Fast Symmetry Discovery Tool for Sparse Graphs
Many computational tools have recently begun to benefit from the use of the symmetry inherent in the tasks they solve, and use general-purpose graph symmetry tools to uncover this symmetry. Common applications include organic chemistry, constraint solvers, logistics, optimization, bio-informatics, and finite group theory. However, older symmetry-finding tools often suffer quadratic runtime (or worse!) in the number of symmetries explicitly returned and are therefore of limited use on very large, sparse, symmetric graphs. Over the last 10+ years, we developed a symmetry-discovery algorithm which exploits the sparsity present not only in the input but also the output, i.e., the symmetry generators themselves. By avoiding quadratic runtime on large graphs, it improved state-of-the-art runtimes from several days to less than a second. Recent improvements to our algorithm include additional pruning that quickly solves the hard Miyazaki graphs.
I just wrapped code. http://vlsicad.eecs.umich.edu/BK/SAUCY for orig ref. The following are the authors of the core C “library”:
- Paul T. Darga pdarga@umich.edu
- Mark Liffiton liffiton@umich.edu
- Hadi Katebi hadik@eecs.umich.edu
The following functions are implemented:
saucy: Searching for Automorphisms in Underlying CNF, yes?shatter: Identifies Symmetries in CNF Instances
devtools::install_github("hrbrmstr/saucy")library(saucy)
# current verison
packageVersion("saucy")## [1] '0.1.0'
Graph 1 (from example files)
graph1 <- saucy::saucy(system.file("extdata", "graphfile", package="saucy"))
graph1## (0 2)(3 4)
## (0 1)(2 4)
##
## input_file: graphfile
## vertices: 5
## edges: 5
## group_size_base: 1
## group_size_exp: 1
## levels: 3
## nodes: 7
## generators: 2
## total_support: 8
## average_support: 4
## nodes_per_generator: 3.5
## bad_nodes: 0
str(graph1)## List of 13
## $ input_file : chr "/Library/Frameworks/R.framework/Versions/3.4/Resources/library/saucy/extdata/graphfile"
## $ vertices : int 5
## $ edges : int 5
## $ group_size_base : num 1
## $ group_size_exp : int 1
## $ levels : int 3
## $ nodes : int 7
## $ generators : int 2
## $ total_support : int 8
## $ average_support : num 4
## $ nodes_per_generator: num 3.5
## $ bad_nodes : int 0
## $ printed_output : chr [1:2] "(0 2)(3 4)" "(0 1)(2 4)"
## - attr(*, "class")= chr [1:2] "saucy" "list"
Graph 2 (from example files)
graph2 <- saucy::saucy(system.file("extdata", "graphfile2", package="saucy"))
graph2## (3 5)
## (3 6)(4 5)
## (0 1)
## (0 2)
##
## input_file: graphfile2
## vertices: 7
## edges: 7
## group_size_base: 4.8
## group_size_exp: 1
## levels: 5
## nodes: 13
## generators: 4
## total_support: 10
## average_support: 2.5
## nodes_per_generator: 3.25
## bad_nodes: 0
str(graph2)## List of 13
## $ input_file : chr "/Library/Frameworks/R.framework/Versions/3.4/Resources/library/saucy/extdata/graphfile2"
## $ vertices : int 7
## $ edges : int 7
## $ group_size_base : num 4.8
## $ group_size_exp : int 1
## $ levels : int 5
## $ nodes : int 13
## $ generators : int 4
## $ total_support : int 10
## $ average_support : num 2.5
## $ nodes_per_generator: num 3.25
## $ bad_nodes : int 0
## $ printed_output : chr [1:4] "(3 5)" "(3 6)(4 5)" "(0 1)" "(0 2)"
## - attr(*, "class")= chr [1:2] "saucy" "list"
s1 <- saucy::shatter(system.file("extdata", "battleship.cnf", package="saucy"))
s1## input_file: battleship.cnf
## vertices: 105
## edges: 320
## group_size_base: 1.6
## group_size_exp: 3
## nodes: 236
## generators: 6
## bad_nodes: 151
## discovery_time: 0.000816
## symmetry_breaking_clauses: 396
## additional_variables: 102
## additional_literals: 1362
## consistency_violations: 0
## sbp_generation_time: 0.000252
## total_time: 0.001068
## variables: 40
## clauses: 105
## non_binary_clauses: 25
## literals: 360
## symmetry_breaking_predicates: 293 symmetry breaking predicates
## printed_output: character(0)
str(s1)## List of 21
## $ input_file : chr "/Library/Frameworks/R.framework/Versions/3.4/Resources/library/saucy/extdata/battleship.cnf"
## $ vertices : int 105
## $ edges : int 320
## $ group_size_base : num 1.6
## $ group_size_exp : int 3
## $ nodes : int 236
## $ generators : int 6
## $ bad_nodes : int 151
## $ discovery_time : num 0.000816
## $ symmetry_breaking_clauses : int 396
## $ additional_variables : int 102
## $ additional_literals : int 1362
## $ consistency_violations : int 0
## $ sbp_generation_time : num 0.000252
## $ total_time : num 0.00107
## $ variables : num 40
## $ clauses : num 105
## $ non_binary_clauses : num 25
## $ literals : num 360
## $ symmetry_breaking_predicates: chr [1:293] "-6 31 0" "41 0" "-41 -6 -7 32 0" "-41 -6 42 0" ...
## $ printed_output : chr(0)
## - attr(*, "class")= chr [1:2] "shatter" "list"