AN IMPROVED INDEXING SCHEME FOR RANGE QUERIES

Yvonne Yao

Adviser: Professor Huiping Guo

DATABASE-AS-A-SERVICE

Business organizations handle a large amount of data (TB)

Cost of managing and maintaining these data onsite is high

DAS DBMSs outsourcing Clients rely on service providers for data

management and maintenance Cost is a lot lowered. But…

DATABASE-AS-A-SERVICE

Security of data is not guaranteed Service providers are untrusted Store only an encrypted form of data onto the

remote server Only users with the correct key(s) can have

access How then can we query the encrypted data?

Retrieve and decrypt the entire table, and apply SQL statements on it. Too expensive!

A more realistic approach was discovered

DATABASE-AS-A-SERVICE

BUCKETIZATION

Various approaches to build meta-data: B+-tree based, hash-based, and bucket-based

What is bucketization? Partition of attribute data into several buckets Each bucket is identified by an ID Bucket IDs are stored, along with encrypted data,

on the remote server Client keeps partition information as meta-data

General bucketization approach Equi-width Equi-depth

EXAMPLE 1

EXAMPLE 1

Partition ID

[0.0 ~ 1.0] Bucket_1

[1.1 ~ 2.0] Bucket_2

[2.1 ~ 3.0] Bucket_3

[3.1 ~ 4.0] Bucket_4

EXAMPLE 1 User query:

SELECT *

FROM grades

WHERE gpa < 3.0 Qserver:

SELECT *

FROM egrades

WHERE gpaID = ‘Bucket_1’ OR

gpaID = ‘Bucket_2’ OR

gpaID = ‘Bucket_3’

Size of superset is 29, of which 7 of them are false positives

QUERY OPTIMAL BUCKETIZATION

General idea: minimizing the bucket cost of each bucket

Input: <D = (V, F), M> V = {v1, v2, v3, …, vn} where v1 < v2 < v3 < … <vn

F = Frequency of each value M = Number of buckets to fill

Output: a matrix indicating the boundary of each bucket

QUERY OPTIMAL BUCKETIZATION

QOB Finds optimum solutions to two smaller sub-

problems one contains the leftmost M-1 buckets covering

the (n-i) smallest points Another contains the rightmost single bucket

covering the remaining i points

V = {v1, v2, v3, v4, v5, v6, …, vn-3, vn-2, vn-1, vn}

n-i points go to last i points go to

M-1 buckets last bucket

EXAMPLE 2

Partition ID

[0.7 ~ 1.2] Bucket_1

[1.5 ~ 2.5] Bucket_2

[2.8 ~ 3.0] Bucket_3

[3.5 ~ 4.0] Bucket_4

EXAMPLE 2

Qserver:

SELECT *

FROM egrades

WHERE gpaID = ‘Bucket_1’ OR

gpaID = ‘Bucket_2’ OR

gpaID = ‘Bucket_3’

Same as the general bucketization method In most cases, QOB can outperform the

conventional bucketization strategy, but not always

DEVIATION BUCKETIZATION

Built upon QOB, takes the same parameters Has two levels of buckets

First level: same as those produced by QOB Second level: bucketization of deviation values,

the difference between the value itself to the average of the bucket

Each first-level-bucket has at most M second level buckets

QOB has at most M buckets, while DB has at most M2 buckets

DEVIATION BUCKETIZATION

DB Run QOB (D, M) Construct First-Level-Buckets from boundary

matrix For each First-Level-Bucket

Initialize empty datasets vi’ and fi’

For each vi in the bucket vi’ = vi’ ∪ vi’ – avg()

fi’ = fi’ ∪ 1

Create a new dataset di = (vi’, fi’)Run QOB(di, M)

EXAMPLE 3

Partition ID Avg

[0.7 ~ 1.2] Bucket_1 0.93

[1.5 ~ 2.5] Bucket_2 1.84

[2.8 ~ 3.0] Bucket_3 2.93

[3.5 ~ 4.0] Bucket_4 3.67

Partition ID Avg

… … …

[2.8 ~ 2.8] Bucket_3_1 2.8

[2.9 ~ 2.9] Bucket_3_2 2.9

[3.0 ~ 3.0] Bucket_3_3 3.0

… … …

EXAMPLE 3

Qserver:

SELECT *

FROM egrades

WHERE gpaID = ‘Bucket_1’ OR

gpaID = ‘Bucket_2’ OR

gpaID = ‘Bucket_3_1’ OR

gpaID = ‘Bucket_3_2’

In this case, no false positives are returned Generally, false positives will still be returned,

just the number of them will be greatly reduced

EXPERIMENTS

Two datasets Synthetic dataset: 105 integers from [0, 999] Real dataset: 103 data points from the Aspect

column of the Forest CoverType database in UCI’s KDD Archive

Two sets of queries Qsyn

Qreal

EXPERIMENT 1

EXPERIMENT 2

Thank You