Depth-First Representation of a $k^2$-Tree

This project implements a depth-first representation of a $k^2$-tree, an efficient data structure for representing sparse matrices. It leverages two external libraries: sdsl-lite for succinct data structures and libsais for efficient suffix array construction.

Requirements

• C++17 compiler
• sdsl-lite – choose one of the following versions:
  • simongog's version
  • vgteam's version (includes support for rle-vector and more updated features)
• libsais – available at libsais repository

Compilation

You can compile the project with or without optimization flags. By default, the Makefile assumes:

• sdsl-lite is located at ~/sdsl-lite
• libsais is located in the libsais directory

Default Build

make

Release Build

To compile with optimization and release flags (-O3 -m64 -DNDEBUG):

make release

Custom Library Paths

If you have custom paths for the libraries, you can override the defaults:

make SDSL_DIR=/your/path/to/sdsl-lite LIBSAIS_DIR=/your/path/to/libsais

Usage

Building the $k^2$-Tree

1. Prepare Your Sparse Matrix

   Create a text file representing your sparse matrix. The file should have the following format for a matrix of size $n\times n$ with $m$ ones:

   x1 y1
   x2 y2
   ...
   xm ym
   

2. Build the $k^2$-Tree

   Execute the build tool with the required parameters:

   path_to_folder/k2bp_build.x path_to_matrix/matrix.txt n m

   This command will generate a file named matrix.txt.k2bp in the same folder as your input matrix.

Compressing the $k^2$-Tree

After building the $k^2$-tree, compress it using:

path_to_folder/k2bp_compr.x path_to_k2bp/matrix.txt.k2bp

This will produce a compressed tree file named matrix.txt.k2bpi.

Operations

Information

To display information about the $k^2$-tree (e.g., space usage and tree size), run:

path_to_folder/k2bp_info.x path_to_k2bp/matrix.txt.k2bp

For the compressed $k^2$-tree (to show details about pruned interchangeable subtrees):

path_to_folder/k2bp_compr_info.x path_to_k2bp/matrix.txt.k2bpi

Multiplication

You can multiply two $k^2$-trees using the following commands:

• For Uncompressed Trees:

  path_to_folder/k2bp_mult_1.x path_to_k2bp1/matrix1.txt.k2bp path_to_k2bp2/matrix2.txt.k2bp

• For Compressed Trees:

  path_to_folder/k2bp_compr_mult.x path_to_k2bpi1/matrix1.txt.k2bpi path_to_k2bpi2/matrix2.txt.k2bpi

Acknowledgments

• sdsl-lite and vgteam's sdsl-lite
• libsais