Classical B-trees constrain key counts for non-root nodes to lie between d and 2d for some d. This means that merging of nodes is only possible if an underflow has already occurred and the other node involved in the merge has minimum occupancy. Together with the separator key pulled from...

It's possible in a variant of B+ tree called PO-B+ tree. In this "preparatory operations B+ tree" the number of keys in a node may be between n-1 and 2n+1 rather than n and 2n in the usual B+-tree (quoted from the paper). For delete operation (called PO-delete in the...

Okay so I have the answer, if anyone come across this: Max - because the leafs should contain all of the values, the MAXIMUM value is: (n-1)n^3 = 74*(75^3) Min: the root minimum is 2, and each of the two middle levels pointers minimum is floor() of n/2 and the...

database,caching,memory,operating-system,b-tree

The 'cache-consciousness' bit refers to a special discipline of page layout that tries to maximise the utilisation of the first-level data cache of the CPU, often optimised for a specific cache line size (e.g. 64 bytes). One standard technique (independent of cache line size) is to use offset-value coding in...

Straight from Wikipedia: The B*-tree balances more neighboring internal nodes to keep the internal nodes more densely packed (Comer 1979, p. 129). This variant requires non-root nodes to be at least 2/3 full instead of 1/2 (Knuth 1998, p. 488). To maintain this, instead of immediately splitting up a node...

Then how much minimum number of entries(not pointers) should be there in a node of a B+ tree.Is it 2 or 1?. 1 ("Every non-leaf, non-root node has at least floor(d / 2) children.") => 2 children => 1 key This is not in fact the real picture. B+...

java,multithreading,concurrency,b-tree,concurrentmodification

As noone replied I would like to summarize what we (I) finally did. The structure is now separated. We have a RTree which leaf are actually Tables. Those tables can be even remote so we have a distribution way that is mostly transparent thanks to RMI and proxies. The rest...

See https://stuff.mit.edu/afs/sipb/user/gamadrid/nscript/btreep.h, which defines a node as: typedef struct node { struct node *parent; struct node *left; struct node *right; } *btnode; Not a b-tree, but the principle is the same. The Parent pointer is just there as a convenience, much like a doubly-linked linked list allows you to traverse...

You can design a system with any order you choose from 1 upwards. If you make the order too big, it becomes difficult to find the key in the node, and the tree will be just 1 or 2 levels deep. For example, if the order is 1,000,000, then you'd...

algorithm,data-structures,b-tree,avl-tree,tree-balancing

The answer is... yes and no. B-trees don't need to perform rotations because they have some slack with how many different keys they can pack into a node. As you add more and more keys into a B-tree, you can avoid the tree becoming lopsided by absorbing those keys into...

algorithm,data-structures,b-tree

Typically, you'd choose the order so that the resulting node is as large as possible while still fitting into the block device page size. If you're trying to build a B-tree for an on-disk database, you'd probably pick the order such that each node fits into a single disk page,...

algorithm,tree,b-tree,2-3-4-tree,insertion-order

Yes, the sequence of insertions matters. Obviously, the tree will be taller for the same number of keys if more nodes are 1-nodes. They way to maximise the number of 1-nodes in the tree is to continually expand one branch of the tree to 4-nodes, increasing the height of the...

Sure. A B-Tree is sorted, so you can find the first element whose value is lexicographically greater than or equal to the prefix, and then simply iterate sequentially until you find an element which does not start with the prefix. If you want to find elements starting with a case-insensitive...

sql,sql-server,indexing,b-tree,non-clustered-index

The nonclustered index will be pretty much the same as with just one column - but each index entry in the B++ navigation tree will have two column values (PersonName, PersonAge). Since both columns are comparable, a clearly defined ordering will be applied - first by PersonName, then by PersonAge...