Storing Tree like Hierarchy Structures With MongoDB, Part 2

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Introduction

In real life, almost any project deals with the tree structures. Different kinds of taxonomies, site structures, etc. require modelling of hierarchy relations. In this article, I will illustrate using last two of five typical approaches of operating with hierarchy data on example of the MongoDB database. Please refer to the first article from the series to read about the first three ones. Those approaches are:

• Model Tree Structures with Child References
• Model Tree Structures with Parent References
• Model Tree Structures with an Array of Ancestors
• Model Tree Structures with Materialized Paths
• Model Tree Structures with Nested Sets

Note: This article is inspired by another article 'Model Tree Structures in MongoDB' by 10gen, but does not copy it, but provides additional examples on typical operations with tree management. Please refer for 10gen's article to get more solid understanding of the approach.

Background

As a demo dataset, I use some fake eshop goods taxonomy.

Challenges to Address

In a typical site scenario, we should be able to

• operate with tree (insert new node under specific parent, update/remove existing node, move node across the tree)
• get path to node (for example, in order to be build the breadcrumb section)
• get all node descendants (in order to be able, for example, to select goods from more general category, like 'Cell Phones and Accessories' which should include goods from all subcategories.

On each of the examples below, we:

• add new node called 'LG' under electronics
• move 'LG' node under Cell_Phones_And_Smartphones node
• remove 'LG' node from the tree
• get child nodes of Electronics node
• get path to 'Nokia' node
• get all descendants of the 'Cell_Phones_and_Accessories' node

Please refer to the image above for a visual representation.

Tree Structure using Materialized Path

For each node, we store (ID, PathToNode)

The approach looks similar to storing array of ancestors, but we store a path in form of string instead. In the example above, I intentionally use comma(,) as a path elements divider in order to keep regular expression simpler.

Adding New Node

New node insertion is done with one select and one insert operation.

var ancestorpath = db.categoriesMP.findOne({_id:'Electronics'}).path;
ancestorpath += 'Electronics,'
db.categoriesMP.insert({_id:'LG', path:ancestorpath});
//{ "_id" : "LG", "path" : "Electronics," } 

Updating/Moving the Node

Node can be moved using one select and one update operation.

ancestorpath = db.categoriesMP.findOne({_id:'Cell_Phones_and_Smartphones'}).path;
ancestorpath +='Cell_Phones_and_Smartphones,'
db.categoriesMP.update({_id:'LG'},{$set:{path:ancestorpath}});
//{ "_id" : "LG", "path" : "Electronics,Cell_Phones_and_Accessories,
//Cell_Phones_and_Smartphones," } 

Node Removal

Node can be removed using single database query:

db.categoriesMP.remove({_id:'LG'}); 

Getting Node Children, Unordered

Note unless you introduce the order field, it is impossible to get ordered list of node children. You should consider another approach if you need order.

db.categoriesMP.find({$query:{path:'Electronics,'}})
//{ "_id" : "Cameras_and_Photography", "path" : "Electronics," }
//{ "_id" : "Shop_Top_Products", "path" : "Electronics," }
//{ "_id" : "Cell_Phones_and_Accessories", "path" : "Electronics," } 

Getting All Node Descendants

Single select, regexp starts with ^ which allows using the index for matching:

var descendants=[]
var item = db.categoriesMP.findOne({_id:"Cell_Phones_and_Accessories"});
var criteria = '^'+item.path+item._id+',';
var children = db.categoriesMP.find({path: { $regex: criteria, $options: 'i' }});
while(true === children.hasNext()) {
  var child = children.next();
  descendants.push(child._id);
}

descendants.join(",")
//Cell_Phones_and_Smartphones,Headsets,Batteries,Cables_And_Adapters,
//Nokia,Samsung,Apple,HTC,Vyacheslav 

Getting Path to Node

We can obtain path directly from node without issuing additional selects.

var path=[]
var item = db.categoriesMP.findOne({_id:"Nokia"})
print (item.path)
//Electronics,Cell_Phones_and_Accessories,Cell_Phones_and_Smartphones, 

Indexes

Recommended index is putting index on path:

db.categoriesAAO.ensureIndex( { path: 1 } ) 

Tree Structure Using Nested Sets

For each node, we store (ID, left, right).

Left field also can be treated as an order field.

Adding New Node

Please refer to the image above. Assume we want to insert LG node after shop_top_products(14,23).
New node would have left value of 24, affecting all remaining left values according to traversal rules, and will have right value of 25, affecting all remaining right values including root one.

Steps

1. Take next node in traversal tree.
2. New node will have left value of the following sibling and right value - incremented by two following sibling's left one
3. Now, we have to create the place for the new node. Update affects right values of all ancestor nodes and also affects all nodes that remain for traversal.
4. Only after creating place, new node can be inserted.

var followingsibling = db.categoriesNSO.findOne({_id:"Cell_Phones_and_Accessories"});
var newnode = {_id:'LG', left:followingsibling.left,right:followingsibling.left+1}

db.categoriesNSO.update({right:{$gt:followingsibling.right}},{$inc:{right:2}}, false, true)

db.categoriesNSO.update({left:{$gte:followingsibling.left}, 
   right:{$lte:followingsibling.right}},{$inc:{left:2, right:2}}, false, true)
db.categoriesNSO.insert(newnode) 

Let's check the result:

+-Electronics (1,46)
   +---Cameras_and_Photography (2,13)
         +------Digital_Cameras (3,4)
         +------Camcorders (5,6)
         +------Lenses_and_Filters (7,8)
         +------Tripods_and_supports (9,10)
         +------Lighting_and_studio (11,12)
     +----Shop_Top_Products (14,23)
         +------IPad (15,16)
         +------IPhone (17,18)
         +------IPod (19,20)
         +------Blackberry (21,22)
     +----LG (24,25)
     +----Cell_Phones_and_Accessories (26,45)
         +------Cell_Phones_and_Smartphones (27,38)
               +---------Nokia (28,29)
               +---------Samsung (30,31)
               +---------Apple (32,33)
               +---------HTC (34,35)
               +---------Vyacheslav (36,37)
           +-------Headsets (39,40)
           +-------Batteries (41,42)
           +-------Cables_And_Adapters (43,44)

Node Removal

While potentially rearranging node order within the same parent is identical to exchanging node's left and right values, the formal way of moving the node is first removing node from the tree and later inserting it to new location. Node: node removal without removing its child is out of scope for this article. For now, we assume, that node to remove has no children, i.e., right-left=1.

Steps are identical to adding the node - i.e., we are adjusting the space by decreasing affected left/right values,
and removing the original node.

var nodetoremove = db.categoriesNSO.findOne({_id:"LG"});

if((nodetoremove.right-nodetoremove.left-1)>0.001) {
    print("Only node without childs can be removed")
    exit
}

var followingsibling = db.categoriesNSO.findOne({_id:"Cell_Phones_and_Accessories"});

//update all remaining nodes
db.categoriesNSO.update({right:{$gt:nodetoremove.right}},{$inc:{right:-2}}, false, true)
db.categoriesNSO.update({left:{$gt:nodetoremove.right}},{$inc:{left:-2}}, false, true)
db.categoriesNSO.remove({_id:"LG"}); 

Let's check the result:

+-Electronics (1,44)
 +--Cameras_and_Photography (2,13)
       +-----Digital_Cameras (3,4)
       +-----Camcorders (5,6)
       +-----Lenses_and_Filters (7,8)
       +-----Tripods_and_supports (9,10)
       +-----Lighting_and_studio (11,12)
   +---Shop_Top_Products (14,23)
       +-----IPad (15,16)
       +-----IPhone (17,18)
       +-----IPod (19,20)
       +-----Blackberry (21,22)
   +---Cell_Phones_and_Accessories (24,43)
       +-----Cell_Phones_and_Smartphones (25,36)
             +--------Nokia (26,27)
             +--------Samsung (28,29)
             +--------Apple (30,31)
             +--------HTC (32,33)
             +--------Vyacheslav (34,35)
       +------Headsets (37,38)
       +------Batteries (39,40)
       +------Cables_And_Adapters (41,42)

Updating/Moving the Single Node

Moving the node can be within the same parent, or to another parent. If the same parent and nodes are without children, then you just need to exchange nodes (left, right) pairs.

The formal way is to remove node and insert to new destination, thus the same restriction applies - only node without children can be moved. If you need to move subtree, consider creating mirror of the existing parent under new location, and move nodes under the new parent one by one. Once all nodes are moved, remove obsolete old parent.

As an example, let's move LG node from the insertion example under the Cell_Phones_and_Smartphones node, as a last sibling (i.e., you do not have the following sibling node as in the insertion example).

Steps

1. to remove LG node from tree using node removal procedure described above
2. to take right value of the new parent. New node will have left value of the parent's right value and right value - incremented by one parent's right one. Now we have to create the place for the new node: update affects right values of all nodes on a further traversal path

var newparent = db.categoriesNSO.findOne({_id:"Cell_Phones_and_Smartphones"});
var nodetomove = {_id:'LG', left:newparent.right,right:newparent.right+1}

//3rd and 4th parameters: false stands for upsert=false and true stands for multi=true
db.categoriesNSO.update({right:{$gte:newparent.right}},{$inc:{right:2}}, false, true)
db.categoriesNSO.update({left:{$gte:newparent.right}},{$inc:{left:2}}, false, true)
db.categoriesNSO.insert(nodetomove) 

Let's check the result:

+-Electronics (1,46)
 +--Cameras_and_Photography (2,13)
       +-----Digital_Cameras (3,4)
       +-----Camcorders (5,6)
       +-----Lenses_and_Filters (7,8)
       +-----Tripods_and_supports (9,10)
       +-----Lighting_and_studio (11,12)
   +---Shop_Top_Products (14,23)
       +-----IPad (15,16)
       +-----IPhone (17,18)
       +-----IPod (19,20)
       +-----Blackberry (21,22)
   +---Cell_Phones_and_Accessories (24,45)
       +-----Cell_Phones_and_Smartphones (25,38)
               +---------Nokia (26,27)
               +---------Samsung (28,29)
               +---------Apple (30,31)
               +---------HTC (32,33)
               +---------Vyacheslav (34,35)
               +---------LG (36,37)
           +-------Headsets (39,40)
           +-------Batteries (41,42)
           +-------Cables_And_Adapters (43,44)

Getting All Node Descendants

This is the core stength of this approach - all descendants retrieved using one select to DB. Moreover, by sorting by node left - the dataset is ready for traversal in a correct order.

var descendants=[]
var item = db.categoriesNSO.findOne({_id:"Cell_Phones_and_Accessories"});
print ('('+item.left+','+item.right+')')
var children = db.categoriesNSO.find({left:{$gt:item.left}, 
               right:{$lt:item.right}}).sort(left:1);
while(true === children.hasNext()) {
  var child = children.next();
  descendants.push(child._id);
}

descendants.join(",")
//Cell_Phones_and_Smartphones,Headsets,Batteries,Cables_And_Adapters,
//Nokia,Samsung,Apple,HTC,Vyacheslav 

Getting Path to Node

Retrieving path to node is also elegant and can be done using single query to database:

var path=[]
var item = db.categoriesNSO.findOne({_id:"Nokia"})

var ancestors = db.categoriesNSO.find({left:{$lt:item.left}, 
                right:{$gt:item.right}}).sort({left:1})
while(true === ancestors.hasNext()) {
  var child = ancestors.next();
  path.push(child._id);
}

path.join('/')
// Electronics/Cell_Phones_and_Accessories/Cell_Phones_and_Smartphones 

Indexes

Recommended index is putting index on left and right values:

db.categoriesAAO.ensureIndex( { left: 1, right:1 } ) 

And, in case you were so patient to read the article till this section, bonus:

Tree Structure Using Combination of Nested Sets and Classic Parent Reference With Order Approach

For each node, we store (ID, Parent, Order, left, right).

Left field also is treated as an order field, so we could omit order field. But from other hand
we can leave it, so we can use Parent Reference with order data to reconstruct left/right values in case of accidental corruption, or, for example, during initial import.

Adding New Node

Adding new node can be adopted from Nested Sets in this manner:

var followingsibling = db.categoriesNSO.findOne({_id:"Cell_Phones_and_Accessories"});
var previoussignling = db.categoriesNSO.findOne({_id:"Shop_Top_Products"});
var neworder = parseInt((followingsibling.order + previoussignling.order)/2);
var newnode = {_id:'LG', left:followingsibling.left,
              right:followingsibling.left+1, parent:followingsibling.parent, order:neworder};
db.categoriesNSO.update({right:{$gt:followingsibling.right}},{$inc:{right:2}}, false, true)
db.categoriesNSO.update({left:{$gte:followingsibling.left}, 
   right:{$lte:followingsibling.right}},{$inc:{left:2, right:2}}, false, true)
db.categoriesNSO.insert(newnode)  

Before insertion:

+----Cameras_and_Photography (2,13)  ord.[10]
+-----Shop_Top_Products (14,23)  ord.[20]
+-----Cell_Phones_and_Accessories (26,45)  ord.[30]

After insertion:

+--Electronics (1,46)
       +----Cameras_and_Photography (2,13)  ord.[10]
                   +-------Digital_Cameras (3,4)  ord.[10]
                   +-------Camcorders (5,6)  ord.[20]
                   +-------Lenses_and_Filters (7,8)  ord.[30]
                   +-------Tripods_and_supports (9,10)  ord.[40]
                   +-------Lighting_and_studio (11,12)  ord.[50]
       +-----Shop_Top_Products (14,23)  ord.[20]
                   +-------IPad (15,16)  ord.[10]
                   +-------IPhone (17,18)  ord.[20]
                   +-------IPod (19,20)  ord.[30]
                   +-------Blackberry (21,22)  ord.[40]
       +-----LG (24,25)  ord.[25]
       +-----Cell_Phones_and_Accessories (26,45)  ord.[30]
                   +-------Cell_Phones_and_Smartphones (27,38)  ord.[10]
                               +----------Nokia (28,29)  ord.[10]
                               +----------Samsung (30,31)  ord.[20]
                               +----------Apple (32,33)  ord.[30]
                               +----------HTC (34,35)  ord.[40]
                               +----------Vyacheslav (36,37)  ord.[50]
                   +--------Headsets (39,40)  ord.[20]
                   +--------Batteries (41,42)  ord.[30]
                   +--------Cables_And_Adapters (43,44)  ord.[40]

Updating/Moving the Single Node

Identical to insertion approach.

Node Removal

Approach from Nested Sets is used.

Getting Node Children, Ordered

Now is possible by using (Parent, Order) pair:

 db.categoriesNSO.find({parent:"Electronics"}).sort({order:1});
/*

{ "_id" : "Cameras_and_Photography", "parent" : "Electronics", 
  "order" : 10, "left" : 2, "right" : 13 }
{ "_id" : "Shop_Top_Products", "parent" : "Electronics", 
  "order" : 20, "left" : 14, "right" : 23 }
{ "_id" : "LG", "left" : 24, "right" : 25, 
  "parent" : "Electronics", "order" : 25 }
{ "_id" : "Cell_Phones_and_Accessories", "parent" : "Electronics", 
  "order" : 30, "left" : 26, "right" : 45 }
*/ 

Getting All Node Descendants

Approach from Nested Sets is used.

Getting Path to Node

Approach from nested sets is used.

Code in Action

The code can be downloaded from repository at https://github.com/Voronenko/Storing_TreeView_Structures_WithMongoDB.

All files are packaged according to the following naming convention:

• MODELReference.js - initialization file with tree data for MODEL approach
• MODELReference_operating.js - add/update/move/remove/get children examples
• MODELReference_pathtonode.js - code illustrating how to obtain path to node
• MODELReference_nodedescendants.js - code illustrating how to retrieve all the descendands of the node

All files are ready to use in mongo shell. You can run examples by invoking mongo < file_to_execute, or, if you want, interactively in the shell or with RockMongo web shell.

History

• 6^th January, 2013: Initial version