Discussion

• Systematically reduce the number of flips
• Greater computational overhead per flip

9

• Reference
• 1Schuurmans,D. and Southey,F.,Local search
  characteristics of incomplete SAT procedures,
  Proceedings of the Seventeenth National
  Conference on Artificial Intelligence
  (AAAI-2000),Austin,TX,July 2000.