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Box-Cover Algorithms


./waf configure


./bin/box_cover -type=tsv -graph=/data/graph_edges.tsv \
 -method=sketch -alpha=1.0 -least_coverage=1.0 -sketch_k=128 -multipass=10000 -rad_min=1 -rad_max=30 \


Options Type Default
-type Graph file type (auto, tsv, gen) string "auto"
-graph Input graph string "-"
-method Using method (see below) string "sketch"
-alpha Index size limit to use MEMB (alpha * N * k) double 1.0
-least_coverage Least coverage. double 1.0
-sketch_k sketch k int32 128
-multipass Maximum number of multi-pass int32 1000000000
-rad_analytical Use analytical diameters? bool false
-rad_min Minimum radius. int32 1
-rad_max Maximum radius. int32 100000000
-random_seed Random seed. int64 922337203685477583

Available Methods

Name Method
sketch Sketch (Akiba et al. 2016)
memb MEMB (Song et al. 2007)
coloring Greedy Coloring (Song et al. 2007)
cbb CBB (Song et al. 2007)
burning Burning (Schneider et al. 2012)
analytical Optimal solutions of Box-Cover of (u,v)-flower or SHM-model

Supported Formats

bin/box_cover works with TSV file and User-Generated graph.

TSV files

  • By using the option -type=tsv, you can specify .tsv file as the graph file with the option -graph=....
  • In a .tsv file, each line should contain two integers describing an edge (see below).
  • Vertices should be described by integers starting from zero.

TSV file example

0 1
0 2
1 2

User-Generated graph

By using the option -type=gen, you can generate and use famous network models.

./bin/box_cover -type=gen -graph="ba 1000 3"

Barabási–Albert model

By using -graph="ba v u", you can generate and use Barabási–Albert model with v nodes, which is generated from complete graph with u nodes.

For example, by using -graph="ba 1000 3", a BA model graph, which has 1000 nodes and 2994 edges, will be genearated.

(u, v)-flower

By using -graph="flower N u v", you can generate and use (u, v)-flower which has at least N nodes.

For example, by using -graph="flower 1000 1 2", (1, 2)-flower, which has 1095 nodes, will be genearated.

Song-Havlin-Makse model

By using -graph="shm N s t", you can generate and use Song-Havlin-Makse model which is generated from s-nodes star graph, added t*d new nodes to each node of degree d in each step, and finally has at least N nodes.

For example, by using -graph="shm 1000 5 2", SHM model, which is generated from 5-nodes star graph and has 2501 nodes and 2500 edges, will be genearated.

Unit Test

Execute bin/test to run tests.


This software is released under the MIT License, see LICENSE.txt.


  • Takuya Akiba, Kenko Nakamura, Taro Takaguchi, "Fractality of Massive Graphs: Scalable Analysis with Sketch-Based Box-Covering Algorithm", ICDM'16 (to appear).


Sketch-Based Box-Covering Algorithm




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