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LBNL-62756

Bitmap Index Design Choices and Their Performance

Implications

Elizabeth O’Neil and Patrick O’Neil

University of Massachusetts at Boston

{eoneil, poneil}@cs.umb.edu

Kesheng Wu

Lawrence Berkeley National Laboratory

kwu@lbl.gov

ABSTRACT

Historically, bitmap indexing has provided an important database capability to accelerate queries.

However, only a few database systems have implemented these indexes because of the difficulties of

modifying fundamental assumptions in the low-level design of a database system and in the expectations

of customers, both of which have developed in an environment that does not support bitmap indexes.

Another problem that arises, and one that may more easily be addressed by a research article, is that there

is no definitive design for bitmap indexes; bitmap index designs in Oracle, Sybase IQ, Vertica and

MODEL 204 are idiosyncratic, and some of them were designed for older machine architectures.

To investigate an efficient design on modern processors, this paper provides details of the Set Query

benchmark and a comparison of two research implementations of bitmap indexes. One, called RIDBit,

uses the N-ary storage model to organize table rows, and implements a strategy that gracefully switches

between the well-known B-tree RID-list structure and a bitmap structure. The other, called FastBit is

based on vertical organization of the table data, where all columns are individually stored. It implements a

compressed bitmap index, with a linear organization of the bitmaps to optimize disk accesses. Through

this comparison, we evaluate the pros and cons of various design choices. Our analysis adds a number of

subtleties to the conventional indexing wisdom commonly quoted in the database community.

1. INTRODUCTION

Bitmap indexes have not seen much new adoption in commercial database systems in recent years. While

ORACLE has offered bitmap indexing since 1995, other major systems such as DB2 and Microsoft SQL

Server do not provide them. Microsoft SQL Server may create bitmaps during hash joins, but not for

general indexing; DB2 has adopted an Encoded Vector Index [16], but this is basically an encoded

projection index rather than a bitmap index. Sybase Adaptive Server Enterprise (ASE), the major Sybase

DBMS, does not have bitmap indexing, although the Sybase Adaptive Server IQ product provides quite

competitive bitmap indexing for data warehousing. This situation arises in part because there is no

definitive design for bitmap indexes. To investigate such a definitive design, we plan to explore different

design choices through a careful study of two research implementations. Since we have control over all

aspects of the research implementations, we are able to try out some new

techniques for improving performances, such as new forms of compression and

careful disk placement. In the process of studying their performance pros and

cons, we also find some surprises.

A basic bitmap index (more simply, bitmap index in what follows) is typically

used to index values of a single column X in a table. This index consists of an

ordered sequence of keyvalues representing distinct values of the column, and

each keyvalue is associated with a bitmap that specifies the set of rows in the

table for which the column X has that value. A bitmap has as many bits as the

number of rows in the table, and the kth bit in the bitmap is set to 1 if the value

of column X in the kth row is equal to the keyvalue associated with the bitmap,

and 0 for any other column value. Table 1 shows a basic bitmap index on a

table with nine rows, where the column X to be indexed has integer values

ranging from 0 to 3. We say that the column cardinality of X is 4 because it has

4 distinct values. The bitmap index for X contains 4 bitmaps, shown as B

, B

Table 1: A bitmap

index for a column

named X. Columns

– B

are

bitmaps.

RID

0 2

1 1

2 3

3 0

4 3

5 1

6 0

7 0

8 2

LBNL-62756

…, B

, with subscripts corresponding to the value represented. In Table 1 the second bit of B

is 1

because the second row of X has the value 1, while corresponding bits of B

, B

and B

are all 0.

To answer a query such as “X > 1,” we perform bitwise OR (|) operations between successive long-words

of B

and B

, resulting in a new bitmap that can take part in additional operations. Since bitwise logical

operations such as OR (|), AND (&) and NOT (~) are well-supported by computer hardware, a bitmap

index software could evaluate SQL predicates extremely quickly. Because of this efficiency, even some

DBMS systems that don’t support bitmap indexes will convert intermediate solutions to bitmaps for some

operations. For example, PostgreSQL 8.1.5 has no bitmap index, but uses bitmaps to combine some

intermediate solutions [10]. Similarly, Microsoft SQL Server has a bitmap operator for filtering out rows

that don’t participate in a join operation [5].

Let N denote the number of rows in the table T and C(X) the cardinality of column X. It is easy to see that

a basic bitmap index like the one in Table 1 requires N•C(X) bits in the bitmaps. In the worst case where

every column value is distinct, so that C(X) = N, such a bitmap index requires N

bits. For a large dataset

with many millions of rows, such an index would be much larger than the table being indexed. For this

reason, much of the research on bitmap indexes has focused on compressing bitmaps to minimize index

sizes. However, operations on compressed bitmaps are often slower than on uncompressed ones, called

verbatim bitmaps. There is a delicate balance between reducing index size and reducing query response

time, which complicates the design considerations for bitmap index implementations.

Two very different approaches to reducing index sizes are used by the research prototypes we study.

FastBit implements the Word-Aligned Hybrid (WAH) compression; the WAH compressed basic bitmap

index was shown to be efficient in [18][19]. RIDBit employs a combination of verbatim bitmaps and

RID-lists composed of compact (two-byte) Row Identifiers (RIDS). Its unique ability to gracefully switch

from verbatim bitmaps to RID-lists based on the column cardinality originated with MODEL 204 [6].

The implementations of FastBit and RIDBit were quite different at the beginning of our study, which

made them ideal for contrasting the different implementation strategies and physical design choices. As

our study progressed, a number of implementation ideas found to be superior in FastBit were copied in

RIDBit; RIDBit software was also modified to better utilize the CPU. The lessons learned in this exercise

will be covered in the Summary section. The following table gives the key differences between RIDBit

and FastBit. We will discuss the detailed design of the two approaches in the next two sections.

FastBit RIDBit

Table layout Vertical storage (columns stored separately) N-ary storage (columns stored together in row)

Index layout Arrays of bitmaps B-tree keyed on keyvalues (improved in project)

Bitmap layout Continuous Horizontally partitioned into 32K-bit Segments

Compression Word-Aligned Hybrid compression Sparse bitmap converted to RID-list

The topics covered in succeeding sections are as follows. In Sections 2 and 3, we describe the architecture

of FastBit and RIDBit. Section 4 provides a theoretical analysis of index sizes for different columns.

Section 5 describes the Set Query Benchmark [7], which is used to compare performance of RIDBit and

FastBit. Section 6 presents the detailed experimental measurements. Finally, Section 7 provides a

summary and lessons learned.

2. FASTBIT

FastBit started out as a research tool for studying how compression methods affect bitmap indexes, and

has been shown since to be an efficient access method in a number of scientific applications [12][17]. It

organizes data into tables (with rows and columns), where each table is vertically partitioned and different

columns stored in separate files. Very large tables are also horizontal partitioned, each partition typically

consisting of many millions of rows. A partition is organized as a directory, with a file containing the

schema, followed by the data files for each column. This vertical data organization is similar to a number

of contemporary database systems such as Sybase IQ [9], MonetDB [1][2], Kx systems [4], and C-Store

LBNL-62756

[14]. Each column is effectively a projection index as defined in [9] and can sometimes be used

efficiently to answer queries without additional indexing structures. FastBit currently indexes only fixed-

sized columns, such as integers and floating-point numbers, although it can index low-cardinality string-

valued columns through a dictionary that converts the strings to integers. Because of this restriction, the

mapping from a row to a row identifier is

straightforward.

FastBit implements a number of different bitmap

indexes with various binning, encoding and

compression strategies [13]. The index used in this

study is the WAH compressed basic bitmap index.

All bitmaps of an index are stored in a single file

as shown in Table 2. Logically, an index file

contains two sets of values: the keyvalues and the

compressed bitmaps. FastBit stores both the keyvalues and bitmaps in arrays on disk. Since each keyvalue

is the same size, it can be located easily. To locate the bitmaps, FastBit stores another array starts[] to

record the starting position of all compressed bitmaps in the index file (in bitmaps[ ]). To simplify the

software, one extra values is used in array starts[] to record the ending position of the last bitmap.

FastBit generates all bitmaps of an entire index for one partition in memory before writing the index file.

This dictates that the entire index must fit in memory and imposes an upper bound on how many rows a

horizontal partition can hold on a given computer system. Typically, a partition has no more than 100

million rows, so that a small number of bitmap indexes may be built in-memory at once.

In general, FastBit store the array keyvalues[ ] in ascending order so that it can efficiently locate any

particular value. In some cases, it is possible to replace this array with a hash function. Using hash

functions typically requires fewer I/O operations to answer a query than using arrays do, but using arrays

more easily accommodates arbitrary keyvalues. FastBit uses memory maps to access the array

keyvalues[] and starts[] if the OS supports it; otherwise it reads the two arrays entirely into memory.

Since the index for a partition has to fit in memory when built, this reading procedure does not impose

any additional constraint on the sizes of the partitions.

One advantage of the linear layout of the bitmaps is that it minimizes the number of I/O operations when

answering a query. For example, to answer the range predicate “3 < KN < 10”, FastBit needs to access

bitmaps for values 4 through 9. Since these bitmaps are laid out consecutively in the index file, FastBit

reads all these bitmaps in one sequential read operation.

The linear layout of bitmaps means that FastBit is not in any way optimized for update. An update that

might add or subtract a 1-bit to one of the bitmaps would require modification of the bitmap, followed by

a reorganization of all successive bitmaps in the set. In scientific applications, changes in real time

between queries are unusual, so this limitation is not a serious drawback, and it is not a problem for most

commercial data warehousing applications either. Furthermore, we will see in Section 7 that the new

Vertica database product [14] provides a model where a fixed index for stable data can be maintained on

disk while new data is inserted to a memory resident dynamic store that takes part in all queries.

FastBit reconstitutes a C++ bitmap data structure from the bytes read into memory. This step makes it

easy to use the bitwise logical operation functions implemented in C++; however, it introduces

unnecessary overhead by invoking the C++ constructor and destructor. Additionally, since FastBit

aggregates the read operations for many bitmaps together, a certain amount of memory management is

required to produce the C++ bitmap objects.

3. RIDBIT

RIDBit was developed as a pedagogical exercise for an advance database internals course, to illustrate

how a bitmap indexing capability could be developed. The RIDBit architecture is based on index design

first developed for the Model 204 Database product from Computer Corporation of America [6]. We can

Table 2: Content of an index file.

N Number of rows

C Column cardinality

keyvalues[C]

Distinct values associate with each bitmap

starts[C+1] Starting position of each compressed bit-

map (final position is end of all bitmaps)

bitmaps[C] WAH Compressed bitmaps

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