language Essence 1.3

$Problem Minimum Energy Broadcast$
$Problem details available at http://www.csplib.org/Problems/prob048/$
$Essence model by Andrew Martin$
$Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ given numNodes : int(1..) given maxPower : int(1..) given initialNode : int(1..) letting dNodes be domain int(1..numNodes) letting dPower be domain int(0..maxPower)$ if a node has power link of 0 to another node, that link is not possible
given linkCosts : matrix indexed by [dNodes, dNodes] of dPower

$if a node has power of 0 it is not broadcasting find nodeBroadcastPower : matrix indexed by [dNodes] of dPower$ AUX FIND VALUES, appear in solution but are not important -
$checking that these exist is much slower than 'find'ing values for them find directChildrenMatrix : matrix indexed by [dNodes] of set of dNodes find totalChildrenMatrix : matrix indexed by [dNodes] of set of dNodes$ minimising total power usage
minimising (sum i : dNodes . nodeBroadcastPower[i])

such that

$NODES DO NOT SHARE CHILDREN forAll i,j : dNodes . i=j \/ |directChildrenMatrix[i] intersect directChildrenMatrix[j]| = 0 ,$ TOTAL CHILD NODES OF NODE initialNode MUST BE SIZE NUMNODES (THUS CONTAINING ALL NODES)
|totalChildrenMatrix[initialNode]| = numNodes

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forAll node : dNodes .

$EACH NODE IS A TOTAL CHILD OF ITSELF node in totalChildrenMatrix[node] /\$ ENSURE NODES TOTAL EQUALS THE SUM OF ITS DIRECT CHILDRENS TOTALS + ITSELF
$(Each link must add a new node to the graph, not including cycles) (sum i in directChildrenMatrix[node] . |totalChildrenMatrix[i]|) = |totalChildrenMatrix[node]| - 1 /\$ NODE MUST HAVE TOTALCHILDREN CONTAIN A SUBSET WHICH IS THE TOTALCHILDREN OF EACH DIRECT CHILD
forAll childNode in directChildrenMatrix[node] .

totalChildrenMatrix[childNode] subsetEq totalChildrenMatrix[node]

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$LINK MUST BE ALLOWED linkCosts[node][childNode] != 0 /\$ CONSTRAINT FOR PROBLEM SOLUTION