5.258. min_size_full_zero_stretch
DESCRIPTION | LINKS | AUTOMATON |
- Origin
Derived from the unit commitment problem
- Constraint
- Arguments
- Restrictions
- Purpose
Given an integer and a sequence of variables enforce to be greater than or equal to the size of the smallest full stretch of zero of or to if no full stretch of zero exists.
A stretch of zero is a maximum sequence of zero, while a full stretch of zero is a stretch of zero that is neither located at the leftmost nor at the rightmost border of the sequence of variables . The size of a stretch of zero is the number of zero of the stretch.
- Example
-
FigureΒ 5.258.1 shows the smallest full stretch of zero associated with the example. The constraint holds since the size of the smallest full stretch of zero of the sequence is greater than or equal to 2.
Figure 5.258.1. Illustration of the Example slot: smallest full stretch of zero in bold and red (); note that the leftmost stretch of zero of size 1 is ignored since it is located at one of the two extremities of the sequence .
- Typical
- Symmetries
- Counting
-
Length () 2 3 4 5 6 7 8 Solutions 9 82 1137 19026 364033 7850291 188987201 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 9 82 1137 19026 364033 7850291 188987201 Parameter value 1 - 9 160 2575 45072 882441 19330432 2 9 9 176 2875 49932 966672 20958912 3 - 64 176 2900 50436 975394 21117888 4 - - 625 2900 50472 976178 21132416 5 - - - 7776 50472 976227 21133568 6 - - - - 117649 976227 21133632 7 - - - - - 2097152 21133632 8 - - - - - - 43046721 Solution count for : domains
- See also
common keyword: Β (sequence).
- Keywords
characteristic of a constraint: joker value, automaton, automaton with counters, automaton with same input symbol.
combinatorial object: sequence.
constraint network structure: alpha-acyclic constraint network(3).
- Automaton
FigureΒ 5.258.2 depicts the automaton associated with the constraint.
Figure 5.258.2. Automaton of the constraint
Figure 5.258.3. Hypergraph of the reformulation corresponding to the automaton (with two counters) of the constraint where (since all states of the automaton are accepting there is no restriction on the last variable )