7.9 Distribution

Given a set M, let ${\it lowerBound}({\tt M})$ and ${\it upperBound}({\tt M})$ denote the greatest lower bound and the least upper bound currently known for M. Also define ${\it unknown}({\tt M}) = {\it upperBound}({\tt M}) \backslash {\it lowerBound}({\tt M})$ .

distribute

{FS.distribute +Dist *Ms}

The vector Ms is distributed according to the specification Dist. The following values for Dist are supported:

naive is equivalent to generic, i. e. the default settings apply.
generic(order: +Order <= order filter: +Filter <= true select: +Select <= id element: +Element <= element rrobin: +RRobin <= false weights: +Weights <= {FS.makeWeights nil} procedure:+Proc <= proc {$} skip end)
- Order
  - naive selects the left-most variable.
  - order(sel: +Sel <= min cost: +Cost <= card comp: +Comp <= unknown)
    - Sel = min selects the left-most variable S from Ss with the minimal cost according to Cost.
    - Sel = max selects the left-most variable S from Ss with the maximal cost according to Cost.
    - Cost = card: The cost is the cardinality of the set determined by Comp.
    - Cost = weightSum: The cost is the sum of the weights associated with the elements of the set determined by Comp.
    - Cost = weightMin: The cost is the minimal weight determined by Comp.
    - Cost = weightMax: The cost is the maximal weight associated with an element of the set determined by Comp.
    - Comp = unknown selects ${\it unknown}({\tt S})$ .
    - Comp = lowerBound selects ${\it lowerBound}({\tt S})$ .
    - Comp = upperBound selects ${\it upperBound}({\tt S})$ .
  - fun {Order +Ss} ... end
- Filter determines if an element S of Ss is choosen for distribution. That is the case if {IsDet S} and the filter yields true.
  - true skips values in Ss.
  - fun {Filter +E} ... end
- Select is used to access the actual finite set variable. Self-defined functions resp. procedures have to apply an appropriate selection function by themselves.
  - id is the identity function.
  - fun {Select +E} ... end
- Element
  - element(sel: +Sel <= min wrt: +Wrt <= unknown)
    - Sel = min selects the minimal element with respect to Wrt.
    - Sel = max selects the maximal element with respect to Wrt.
    - Wrt = unknown chooses an element from ${\it unknown}(S)$ . and interprets it as an integer.
    - Wrt = weight chooses an element from ${\it unknown}(S)$ and takes its weight as selection criterion.
  - fun {Element +E} ... end
- RRobin
  - true causes the distribution to step through the variable list in a round-robin fashion.
  - false causes the distribution to completely enumerate the head of the variable list and then proceeds with the head of the tail of the variable list.
- Weights must be a list of the form [E#W ...]. The variable E denotes an element and W the element's weight. An list element of the form default#W assigns to all not explicitely mentioned elements the weight W. If there is no element default#W then default#0 is implicitely added.
- Proc is applied when stability is reached. Since this application may cause instability, distribution is continued when stability is reached again.