An Improved Indexing Scheme for Range Queries

1
An Improved Indexing Scheme for Range Queries

• Yvonne Yao
• Adviser Professor Huiping Guo

2
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

3
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

4
Database-as-a-Service
5
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

6
Example 1
7
Example 1
8
Example 1

• User query
• SELECT
• FROM grades
• WHERE gpa lt 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

9
Query Optimal Bucketization

• General idea minimizing the bucket cost of each
  bucket
• Input ltD (V, F), Mgt
• V v1, v2, v3, , vn where v1 lt v2 lt v3 lt
  ltvn
• F Frequency of each value
• M Number of buckets to fill
• Output a matrix indicating the boundary of each
  bucket

10
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

11
Example 2
12
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

13
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

14
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)

15
Example 3
16
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

17
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 UCIs
  KDD Archive
• Two sets of queries
• Qsyn
• Qreal

18
Experiment 1
19
Experiment 2
20

• Thank You