Create groups from sets of nodes

Question

I have a list of sets (a,b,c,d,e in below example). Each of the sets contains a list of nodes in that set (1-6 below). I was wondering that there probably is a general known algorithm for achieving the below, and I just do not know about it.

sets[
 a[1,2,5,6],
 b[1,4,5],
 c[1,2,5],
 d[2,5],
 e[1,6],
]

I would like to generate a new structure, a list of groups, with each group having

• all the (sub)sets of nodes that appear in multiple sets
• references to the original sets those nodes belong to

So the above data would become (order of groups irrelevant).

group1{nodes[2,5],sets[a,c,e]}
group2{nodes[1,2,5],sets[a,c]}
group3{nodes[1,6],sets[a,e]}
group4{nodes[1,5],sets[a,b,c]}

I am assuming I can get the data in as an array/object structure and manipulate that, and then spit the resulting structure out in whatever format needed.

It would be a plus if:

• all groups had a minimum of 2 nodes and 2 sets.
• when a subset of nodes is contained in a bigger set that forms a group, then only the bigger set gets a group: in this example, nodes 1,2 do not have a group of their own since all the sets they have in common already appear in group2.

(The sets are stored in XML, which I have also managed to convert to JSON so far, but this is irrelevant. I can understand procedural (pseudo)code but also something like a skeleton in XSLT or Scala could help to get started, I guess.)

Answer 1

/*
Pseudocode algorithm for creating groups data from a set dataset, further explained in the project documentation. This is based on 
http://stackoverflow.com/questions/1644387/create-groups-from-sets-of-nodes

I am assuming 
- Group is a structure (class) the objects of which contain two lists: a list of sets and a list of nodes (group.nodes). Its constructor accepts a list of nodes and a reference to a Set object
- Set is a list structure (class), the objects (set)  of which contain the nodes of the list in set.nodes
- groups and sets are both list structures that can contain arbitrary objects which can be iterated with foreach(). 
- you can get the objects two lists have in common as a new list with intersection()
- you can count the number of objects in a list with length()
*/

//Create groups, going through the original sets
foreach(sets as set){
    if(groups.nodes.length==0){
        groups.addGroup(new Group(set.nodes, set));
    }
    else{
        foreach (groups as group){
                if(group.nodes.length() == intersection(group.nodes,set.nodes).length()){
                    // the group is a subset of the set, so just add the set as a member the group
                    group.addset(set);
                    if (group.nodes.length() < set.nodes.length()){
                    // if the set has more nodes than the group that already exists, 
                    // create a new group for the nodes of the set, with set as a member of that group
                    groups.addGroup(new Group(set.nodes, set));
                    }
                }

                // If group is not a subset of set, and the intersection of the nodes of the group 
                // and the nodes of the set
                // is greater than one (they have more than one person in common), create a new group with 
                // those nodes they have in common, with set as a member of that group
                else if(group.nodes.length() > intersection(group.nodes,set.nodes).length() 
                    && intersection(group.nodes,set.nodes).length()>1){
                    groups.addGroup(new Group(intersection(group.nodes,set.nodes), set);
                }
        }
    }

}

// Cleanup time!
foreach(groups as group){
    //delete any group with only one member set (for it is not really a group then)
    if (group.sets.length<2){
        groups.remove(group);
    }
    // combine any groups that have the same set of nodes. Is this really needed? 
    foreach(groups2 as group2){
        //if the size of the intersection of the groups is the same size as either of the 
        //groups, then the groups have the same nodes.
        if (intersection(group.nodes,group2.nodes).length == group.nodes.length){
            foreach(group2.sets as set2){
                if(!group.hasset(set)){
                    group.addset(set2);
                }
            }
            groups.remove(group2);
        }
        }

}