
Hypertree Complementary
Approaches to Constraint Satisfaction 
We have
designed and implemented several algorithms for generations of hypertree decompositions. The algorithms have been
evaluated for benchmark examples from the literature and the industry.
Currently we have implemented the following algorithms:
Detailed information for the implemented algorithms
can be found in project publications: http://www.dbai.tuwien.ac.at/proj/hypertree/publications.html If you have questions considering programs please
sent email to: [Project Name]@dbai.tuwien.ac.at
Benchmarks examples
Executable
and object files:
Windows: BE_Win32.zip (faster reimplementation of the bucket elimination based algorithm) Linux: System
requirements
Windows: Win32 (Windows 9x, Windows ME, Windows NT,
Windows 2000,Windows XP) Linux:
Programs have been tested in SUSE Linux 10.0 CPU and memory requirements depend on the input
problem size. However in order to avoid a very large running time you should
have at least 128 MB RAM. For graphical representation of output files, which
are in GML format, are required Java 2 and VGJ (Visualizing Graphs with
Java). VGJ can be downloaded from this link: http://www.eng.auburn.edu/department/cse/research/graph_drawing/graph_drawing.html Installing
of program
Windows:
Afterwards
you have to execute the following command line for linking: LINK /out:htdecomp.exe *.* With
this file you can use the following methods:
and the
files from (Author:EngelnMüllges, Gisela NumerikAlgorithmen mit ANSI CProgrammen ):
Afterwards
you have to execute the following command lines for linking: CL /c *.c LINK /out:htdecomp.exe *.obj With
this file you can use the following methods: 1.
BE 2.
DBE 3.
SAND 4.
FM_PURE 5.
FM_PURE_WEIGHTS 6.
FM_NAIVE 7.
FM_NAIVE_WEIGHTS 8.
EV 9.
DEV 10. BD 11. DBD
Linux:
Afterwards
you have to execute the following command line for linking: g++ o htdecomp *.o lhmetis L
HMETIS With this
file you can use the following methods:
and the
files from (Author:EngelnMüllges, Gisela NumerikAlgorithmen mit ANSI CProgrammen ):
Afterwards
you have to execute the following command lines for linking: gcc c *.c g++ o htdecomp
*.o With
this file you can use the following methods: 1.
BE 2.
DBE 3.
SAND 4.
FM_PURE 5.
FM_PURE_WEIGHTS 6.
FM_NAIVE 7.
FM_NAIVE_WEIGHTS 8.
EV 9.
DEV 10.
BD 11.
DBD Starting
of program
Decomposition
program is started by the htdecomp command. htdecomp f inputfile d algorithm [d algorithm].
. . [d algorithm] [o outputfile] [def]
[stats] Please
note that the sequence of command line arguments does not matter. The
decomposition program will accept the following command line arguments. Part Description f inputfile A hypergraph H=(V,E) where V denotes
vertices and E denotes hyperedges have to be stored in a txt file where each
line contains a relation between an hyperedge and
vertices contained in that hyperedge. The different relations must be separated with a coma. Any line that
starts with “%” is a comment line and will be skipped. There
are two different forms of the input file dependent on it whether the
variables and atoms are already predefined or not. A
predefinition is given as: <defVar :
Var_{1},Var_{2},...,Var_{n} > <defRel : Edge_{1}/N_{1 , }Edge_{2}/N_{2
}, . . ., Edge_{m}/N_{m }> ,where ‘defVar’ denotes all vertices, ‘defRel’
denotes all Edges and ‘/N’ shows how many vertices in an hyperedge
are contained. If an predefinition exists and –def
command line is given than an consistency is required (see –def ). Example: d algorithm d command option require an decomposition algorithm which have
to be indicated by ‘algorithm’.
Dependent on the selected decomposition algorithm the argument algorithm can require
further parameters indicated as constructionscheme (see the algorithms which
require a constructionscheme). There are the
following possibilities of ‘algorithm’: 1. The algorithms which requires no
constructionscheme ·
BE: Bucket Elimination Algorithm This decomposition algorithm uses the topoligical
structure of the problem, with property that an optimal variable order
produce a tree decomposition of optimal width which is
afterwards extended to a hypertree decomposition by
using set covering heuristics. The variable order will be choose
heuristically. For more information about Bucket Elimination Algorithm please
see project publications Example: htdecomp –f myFile.txt –d BE ·
DBE: Dual Bucket Elimination Algorithm This decomposition algorithm applies Bucket
Elimination algorithm in order to produce a tree decomposition of the dual hypergraph, which is afterwards extended to hypertree decomposition by adding chilabels. For more
information about Dual Bucket Elimination Algorithm please see project
publications Example: htdecomp –f myFile.txt –d DBE ·
EV: Eigenvector Heuristic This decomposition algorithm applies the Eigenvector
branch decomposition heuristic which produces an
branch decomposition of the hypergraph which is
afterwards transformed into tree decomposition and a hypertree
decomposition. For more information about Eigenvector Branch Decomposition
Algorithm please see project publications Example: htdecomp –f myFile.txt –d EV ·
DEV: Dual Eigenvector Heuristic This decomposition algorithm applies the Eigenvector
branch decomposition heuristic which produces a branch decomposition of the
dual hypergraph which is afterwards transformed
into tree decomposition and hypertree decomposition.
For more information about Dual Eigenvector Branch Decomposition Algorithm
please see project publications Example: htdecomp –f myFile.txt –d DEV ·
BD: Branch Decomposition Heuristic This decomposition algorithm applies the branch decomposition
heuristic of Cook and Seymour which produce a branch decomposition of the hypergraph which is afterwards transformed into tree
decomposition and hypertree decomposition. For more
information about Branch Decomposition Algorithm please see project
publications Example: htdecomp –f myFile.txt –d BD ·
DBD: Dual Branch Decomposition Heuristic This decomposition algorithm applies the branch
decomposition heuristic of Cook and Seymour which produce a branch
decomposition of the dual hypergraph which is
afterwards transformed into tree decomposition and hypertree
decomposition. For more information about Branch Decomposition Algorithm
please see project publications Example: htdecomp –f myFile.txt –d DBD ·
HMET_BUCKET: HMETIS  BUCKET Algorithm This decomposition algorithm is a combination of hMETIS
(see HMETIS: hMETIS
Algorithm) algorithm and Bucket Elimination (see BE: Bucket Elimination Algorithm) algorithm. For more information
about HMETIS  BUCKET Algorithm please see project publications Example: htdecomp –f myFile.txt –d HMET_BUCKET ·
SAND: This decomposition algorithm finds the hypertree
of given hypergraph based on the algorithm for the
acyclic hypergraph sandwich problem. The algorithm
requires two additionally integer parameters which represents our imposed
decomposition width and type of ordering for nodes of input hypergraph. Example: htdecomp –f myFile.txt –d SAND Width OrderType Width: Our imposed decomposition Width (Integer value) OrderType: Determines type of
ordering for nodes of input Hypergraph, where OrderType: 1  Normal order of nodes 2  Nodes are ordered based on MCS heuristic 3  Nodes are ordered based on Minfill (MF) Heuristic. 2. The algorithms which requires a
constructionscheme Some decomposition algorithm requires additionally parameters
indicated as constructionscheme. The constructionscheme actually shows us how the heuristics have to
be used. Use: d myAlgorithm costructionscheme There are four different constructionschemes: 1) This constructionscheme builds a hypertree
decomposition of a given hypergraph by using of
already given hypergraph decomposition algorithm. Example: htdecomp –d myAlgorithm 2) LOCALOPT This constructionscheme builds a hypertree
decomposition of a given hypergraph by using of
already given hypergraph decomposition algorithm,
where in each step, the hypergraph is partitioned
using all parameters (these parameters are internal already given in the
program) one after the other, and the best partitioning is chosen afterwards. Example: htdecomp –d myAlgorithm LOACALOPT 3) BACKTRACKING This constructionscheme requires an additionally integer parameter
which represent our imposed decomposition width. A hypertree
decomposition of a given hypergraph is built by
using of already given hypergraph decomposition
algorithm, where for each parameter (these parameters are internal already
given in the program) is tested whether a decomposition of a given width is
possible. If not, than the program gives an message
like “No decomposition possible with imposed restrictions (…)”. Example: htdecomp –d myAlgorithm
BACKTRACKING width 4) EARLYEXIT This constructionscheme builds a hypertree
decomposition of a given hypergraph by using of
already given hypergraph decomposition algorithm.
The hypergraph is partitioned using each parameter
(these parameters are internal already given in the program) separately and
the best partitioning is temporally stored. If during that the best stored
partitioning exceeds, the program breaks further decomposing of the process
with that parameter and begins with the next one. The remained stored
partitioning is the best one. Example: htdecomp –d myAlgorithm
EARLYEXIT The algorithms which requires a constructionscheme ·
FM_PURE:
FiducciaMattheyses Pure Algorithm This decomposition algorithm applies an algorithm proposed by Fiduccia and Matteyses which is
an iterative refinement heuristic which produced an arbitrarily partitioning
of hypergraph into two parts (our implementation
supports only partitioning into two parts). In order to get an optimized
partitioning the algorithm moves successively vertices to the opposite
partition. To ensure the ‘connectedness’ condition of the hypertree
decomposition after each decomposition step the special hyperedges
are introduced. A characteristic of this decomposition algorithm is not
differentiation between ‘normal’ and ‘special’ hyperedges
during cost evaluating of the cut that contain such special hyperedges (the weight of each hyperedge
is set to one). For more information about FiducciaMattheyses
Pure Algorithm please see project publications Example: htdecomp –f myFile.txt –d FM_PURE ·
FM_PURE_WEIGHTS: FiducciaMattheyses Pure Weights Algorithm This decomposition algorithm applies an algorithm proposed by Fiduccia and Matteyses which is
an iterative refinement heuristic which produced an arbitrarily partitioning
of hypergraph into two parts (our implementation
supports only partitioning into two parts). In order to get an optimized
partitioning the algorithm moves successively vertices to the opposite
partition. To ensure the ‘connectedness’ condition of the hypertree
decomposition after each decomposition step the special hyperedges
are introduced. A characteristic of this decomposition algorithm is differentiation
between ‘normal’ and ‘special’ hyperedges where the special hyperedges
have associated weights and are not as is the case at FiducciaMattheyses
Pure where the weight of each hyperedge is set to
one. For more information about FiducciaMattheyses
Pure Weights Algorithm please see project publications Example: htdecomp –f myFile.txt –d FM_PURE_WEIGHTS ·
FM_NAIVE: FiducciaMattheyses
Naive Algorithm This decomposition algorithm is a variant of implementing of algorithm
proposed by Fiduccia and Matteyses
which is an iterative refinement heuristic which produced an arbitrarily partitioning
of hypergraph into two parts (our implementation
supports only partitioning into two parts). For more information about FiducciaMattheyses Naive Algorithm please see project
publications Example: htdecomp –f myFile.txt –d FM_NAIVE ·
FM_NAIVE_WEIGHTS: FiducciaMattheyses Naive Weights Algorithm This decomposition algorithm is a variant of implementing of algorithm
proposed by Fiduccia and Matteyses
which is an iterative refinement heuristic which produced an arbitrarily
partitioning of hypergraph into two parts (our
implementation supports only partitioning into two parts). For more
information about FiducciaMattheyses Naive
Algorithm please see project publications Example: htdecomp –f myFile.txt –d
FM_NAIVE_WEIGHTS ·
HMETIS: hMETIS Algorithm This decomposition algorithm is based on hMETIS
algorithm which according to the literature is one of the best available
packages for hypergraph partitioning. For more
information about hMETIS Algorithm please see
project publications. Example: htdecomp –f myFile.txt –d HMETIS  o outputfile The output of htdecomp contains
the hypertree decomposition computed by the given
algorithm/s and have an GML (Graph Modeling
Language) format , so you can see an
visualised hypertree. To do that please download Java2 and VGJ
Tool (see System
requirements) and execute vis
[otputfile] to
start VGJ and visualize hypertree decompositions. If no outputfile
is given than an default outputfile exist
consisting of inputfile
in form of inputfile.gml Example: vis myOutputFile.gml def If at the inputfile the variables and atoms are already predefined
(see f inputfile)
the def command option checks the
consistency between predefined variables and predefined atoms and variables
and atoms which are read; If no consistency exists the program give an
errormessage and aborts with exit(EXIT_FAILURE); If one ore more atoms and
variables are not predefined the program give an errormessage and aborts
with exit(EXIT_FAILURE); Example: htdecomp
–def –f myFile.txt stats A program writes detailed statistics about decomposition, like: ·
Name of used algorithm and
heuristic (e.g., BE[MCS]); ·
Time at which decomposition
started and finished, respectively ·
Hypergraph which was decomposed; ·
Hypertreedecomposition of hypergraph; ·
Optional comment written to
statistics file with special informations which are
not unique for the different decomposition algorithms; Example: htdecomp –stats –f myFile.txt 
2006 © Database and Artificial
Intelligence Group, Vienna University of Technology 