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 SpatialIndex Reference 
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:Author: Marios Hadjieleftheriou
:Contact: mhadji@gmail.com
:Revision: $Revision: 185 $
:Date: $Date: 2010-04-21 13:50:02 -0500 (Wed, 21 Apr 2010) $

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Introduction
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You have downloaded the SpatialIndex Library. This is free software under LGPL.
The library is in beta testing stage. Use at your own risk.

The purpose of this library is to provide:
 1. An extensible framework that will support robust spatial indexing
    methods.
 2. Support for sophisticated spatial queries. Range, point location,
    nearest neighbor and k-nearest neighbor as well as parametric
    queries (defined by spatial constraints) should be easy to deploy and run.
 3. Easy to use interfaces for inserting, deleting and updating information.
 4. Wide variety of customization capabilities. Basic index and storage 
    characteristics like the page size, node capacity, minimum fan-out, 
    splitting algorithm, etc. should be easy to customize.
 5. Index persistence. Internal memory and external memory structures 
    should be supported.  Clustered and non-clustered indices should 
    be easy to be persisted.

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Installation
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By default include files and library files will be installed in /usr/local. If 
you would like to use a different installation directory (e.g., in case 
that you do not have root access) run the configure script with 
the --prefix option:

::

    ./configure --prefix=/home/marioh/usr

Make the library::

     make

Install the library::

     make install

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Using the Library
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You are ready to use the library. All you have to
do is to include the file SpatialIndex.h in your source
files and then compile with the following options:

::
 
  g++ MyFile.cc -o MyFile -L/home/marioh/usr/lib -I/home/marioh/usr/include -lpthread -lspatialindex

If the library is installed in the default /usr/local path, then the 
-I and -L options are not necessary.

If you are compiling on Mac OS X you will might need to add the -bind_at_load 
option when linking against the dynamic link libraries.  OS X Tiger should 
work out of the box, however, with XCode 3.0.

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Library Overview
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The library currently consists of six packages:
 1. The core spatialindex utilities.
 2. The storagemanager files.
 3. The spatialindex interfaces.
 4. The rtree index.
 5. The mvrtree index.
 6. The tprtree index.

I will briefly present the basic features supported by each package. 
For more details you will have to refer to the code, for now.

Spatial Index Utilities
------------------------------------------------------------------------------

To provide common constructors and uniform initialization for all objects 
provided by the library a PropertySet class is provided. A PropertySet 
associates strings with Variants. Each property corresponds to one string.

A basic implementation of a Variant is also provided that supports a 
number of data types. The supported data types can be found in SpatialIndex.h

PropertySet supports three functions:

 1. getProperty returns the Variant associated with the given string.
 2. setProperty associates the given Variant with the given string.
 3. removeProperty removes the specified property from the PropertySet.

A number of exceptions are also defined here. All exceptions extend 
Exception and thus provide the what() method that returns a string 
representation of the exception with useful comments.  It is advisable to 
use enclosing try/catch blocks when using any library objects. Many 
constructors throw exceptions when invalid initialization properties are specified.

A general IShape interface is defined. All shape classes should extend 
IShape. Basic Region and Point classes are already provided. Please 
check Region.h and Point.h for further details.

Storage Manager
------------------------------------------------------------------------------

The library provides a common interface for storage management of all 
indices. It consists of the IStorageManager interface, which provides functions 
for storing and retrieving entities.  An entity is viewed as a simple byte 
array; hence it can be an index entry, a data entry or anything else that the 
user wants to store. The storage manager interface is generic and does not apply 
only to spatial indices.

Classes that implement the IStorageManager interface decide on how to 
store entities.  simple main memory implementation is provided, for example, 
that stores the entities using a vector, associating every entity with a 
unique ID (the entry's index in the vector). A disk based storage manager 
could choose to store the entities in a simple random access file, or a 
database storage manager could store them in a relational table, etc. as long 
as unique IDs are associated with every entity. Also, storage managers should 
implement their own paging, compaction and deletion policies transparently 
from the callers (be it an index or a user).

The storeByteArray method gets a byte array and its length and an entity ID. 
If the caller specifies NewPage as the input ID, the storage manager allocates 
a new ID, stores the entity and returns the ID associated with the entity. 
If, instead, the user specifies an already existing ID the storage manager 
overwrites the old data. An exception is thrown if the caller requests 
an invalid ID to be overwritten.

The loadByteArray method gets an entity ID and returns the associated byte 
array along with its length. If an invalid ID is requested, an exception is thrown.

The deleteByteArray method removes the requested entity from storage.

The storage managers should have no information about the types of entities 
that are stored. There are three main reasons for this decision:

 1. Any number of spatial indices can be stored in a single storage manager
    (i.e. the same relational table, or binary file, or hash table, etc., can 
    be used to store many indices) using an arbitrary number of pages and 
    a unique index ID per index (this will be discussed shortly).
 2. Both clustered and non-clustered indices can be supported. A clustered 
    index stores the data associated with the entries that it contains along 
    with the spatial information that it indexes. A non-clustered index stores 
    only the spatial information of its entries. Any associated data are 
    stored separately and are associated with the index entries by a unique ID. 
    To support both types of indices, the storage manager interface should be 
    quite generic, allowing the index to decide how to store its data.  
    Otherwise clustered and non-clustered indices would have to be 
    implemented separately.
 3. Decision flexibility. For example, the users can choose a clustered index 
    that will take care of storing everything. They can choose a main memory 
    non-clustered index and store the actual data in MySQL.  They can choose 
    a disk based non-clustered index and store the data manually in a 
    separate binary file or even in the same storage manager but doing a low 
    level customized data processing.

Two storage managers are provided in the current implementation:

 1) MemoryStorageManager
 2) DiskStorageManager

MemoryStorageManager
~~~~~~~~~~~~~~~~~~~~~~~

As it is implied be the name, this is a main memory implementation. Everything 
is stored in main memory using a simple vector. No properties are needed to 
initialize a MemoryStorageManager object. When a MemoryStorageManager instance 
goes out of scope, all data that it contains are lost.

DiskStorageManager
~~~~~~~~~~~~~~~~~~~~~~~

The disk storage manager uses two random access files for storing information. 
One with extension .idx and the other with extension .dat.

A list of all the supported properties that can be provided during 
initialization, follows:

=========   ======== ===========================================================
Property      Type     Description
=========   ======== ===========================================================
FileName    VT_PCHAR The base name of the file to open (no extension)
Overwrite   VT_BOOL  If Overwrite is true and a storage manager with the 
                     specified filename already exists, it will be 
                     truncated and overwritten. All data will be lost.
PageSize    VT_ULONG The page size to use. If the specified filename 
                     already exists and Overwrite is false, PageSize is ignored.
=========   ======== ===========================================================

For entities that are larger than the page size, multiple pages are used. 
Although, the empty space on the last page is lost. Also, there is no effort 
whatsoever to use as many sequential pages as possible. A future version 
might support sequential I/O. Thus, real clustered indices cannot be supported yet.

The purpose of the .idx file is to store vital information like the page size, 
the next available page, a list of empty pages and the sequence of pages 
associated with every entity ID.

This class also provides a flush method that practically overwrites the 
.idx file and syncs both file pointers.

The .idx file is loaded into main memory during initialization and is 
written to disk only after flushing the storage manager or during object 
destruction. In case of an unexpected failure changes to the storage manager
will be lost due to a stale .idx file. Avoiding such disasters is future work.

SpatialIndex Interfaces
------------------------------------------------------------------------------

A spatial index is any index structure that accesses spatial information 
efficiently. It could range from a simple grid file to a complicated tree 
structure. A spatial index indexes entries of type IEntry, which can be index 
nodes, leaf nodes, data etc. depending on the structure characteristics. 
The appropriate interfaces with useful accessor methods should be provided 
for all types of entries.

A spatial index should implement the ISpatialIndex interface.

The containmentQuery method requires a query shape and a reference to a 
valid IVisitor instance (described shortly). The intersectionQuery method 
is the same. Both accept an IShape as the query. If the query shape is a simple
Region, than a classic range query is performed. The user though has the 
ability to create her own shapes, thus defining her own intersection and 
containment methods making possible to run any kind of range query without
having to modify the index. An example of a trapezoidal query is given in the 
regressiontest directory. Have in mind that it is the users responsibility 
to implement the correct intersection and containment methods between their 
shape and the type of shapes that are stored by the specific index that they 
are planning to use.  For example, if an rtree index will be used, a trapezoid 
should define intersection and containment between itself and Regions, since 
all rtree nodes are of type Region. Hence, the user should have some knowledge
about the index internal representation, to run more sophisticated queries.

A point location query is performed using the pointLocationQuery method. It 
takes the query point and a visitor as arguments.

Nearest neighbor queries can be performed with the nearestNeighborQuery method. 
Its first argument is the  number k of nearest neighbors requested. This 
method also requires the query shape and a visitor object.  The default 
implementation uses the getMinimumDistance function of IShape for calculating 
the distance of the query from the rectangular node and data entries stored 
in the tree. A more sophisticated distance measure can be used by implementing 
the INearestNeighborComparator interface and passing it as the last argument 
of nearestNeighborQuery. For example, a comparator is necessary when the query
needs to be checked against the actual data stored in the tree, instead of 
the rectangular data entry approximations stored in the leaves.

For customizing queries the IVisitor interface (based on the Visitor 
pattern [gamma94]) provides callback functions for visiting index and 
leaf nodes, as well as data entries. Node and data information can be obtained
using the INode and IData interfaces (both extend IEntry). Examples of using 
this interface include visualizing a query, counting the number of leaf 
or index nodes visited for a specific query, throwing alerts when a
specific spatial region is accessed, etc.

The queryStrategy method provides the ability to design more sophisticated 
queries. It uses the IQueryStrategy interface as a callback that is called 
continuously until no more entries are requested. It can be used to
implement custom query algorithms (based on the strategy pattern [gamma94]).

A data entry can be inserted using the insertData method. The insertion 
function will convert any shape into an internal representation depending on 
the index. Every inserted object should be assigned an ID (called object 
identifier) that will allow updating, deleting and reporting the object.
It is the responsibility of the caller to provide the index with IDs 
(unique or not). Also, a byte array can be associated with an entry. The 
byte arrays are stored along with the spatial information inside the leaf 
nodes. Clustered indices can be supported in that way. The byte array can
also by null (in which case the length field should be zero), and no extra 
space should be used per node.

A data entry can be deleted using the deleteData method. The object shape 
and ID should be provided. Spatial indices cluster objects according to 
spatial characteristics and not IDs. Hence, the shape is essential for 
locating and deleting an entry.

Useful statistics are provided through the IStatistics interface and 
the getStatistics method.

Method getIndexProperties returns a PropertySet with all useful index 
properties like dimensionality etc.

A NodeCommand interface is provided for customizing Node operations. Using 
the addWriteNodeCommand, addReadNodeCommand and addDeleteNodeCommand methods, 
custom command objects are added in listener lists and get executed after 
the corresponding operations.

The isIndexValid method performs internal checks for testing the 
integrity of a structure. It is used for debugging purposes.

When a new index is created a unique index ID should be assigned to it, that 
will be used when reloading the index from persistent storage. This index ID 
should be returned as an IndexIdentifier property in the instance of the 
PropsertySet that was used for constructing the index instance. Using 
index IDs, multiple indices can be stored in the same storage manager. 
It is the users responsibility to manager the index IDs. Associating the 
wrong index ID with the wrong storage manager or index type has undefined
results.

The RTree Package
------------------------------------------------------------------------------

The RTree index [guttman84] is a balanced tree structure that consists of 
index nodes, leaf nodes and data. Every node (leaf and index) has a fixed 
capacity of entries, (the node capacity) chosen at index creation An RTree 
abstracts the data with their Minimum Bounding Region (MBR) and clusters 
these MBRs according to various heuristics in the leaf nodes. Queries are 
evaluated from the root of the tree down the leaves. Since the index is 
balanced nodes can be under full. They cannot be empty though. A fill
factor specifies the minimum number of entries allowed in any node. The
fill factor is usually close to 70%.

RTree creation involves:

 1. Deciding if the index will be internal or external memory and selecting 
    the appropriate storage manager.
 2. Choosing the index and leaf capacity (also known as fan-out).
 3. Choosing the fill factor (from 1% to 99% of the node capacity).
 4. Choosing the dimensionality of the data.
 5. Choosing the insert/update policy (the RTree variant).

If an already stored RTree is being reloaded for reuse, only the index ID 
needs to be supplied during construction. In that case, some options cannot 
be modified. These include: the index and leaf capacity, the fill factor and 
the dimensionality. Note here, that the RTree variant can actually be 
modified. The variant affects only when and how splitting occurs, and 
thus can be changed at any time.

An initialization PropertySet is used for setting the above options, 
complying with the following property strings:

==========================    ===========  ============================================================
Property                       Type         Description
==========================    ===========  ============================================================
IndexIndentifier              VT_LONG      If specified an existing index will be 
                                           opened from the supplied storage manager with 
                                           the given index id. Behavior is unspecified
                                           if the index id or the storage manager are incorrect.
Dimension                     VT_ULONG     Dimensionality of the data that will be inserted.
IndexCapacity                 VT_ULONG     The index node capacity. Default is 100.
LeafCapactiy                  VT_ULONG     The leaf node capacity. Default is 100.
FillFactor                    VT_DOUBLE    The fill factor. Default is 70%
TreeVariant                   VT_LONG      Can be one of Linear, Quadratic or Rstar. Default is Rstar
NearMinimumOverlapFactor      VT_ULONG     Default is 32.
SplitDistributionFactor       VT_DOUBLE    Default is 0.4
ReinsertFactor                VT_DOUBLE    Default is 0.3
EnsureTightMBRs               VT_BOOL      Default is true
IndexPoolCapacity             VT_LONG      Default is 100
LeafPoolCapacity              VT_LONG      Default is 100
RegionPoolCapacity            VT_LONG      Default is 1000
PointPoolCapacity             VT_LONG      Default is 500
==========================    ===========  ============================================================

Performance
------------------------------------------------------------------------------

Dataset size, data density, etc. have nothing to do with capacity and page
size. What you are trying to achieve is fast reads from the disk and take
advantage of disk buffering and prefetching.

Normally, you select the page size to be equal to the disk page size (depends
on how you format the drive). Then you choose the node capacity to be enough
to fill the whole page (including data entries if you have any).

There is a tradeoff though in making node capacity too large. The larger the
capacity, the longer the "for loops" for inserting, deleting, locating node
entries take (CPU time). On the other hand, the larger the capacity the
shorter the tree becomes, reducing the number of random IOs to reach the
leaves. Hence, you might want to fit multiple nodes (of smaller capacity)
inside a single page to balance I/O and CPU cost, in case your disk page size
is too large.

Finally, if you have enough buffer space to fit most of the index nodes in
main memory, then large capacities do not make too much sense, because the
height of the tree does not matter any more. Of course, the smaller the
capacity, the larger the number of leaf nodes you will have to retrieve from
disk for range queries (point queries and nearest neighbor queries will not
suffer that much). So very small capacities hurt as well.

There is another issue when trying to fit multiple nodes per page: Leftover
space. You might have leftover space due to data entries that do not have a
fixed size. Unfortunately, in that case, leftover space per page is lost,
negatively impacting space usage.

Selecting the right page size is easy; make it equal to the disk page size.
Selecting the right node capacity is an art...

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Contact Information
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You can contact me at mhadji@gmail.com for further assistance. Please read the 
above information carefully and also do not be afraid to browse through the 
code and especially the test files inside regressiontest directory.

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References
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[guttman84] "R-Trees: A Dynamic Index Structure for Spatial Searching"
            Antonin Guttman, Proc. 1984 ACM-SIGMOD Conference on Management of Data (1985), 47-57.
[gamma94] "Design Patterns: Elements of Reusable Object-Oriented Software"
          Erich Gamma, Richard Helm, Ralph Johnson and John Vlissides, Addison Wesley. October 1994.