Datomic R-trees

James Sofra@sofra

https://github.com/jsofra/datomic-rtree

Summary

● Motivations● Datomic overview● Datomic R-tree implementation● Hilbert Curves● Bulk loading (via Hilbert Curves)● Future plans

Motivations

● I have an interest in geospatial applications– e.g. Thunderstorm probability application

(THESPA)

● Datomic is an interesting database that makes different trade-offs to other databases– Wonder how far we can take the ability to

describe arbitrary structures in Datomic

Why don't we have both?

Datomic Overview

● Immutable database● Time-base facts (stored as entites)● ACID transactions● Expressive queries using Datalog● Pluggable storage● Flexible enough to act as row, column or graph database● Schema that describes attributes that can be attached to

entities– Attributes have a type; String, Long, Double, Inst, Ref etc.

● Database functions– Stored in the database, see the in transaction value

Datomic Overview - Architecture

Datomic Motivations

● Things that make Datomic appealing for spatial data– Time-base nature of Datomic is useful for time series data which we

often have– No need to add spatial operations (union, intersection, etc.) to the

database, can be handled by libraries in the peers– Spatial indexes can be stored as regular data, allows for a lot of

freedom over choice of index, handling multiple indexes over subsets of the data in space and time

– Flexible entity structures are useful because spatial data frequently does not fit nicely in a table

– Immutability is surprisingly useful in lots of different applications!

R-trees

● "R-Trees: A Dynamic Index Structure for Spatial Searching"– Guttman, A (1984)

● Efficient query of multi-dimensional data

● Groups nearby objects● Balanced (all leaf nodes at

same level)● Aims for nodes minimise

empty space coverage and overlap

● Designed for storage on disk (as used in databases)

R-trees - Insertions

● Choose a leaf node to insert● Insert entry into leaf node and enlarge

node● If node has more than max number of

children split the node and propagate enlargement and splits up tree

Datomic R-tree - Schema

:rtree/root :db.type/ref

:rtree/max-children :db.type/long

:rtree/min-children :db.type/long

:node/children :db.type/ref

:node/is-leaf? :db.type/boolean

:node/entry :db.type/ref

:bbox/min-x :db.type/double

:bbox/min-y :db.type/double

:bbox/max-x :db.type/double

:bbox/max-y :db.type/double

Datomic R-tree - choose-leaf

Datomic R-tree - split-node

Datomic R-tree - pick-seeds

Datomic R-tree - pick-next

Datomic R-tree – regular transaction

Database function

New entry with new ID

Add new entry as child to leaf node

Transaction for adding new entry, calls database function

Datomic R-tree – split transaction

New entry

Remove root

Create new leaf nodes

Add new root

Bulk loading

● Issues with single insertion loading of R-tree– Becomes slow with with many insertions

– The resulting tree is not as always as efficient as it could be

● Bulk loading builds a tree once from a number of entities

● Two basic approaches top-down and bottom-up

● Bulk loading does not imply bulk insertion

Bulk loading – sort based loading

● Aims for better R-tree performance● Bottom-up approach● Sorts all entities in an order that aims to preserve locality● Partitions the entities into clusters that are (hopefully)

spatially collocated● Recursively apply partitioning to build up the tree

● “Sort-based Query-adaptive Loading of R-trees”– D. Achakeev; B. Seeger; P. Widmayer (2012)

● “Sort-based parallel loading of R-trees”– D. Achakeev; M. Seidemann; M. Schmidt; B. Seeger (2012)

Hilbert Curves● a continuous fractal

space-filling curve● first described by

mathematician David Hilbert in 1891

● useful because it enables mapping from 2D to 1D preserving some notion of locality

● Other options are; Peano curve, Z-order curve (aka Morton Curve)

Hilbert Curves● a continuous fractal

space-filling curve● first described by

mathematician David Hilbert in 1891

● useful because it enables mapping from 2D to 1D preserving some notion of locality

● Other options are; Peano curve, Z-order curve (aka Morton Curve)

Bulk loading – hilbert sort based

● Better Hilbert partitioning

Bulk loading via Hilbert curves

● Insert all entities into Datomic (or using existing entities)

● Entities include an indexed Hilbert value attribute

● Obtain a seq of the entities using the :avet index with the Hilbert value

● Perform partioning

Bulk - hilbert-ents

Takes advantage of Datomic index API to get direct access to the Hilbert index

Bulk - min-cost-index

List of options for the next partition point

Must be at least min-children in the partition

Bulk - cost-partition

Bulk - p-cost-partition

Bulk - dyn-cost-partition

Conclusions

● It works!

(install-single-insertions conn 50000 20 10)– "Elapsed time: 119114.342783 msecs"

(install-and-bulk-load conn 50000 20 10)– "Elapsed time: 6511.543299 msecs"

(time (naive-intersecting all-entries search-box))– "Elapsed time: 870.575802 msecs"

(time (intersecting root search-box))– "Elapsed time: 2.927883 msecs"

* note these times should be regarded with suspicion since they only use the in memory database

Future plans

● Retractions and updates● Bulk insertions● More search and query support● Schema for supporting Meridian Shapes

and Features● Investigate other R-trees; R* tree, R+ tree

Questions?

Thanks you! Any questions?

James Sofra@sofra

Other Interesting Resources● "The R*-tree: an efficient and robust access method for points

and rectangles"● “OMT: Overlap Minimizing Top-down Bulk Loading Algorithm for

R-tree.”– T. Lee; S. Lee (2003)

● “The Priority R-Tree: A Practically Efficient and Worst-Case Optimal R-Tree”– L. Arge; M. de Berg; K. Yi (2004)

● “Compact Hilbert Indices”– Hamilton. C (2006)

● “R-Trees: Theory and Applications”– Manolopoulos. Y; Nanopoulos. A; Papadopoulos. A. N; Theodoridis. Y

(2006)