Memory Hierarchy

Important consequence:


Block and Record Addresses

Blocks (and Records) can be in

  • the main memory
    • their address is the address of the 1st byte of the block (record)
  • the secondary storage
    • and the address is: device id, cylinder number, etc.
    • A record can be identified by an offset within a block

There are several ways to represent an address in the secondary memory


Physical Address

  • host, disk id, cylinder id, track, block, offset


Logical (Structured) Address

  • arbitrary string of some fixed length
  • a map table knows how to translate logical address to physical
  • map-table.png

Logical table and map table give us flexibility

  • may move data around as we want
  • making sure we maintain same logical address


Point Swizzling

  • Initially all pointers have physical address
  • but when we load them into memory, we need to swizzle (translate) them to main memory address


Arranging Data on Disk

physical algorithms depend on

  • how data (relations, records, shemas) is organized on disk
  • what data structures are used

Definitions

  • a data element (a tuple of object) is represented by a record, which consists of consecutive bytes on some disk block
  • header is a region that contains some meta information about the record

many machines allow more efficient access for main memory chunks when the data is addressed by a multiplier of 4 or 8


Fixed-Length Records

This is the simplest sort of records

  • they consist only of fixed-length fields

a record starts with a fixed-length header, which may store

  • a pointer to the schema
  • length of the record (to go through records without looking at the schema)
  • timestamps - when the record was last modified or read (useful for transactions)

Example

CREATE TABLE MovieStar (
  name CHAR(30) PRIMARY KEY,
  address VARCHAR(255),
  gender CHAR(1),
  birthday DATE
);
  • name: 30 bytes - allocate 32 (multiplier of 4) to allow faster access
  • address: 255 + 1 bytes (255 bytes for text, 1 for the string endmarker)
  • gender: either M or F, 4 bytes
  • birthday: 10 bytes, allocate 12 bytes

layout-fixed-record.png

Blocks

  • There records are stored in blocks of the disk and moved into the main memory along with the entire block
  • layout-fixed-block.png
  • we pack as much as possible to the block, and leave the remaining space unused

A block header may hold

  • which relation this block belongs to
  • timestamp that shows time of the last access
  • other things


Offset Table

Another way to organize records within a block is to keep an offset table in the header

offset-table.png

The block is populated with records from the end

  • useful when records can be of different length
  • in this case don't know in advance how many records the block will hold


Variable-Length Data Records

Not everything can be represented by fixed-length records:

  • data items with varying size
    • addresses can be 256 bits, but usually not longer than 50 bits
    • can safe a lot of space!
  • repeated fields
    • for example in many-to-many relationships we want to store many pointers within one record
  • variable-format records
    • when schema is not knows in advance (say JSON or XML)
  • media streams
    • MPEG video or audio

When there are fields whose length can vary we should locate them in such a way that we can find them

Put Fixed-Length Fields Ahead

  • Put all fixed-length fields ahead
  • then add to the header:
    • length of the whole record
    • pointers (offsets) to all variable-length fields
    • not needed to include the pointer to the first such field - since there are only fixed-length fields before it, can already calculate the address

To represent a NULL value we just put a null-pointer value to the pointer

Example

  • var-len-records-1.png

Repeating Fields

Say we have a fixed-length field $F$ but it can repeat a number of times

  • in this case we can group all occurrences together
  • to locate an item we keep 2 values: length $L$ and offset $O$ to the first item
    • to get $i$th value we can:
    • $O + (i - 1) \cdot L$

Example

  • one movie star can have several movies
  • we can represent it by pointers to movie records
  • var-len-fixed-len.png

Alternative Approach

Alternatively to #Put Fixed-Length Fields Ahead

  • we keep records of fixed length in the block, but
  • the variable-length portion of a record - in a separate block
  • good for variable-length fields and repeating fields

So in records we keep

  • pointers to place where each var-length field begins and
  • either how many repetitions there are or
  • where the field ends

Example

  • address + len, name + len, movies + number of references
  • var-len-alt1.png

Advantages

  • keeping records fixed-sized allows for more efficient serach
  • minimizes overhead in block records
  • allows records to be moved easier

Disadvantaged

Records Spanning Several Blocks

How to store records that are larger than a block?

  • technique for storing such records as called spanned records

This technique is also useful when records are smaller than a block, but storing them within a block wastes lots of space

  • say a record takes 51% of a block
  • then 49% of each block will be wasted (cannot put another record there)
  • A portion of a record that appears in one block is called a record fragment
  • A record with 2 or more fragments is called spanned, otherwise (it lays within one block) - it's unspanned


To store a record fragment we need some extra information in the header

  • a bit to indicate if it's a fragment or not
  • 2 bits to tell if it's the first of the last fragment of a record
  • if there's a next or previous fragment we need a pointer to them

Example of a record spanning 2 blocks:

  • spanned-record.png


BLOBs

Now let's consider truly enormous records

  • Such objects are binary and large
  • BLOBs - binary large objects

Storage of BLOBs

  • a BLOB should be stored sequentially, so it may be retrieved efficiently
  • it's also possible to store it in a linked list of blocks


Column Stores

See Column-Oriented Databases

TODO: add more info


Record Modification

  • Insertions, deletions and updates of records often cause problems
  • Most severe problems happen when records change their length


Insertion

Suppose we insert a new record into a relation

if there's no particular order,

  • we just find a block with some empty space (or get a new one)
  • and put the record there

But if we must keep some order (say we want records be sorted on the primary key):

  • first locate the appropriate block
  • suppose there's room to fit the record
    • to preserve order we may need to slide down some records to free space at the proper point
    • and then we just put the record into that place
    • in this case may also need to modify the offset table:
      • change pointers for the moved records
      • add a pointer to the new one
      • be careful with Point Swizzling
  • if no room for a records in the block
    • need to find space outside of the block
    • (2 major approaches discussed below)

Approach 1: Nearby Blocks

Look for room on a nearby block

For example

  • block $B_1$ doesn't have space, but following it $B_2$ has
  • so we move the highest records of $B_1$ to $B_2$
  • slide the records around on both blocks

Approach 2: Overflow Blocks

We can create an overflow block

  • each block $B$ has a pointer to a special block where additional records are kept
  • by "additional" we mean records that theoretically belong to $B$, but don't fit in
  • these blocks are called overflow blocks
  • in such a way we can link blocks together to have a list of overflow blocks
overflow-blocks.png


Deletion

When we delete a record, we may want to reclaim the freed space

If we use an offset table, and can move records around the block,

  • then we can compact the space
offset-table.png
  • note the unused space: we can just shift all the remaining records a bit

If we cannot move records,

  • we should maintain a list of available space addresses in the header
  • to be used afterwards when inserting


Tombstones

Dangling Pointers

  • there might be pointers to occupied records (e.g. see Point Swizzling)
  • we don't want these pointers to dangle or point to wrong records

Usual technique in this case

  • to place a tombstone in place of the record being deleted
  • the tombstone is permanent: it must exist until the DB is reconstructed

Where to put a tombstone depends on the nature of record pointers


If we need to replace records by tombstones,

  • we should have a bit that indicates whether a record is a tombstone or not
  • only this bit (or byte) must remain untouched
  • the rest can be reused safely
  • example
tombstones.png


Update

When a fixed-length record is updated, it causes no effect on the storage system

But it's not the case for variable-length records

  • here we have all problems associated with both insertions and deletions
  • (except for tombstones - we won't create them)

If the updated version is longer that the old one

  • we'll need to find more space on the block
  • it may involve sliding records or creating overflow blocks
  • if portions are stored on another block, we may need to move elements around that block or create a new one

If the new version is shorter, we may want to reclaim the freed space for later use


Sources

Machine Learning Bookcamp: Learn machine learning by doing projects. Get 40% off with code "grigorevpc".

Share your opinion