Answers.Body: <p>I think I found the solution. When in <code>PR(W)</code>, <code>D=∅</code>, the weight is:</p>
  
  <p><code>b[i] = 0          for { i | w[i]&lt;max(w) }</code>, </p>
  
  <p>and</p>
  
  <p><code>b[i] = 1.0/max(w) for { i | w[i]==max(w) }</code>.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-02-18T11:38:34.770Z
Answers.LastActivityDate: 2017-10-03T21:24:09.727Z
Answers.LastEditDate: 2017-10-03T21:24:09.727Z
Answers.UserDisplayName: stustd
Body: <p>How does in the (famous Zilberstein) <code>PR</code>(uning) algorithm below the <code>LP-dominate</code> function get started: the first time it's called, <code>D=∅</code> and the linear program deteriorates (i.e. no constraint equations)? </p>
  
  <pre><code>procedure POINTWISE-DOMINATE(w, U)
  ...
  3. return false
  procedure LP-DOMINATE(w, U)
  4. solve the following linear program variables: d, b(s) ∀s ∈ S
        maximize d
        subject to the constraints
          b · (w − u) ≥ d, ∀u ∈ U
          sum(b) = 1
  5. if d ≥ 0 then return b
  6. else return nil
  procedure BEST(b, U )
  ...
  12. return w
  procedure PR(W)
  13. D ← ∅
  14. while W = ∅
  15.   w ← any element in W
  16.   if POINTWISE-DOMINATE(w, D) = true
  17.      W ← W − {w}
  18.   else
  19.      b ← LP-DOMINATE(w, D)
  20.      if b = nil then
  21.         W ← W − {w}
  22.      else
  23.         w ← BEST(b, W)
  24.         D ← D ∪ {w}
  25.         W ← W − {w}
  26. return D
  </code></pre>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-04-13T23:56:21.490Z
Comments.Text: check a book about algorithms heuristics using python. good luck!
Comments.UserDisplayName: Youness Abdus Salam
Tags: <decision-theory>
Title: Zilberstein's "LP-dominate" pruning explained?
UserDisplayName: stustd
ThreadText: # Zilberstein's "LP-dominate" pruning explained?
  
  (Asked by: username_0 on 2017-02-16)
  
  How does in the (famous Zilberstein) PR(uning) algorithm below the LP-dominate function get started: the first time it's called, D=∅ and the linear program deteriorates (i.e. no constraint equations)? 
  procedure POINTWISE-DOMINATE(w, U)
  ...
  3. return false
  procedure LP-DOMINATE(w, U)
  4. solve the following linear program variables: d, b(s) ∀s ∈ S
        maximize d
        subject to the constraints
          b · (w − u) ≥ d, ∀u ∈ U
          sum(b) = 1
  5. if d ≥ 0 then return b
  6. else return nil
  procedure BEST(b, U )
  ...
  12. return w
  procedure PR(W)
  13. D ← ∅
  14. while W = ∅
  15.   w ← any element in W
  16.   if POINTWISE-DOMINATE(w, D) = true
  17.      W ← W − {w}
  18.   else
  19.      b ← LP-DOMINATE(w, D)
  20.      if b = nil then
  21.         W ← W − {w}
  22.      else
  23.         w ← BEST(b, W)
  24.         D ← D ∪ {w}
  25.         W ← W − {w}
  26. return D
  
  **Tags:** decision-theory
  > **Comments:**
  > **username_1**: check a book about algorithms heuristics using python. good luck!  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_0 on 2017-02-18. Score: 1
  
  I think I found the solution. When in `PR(W)`, `D=∅`, the weight is:
  
  `b[i] = 0 for { i | w[i],`
  
  and
  
  `b[i] = 1.0/max(w) for { i | w[i]==max(w) }`.
  
  
  ---
  
  