Data Structures for Inverted Indexes (ds2i) is a library of data structures to represent the integer sequences used in inverted indexes.

This code was used in the experiments of the following papers.

• Giuseppe Ottaviano, Rossano Venturini, Partitioned Elias-Fano Indexes, ACM SIGIR 2014.

• Giuseppe Ottaviano, Nicola Tonellotto, Rossano Venturini, Optimal Space-Time Tradeoffs for Inverted Indexes, ACM WSDM 2015.

The code is tested on Linux with GCC 4.9 and OSX Yosemite with Clang.

The following dependencies are needed for the build.

• CMake >= 2.8, for the build system
• Boost >= 1.51

The code depends on several git submodules. If you have cloned the repository without --recursive, you will need to perform the following commands before building:

$ git submodule init
$ git submodule update

To build the code:

$ mkdir build
$ cd build
$ cmake . -DCMAKE_BUILD_TYPE=Release
$ make

It is also preferable to perform a make test, which runs the unit tests.

The directory test/test_data contains a small document collection used in the unit tests. The binary format of the collection is described in a following section.

To create an index use the command create_freq_index. The available index types are listed in index_types.hpp. For example, to create an index using the optimal partitioning algorithm using the test collection, execute the command:

$ ./create_freq_index opt ../test/test_data/test_collection test_collection.index.opt --check

where test/test_data/test_collection is the basename of the collection, that is the name without the .{docs,freqs,sizes} extensions, and test_collection.index.opt is the filename of the output index. --check perform a verification step to check the correctness of the index.

To perform BM25 queries it is necessary to build an additional file containing the parameters needed to compute the score, such as the document lengths. The file can be built with the following command:

$ ./create_wand_data ../test/test_data/test_collection test_collection.wand

Now it is possible to query the index. The command queries parses each line of the standard input as a tab-separated collection of term-ids, where the i-th term is the i-th list in the input collection. An example set of queries is again in test/test_data.

$ ./queries opt and test_collection.index.opt test_collection.wand < ../test/test_data/queries

This performs conjunctive queries (and). In place of and other operators can be used (or, wand, ..., see queries.cpp), and also multiple operators separated by colon (and:or:wand).

To construct an index time-optimal for a given query distribution and space budget it is necessary to follow the following steps.

First, a block-based index must be built on the collection. This will be used to collect the block-access statistics.

$ ./create_freq_index block_optpfor ../test/test_data/test_collection test_collection.index.block_optpfor
$ ./create_wand_data ../test/test_data/test_collection test_collection.wand

Then, given a sequence of queries sampled from the query distribution, we can produce the statistics.

$ ./profile_queries block_optpfor ranked_and:wand:maxscore \
    test_collection.index.block_optpfor test_collection.wand \
    < ../test/test_data/queries \
    > query_profile

To predict the block decoding time we need to measure it on a sample.

$ ./profile_decoding block_optpfor test_collection.index.block_optpfor 0.1 > decoding_times.json

0.1 is the fraction of sampled blocks. For large indexes a very small number can be used. The measured times can be used to train the linear model.

$ ./dec_time_regression.py parse_data decoding_times.json decoding_times.pandas
$ ./dec_time_regression.py train decoding_times.pandas > linear_weights.tsv

The above script requires Numpy, Scipy, Pandas, and Theano.

We can finally build the new index, for example something slightly smaller than the block_optpfor index generated above.

$ ./optimal_hybrid_index block_optpfor linear_weights.tsv \
    query_profile test_collection.index.block_optpfor \
    lambdas.bin 4000000 test_collection.index.block_mixed

The critical points computed in the greedy algorithm are cached in the lambdas.bin file, which can be re-used to produce other indexes with different space-time tradeoffs. To recompute them (for example if the query profile changes) just delete the file.

We can now query the index.

$ ./queries block_mixed ranked_and test_collection.index.block_mixed \
    test_collection.wand < ../test/test_data/queries
...
Mean: 9.955
...

$ ./queries block_optpfor ranked_and test_collection.index.block_optpfor \
    test_collection.wand < ../test/test_data/queries
...
Mean: 11.125
...

Note that the new index is both faster and smaller than the old one. Of course we are cheating here because we are testing it with the same queries we trained it on; on a real application training and test set would be independent.

It is also possible to output a sample of the trade-off curve with the following command.

$ ./optimal_hybrid_index block_optpfor linear_weights.tsv \
    query_profile test_collection.index.block_optpfor \
    lambdas.bin 0 lambdas.tsv

The file lambdas.tsv will contain a sample of triples (lambda, space, estimated time).

A binary sequence is a sequence of integers prefixed by its length, where both the sequence integers and the length are written as 32-bit little-endian unsigned integers.

A collection consists of 3 files, <basename>.docs, <basename>.freqs, <basename>.sizes.

• <basename>.docs starts with a singleton binary sequence where its only integer is the number of documents in the collection. It is then followed by one binary sequence for each posting list, in order of term-ids. Each posting list contains the sequence of document-ids containing the term.

• <basename>.freqs is composed of a one binary sequence per posting list, where each sequence contains the occurrence counts of the postings, aligned with the previous file (note however that this file does not have an additional singleton list at its beginning).

• <basename>.sizes is composed of a single binary sequence whose length is the same as the number of documents in the collection, and the i-th element of the sequence is the size (number of terms) of the i-th document.

• Giuseppe Ottaviano giuott@gmail.com
• Rossano Venturini rossano@di.unipi.it
• Nicola Tonellotto nicola.tonellotto@isti.cnr.it