[DMDB] Hashing

semester4/dmdb/parts/03_systems/02_indexing/01_b-trees/00_b-trees.tex

@@ -1,4 +1,3 @@
-\subsubsection{B+ Trees}
 \paragraph{B-Tree}
 In B-Trees of order $k$, each node (except the root) has between $k \div 2$ and $k$ child nodes.
 The root node has at least two children, unless it is also a leaf and any non-leaf node contains at exactly $k - 1$ keys.

semester4/dmdb/parts/03_systems/02_indexing/02_hashing/00_hash-tables.tex

@@ -0,0 +1,54 @@
+\paragraph{Hashing in Databases}
+Hashing is a very common operation in many systems, including databases.
+Many internal data structures, such as buffer caches and lock tables, are implemented as hash tables.
+Some operators also use hashing to speed things up, such as hash join and group by operators.
+
+It can also be used as an indexing and partitioning strategy.
+
+Hashing is on the other side compared to B+ trees when it comes to the trade-off between storage and compute,
+by using more compute, it can save on storage space requirements.
+
+
+\paragraph{Hash Tables}
+There are many hashing functions with strong properties, but in databases, the hash function has to be very cheap, as it is used very often.
+
+Perfect hash functions do exist, but they need a hash table that is as big as the cardinality of the attributes,
+so for 4 byte keys, it needs a 4 GB table.
+Thus, to save on storage, we use a hash table that is smaller than that.
+If we were to choose it too small, there would be too many collisions, if it is chosen too large, then we waste lots of space.
+
+Collisions may also occur when the index key is not \texttt{UNIQUE}, and thus it could be that multiple tuples have the same key.
+
+That may lead you to think, why not grow it if we have a collision. That is a valid idea, but growing hash tables is expensive, thus should be avoided.
+
+Another shortcoming of hash indexes is that it only supports \bi{point queries}, i.e. it only works for the primary key, but barely anything else.
+
+
+\paragraph{Collisions}
+A way to handle collisions safely is to use \bi{chaining}. When a collision occurs, we add another entry in a linked list.
+If these lists are reasonably short, then it is reasonably efficient. We can also already reserve space for the linked lists to speed things up,
+if we expect (many) collisions to occur.
+
+Another option is to use \bi{open addressing}. Here, when a collision occurs, we look for an empty slot in the hash table using some rule.
+Here, two ways of achieving this are covered in the course:
+\begin{itemize}
+    \item \bi{Linear probing}, where we go to the next slot(s) and place the attribute there
+    \item \bi{Cuckoo hashing}, where we use several hash functions and move to the next one, if we have a collision with the first, and so on
+\end{itemize}
+
+
+\paragraph{Extensible Hashing}
+When the hash table is full, in a basic system, we would need to create a new, larger hash table with more buckets (typically double the number) and then rehash all existing items.
+This of course is very expensive both computationally and in terms of memory accesses, as we do lots of random accesses, which leads to cache misses.
+
+This is where extensible comes in. It is based on sharing buckets and unsharing them when needed.
+These hash table buckets are mapped into blocks and initially several buckets share the same block
+
+Then, when a bucket gets full, we split the bucket and move entries as needed into a new bucket.
+
+In \bi{local sharing}, the size of a table can be doubled without immediately adding more space, allowing for more splitting.
+We simply increase the number of buckets and the degree of sharing and split the buckets as they become full.
+
+Again, if we initially provide more space than needed, we can allow for the first growth to happen without disruption.
+
+We want (ideally) to have two page lookups to access an item, so we typically have a lookup in the bucket directory and the data block and they both can grow independently.

semester4/dmdb/parts/03_systems/02_indexing/02_hashing/01_linear-hashing.tex

@@ -0,0 +1,11 @@
+\paragraph{Linear hashing}
+Here, a split pointer is used to indicate which bucket will be split in case of overflow.
+When it occurs, we chain the block that overflows, split the bucket indicated by the pointer and move the pointer.
+
+This allows for a gradual increase in the size of the table and the idea is to gradually redistribute the data.
+We always split on the pointer, even if the overflow is elsewhere. The pointer will eventually reach a bucket with chains
+and when the bucket is split, the data is reorganized.
+
+This has the advantage that the directory (i.e. the list of buckets) grows page by page, instead of doubling.
+
+When all buckets have been split, start fresh.

semester4/dmdb/parts/03_systems/02_indexing/02_hashing/02_in-postgres.tex

@@ -0,0 +1,17 @@
+\paragraph{In Postgres}
+PostgreSQL uses a variation of linear (overflow) hashing and extensible hashing (with doubling).
+Buckets are initially allocated in groups with powers of two. Overflows are captured in overflow pages (like in linear hashing).
+When a split occurs, we do not allocate all the pages, but a fraction of them.
+
+These ideas can be combined in many different ways.
+
+\paragraph{When to use}
+For memory structures:
+\begin{itemize}
+    \item For shared resources (System Global Area)
+    \item Database Buffer Cache for I/O
+    \item Redo log buffer for recovery
+    \item For large memory pools
+\end{itemize}
+
+Then of course, it can be used for a hash join, for the \texttt{SELECT DISTINCT} function and for aggregation (\texttt{GROUP BY}).

semester4/dmdb/parts/03_systems/main.tex

@@ -22,10 +22,18 @@
 \newpage
 \subsection{Indexing}
 \input{parts/03_systems/02_indexing/00_access-methods.tex}
-\input{parts/03_systems/02_indexing/00_b-trees/00_b-trees.tex}
-\input{parts/03_systems/02_indexing/00_b-trees/01_basics.tex}
-\input{parts/03_systems/02_indexing/00_b-trees/02_operations.tex}
-\input{parts/03_systems/02_indexing/00_b-trees/03_optimizations.tex}
-% \input{parts/03_systems/02_indexing/00_b-trees/}
+
+\subsubsection{B+ Trees}
+\input{parts/03_systems/02_indexing/01_b-trees/00_b-trees.tex}
+\input{parts/03_systems/02_indexing/01_b-trees/01_basics.tex}
+\input{parts/03_systems/02_indexing/01_b-trees/02_operations.tex}
+\input{parts/03_systems/02_indexing/01_b-trees/03_optimizations.tex}
+% \input{parts/03_systems/02_indexing/01_b-trees/}
+
+\subsubsection{Hashing}
+\input{parts/03_systems/02_indexing/02_hashing/00_hash-tables.tex}
+\input{parts/03_systems/02_indexing/02_hashing/01_linear-hashing.tex}
+\input{parts/03_systems/02_indexing/02_hashing/02_in-postgres.tex}
+% \input{parts/03_systems/02_indexing/02_hashing/}
 % \input{parts/03_systems/02_indexing/}
 % \input{parts/03_systems/}