Tudor Hulubei » The CSP Library

Introduction

The CSP Library consists of a set of classes that can be used to efficiently represent and solve Constraint Satisfaction Problems (CSPs).

This library is not a general purpose solver. It does not support many features that are useful in representing real life problems (like continuous domains, n-ary constraints, composite representations, etc). It is however an useful testbench for experimenting with new algorithms and ideas, do performance measurements, etc.

The design behind the CSP Library emphasizes flexibility, rather than raw performance. The goal has been to create a library that can be easy to use in new experiments, by providing an infrastructure in which researchers can play with new algorithms and ideas. It has not been designed to squeeze every single drop of performance out of a certain algorithm.

The library has mechanisms for allowing search to use different decompositions at different levels in the tree, whereby a decomposition can decide it would be overkill to continue the search in the remaining subproblem and can yield control to a less sophisticated search method that is more efficient on small problems. The library implements retraction plug-ins, like Chronological or CBJ that can simply be plugged in into any decomposition or filter. It can hide parts of a problem and allow a decomposition to temporarily work on a subproblem, it allows chaining of any number of heuristics for the purpose of breaking ties, it allows multiple constraints between the same pair of variables, and it has the ability to create problems with many types of values, not just integers. The library can represent small problems as well as large ones and has no artificial limitations implemented solely for the purpose of improving performance on certain types of problems or benchmarks. The library sports a sophisticated, low-overhead logging mechanism that can be compiled in optimized code with minimal impact. All this flexibility comes at a slight cost in performance. That is not to say, however, that the CSP Library is inefficient - it is not. However, hand coded algorithms that work on integers only and allocate everything statically will probably be faster.

The graph above is a representation of the RLFAP CELAR SCEN11 problem drawn by the CSP Library using AT&T's Graphviz graph drawing software. The following links point to higher resolution versions of the same thing:

News

Version 1.0.1 (May 6th, 2009):

Updated to work with GCC 4.3 on 64bit Linux machines.
Fixed an obscure bug/crash in the Solver::branching() that was only happening on 64bit machines.
Changed to use SIZE_T_MAX=static_cast<size_t>(-1) instead of UINT_MAX since size_t is 8 bytes on 64 bit machines.

Version 1.0.0 (January 1st, 2008):

Ported to Mac OS X (Tiger and Leopard).
Added support for computing and performing refutation analysis on leftovers, i.e. those insoluble subtrees that make up the proof of optimality in optimization problems (or the part of the search tree that comes between the last solution and the end of the search tree when looking for all solutions).
Added support for computing (quasi/restricted-)optimal refutations for optimization problems.
Added support for optimization problems. An objective function such as branch-and-bound can be implemented by deriving from csp::Objective. The RLFAP problem can be used as an example.
Added support for computing heatmaps that help visualizing the internals of search, i.e. where the bulk of the effort is over a population of instances.
Added support for modeling quasigroup problems as binary problems, using global constraints, or anything in-between, i.e. hybrid models using both binary and global (all-different) constraints.
Unary constraints are now properly supported.
Better documentation, generated with doxygen. `make html' and `make latex' now generate HTML, DVI, PostScript and PDF documentation in the doc/html and doc/latex directories. The HTML documentation is available online here and the other formats are available through the menus on this page. The old Texinfo documentation has been removed.
Removed the IDC branching methods, as they have not been used in a long time and had problems to begin with.
Added support for global constraints. Implemented a propagate()-based filter that runs the propagate() method of all the constraints until there are no more changes to be propagated. The filter is called Propagate and it is now the default command line filter (equivalent of -f propagate).
Implemented GAC-Schema as per "Arc consistency for general constraint networks: preliminary results" by Christian Bessiere and Jean-Charles Regin. The object is csp::constraints::Table. This is based on a set of tuples of combinations of values allowed.
Implemented a very inefficient AllDifferent global constraint based on GAC-Schema, as a quick exercise. It runs out of memory for more than 8 variables, but it is useful for testing. See csp::constraints::AllDifferent.
Implemented a real AllDifferent global constraint that works for permutation constraints only (for now) because it does not implement free path analysis yet. It is good for the likes of n-queens and quasigroups. See csp::constraints::PermutationAllDifferent.
Added the posibility of controlling the heuristics used in the pre-refutation analysis rapid-randomized-restarts loop that attempts to find lower upper bounds for the refutations of insoluble subtrees. The heuristics can be specified using the --ra-rrr-heuristic flag.
Implemented heuristic equivalence (see "Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problem" by Carla P. Gomes, Bart Selman, Nuno Crato and Henry Kautz). This is passed as an additional colon-separated field in the heuristic specification. Setting this to a value greater H than 0 means all choices that receive a score within (100*H)-percent of the highest score are considered equally good. This is useful for expanding the choice of tie-breaking. Quality and equivalence are mutually exclusive, i.e. if quality is less than 1, then equivalence must be 0, and if equivalence is greater than 0, then quality must be 1. Example: -h min-domain:1::off:0.15
Refactored the code. The object called Decomposition is now called Solver. The decompositions have been renamed branchings and instead of being derived from Decomposition they are derived from a much lighter object called Branching. The Maintaining Consistency branching method (MC) is now called Binary. The code analyzing refutations is now a separate branching method called RefutationAnalysis. The code common to all examples is much, much cleaner.
Added code to compute restricted optimal refutations, i.e. refutations that only include the variables involved in the corresponding actual refutation. The command line flag is --ra-restricted.
All --ffa* command line options have been renamed to --ra* (from refutation analysis).
Renamed csp_pareto_levy to csp_cdf and csp_power_law to csp_pdf.
Renamed --phase-transition and PHASE_TRANSITION to --crosover-point and CROSSOVER_POINT.
Added code for computing the variables involved in each refutation. Useful for comparisons between actual, optimal and quasi-optimal refutations, among other things. The command line flag is --refutation-variables.

Version 0.4.2 (May 18th, 2005):

The QuasiGroup example has been enhanced to handle Quasigroup with Holes problems using both random and balanced holes. The code solving quasigroup existence problems has been disabled as the constraint model was incorrect. The Quasigroup with Holes problems are known to exhibit heavy-tails and have been used, together with random problems, in our analysis of search heuristics, optimal refutations and heavy-tails.
The network streaming code has been taken out, as it has not been used in a while and it serves no purpose in my current research.
The variable orderings described in "Boosting systematic search by weighting constraints" by Boussemart et al. have been implemented. The names are max-weighted-degree-variable, min-weighted-degree-variable, min-domain/weighted-degree-variable and max-domain/weighted-degree-variable.
The naming scheme for the variable and value ordering heuristics command line flags has been made more consistent. All variable ordering heuristics end with -variable and all value ordering heuristics end with -value.
The min-*-inconsistency value ordering heuristics have been renamed to min-*-conflicts. See "Look-ahead value ordering for constraint satisfaction problems", Daniel Frost and Rina Dechter.
The max-domain-size heuristic (which really means largest post-propagation minimum domain size) heuristic has been implemented. See "Look-ahead value ordering for constraint satisfaction problems", Daniel Frost and Rina Dechter. The command line flag for the heuristic is -h max-min-domain-value and -h min-min-domain-value for the anti-heuristic.
The experiment scripts now plot both scattered and average graphs.
Value ordering heuristic analysis is now possible for the Random, Lexical and SolutionProbability heuristics.
When the value ordering analysis is turned on, the library prints out the proximity of each bad selection to a perfect choice.
New variable ordering heuristic that selects the variables with the highest/lowest conflict count (over all their values). The command line flags for the static versions of the heuristic are -h max-static-impact and -h min-static-impact (for the anti-heuristic). For the dynamic versions the command line flags are -h max-static-impact and -h min-static-impact (for the anti-heuristic).
New variable and value ordering heuristics based on the best post-propagation branching contribution. The command line flags are -h min-branching-variable and -h max-branching-variable (for the variable ordering heuristic and anti-heuristic), and -h min-branching-value and -h max-branching-value (for the value ordering heuristic and anti-heuristic).
Code to analyze per-mistake-point fail-firstness and compute optimal refutations has been added. The command line option is --fail-firstness-analysis, or --ffa. Such an analysis can take a very long time - running it for anything but the smallest problems requires a good-size cluster. See all the --ffa* command line flags for details. Separate search trees are generated for each mistake point if --ffa and --search-tree are both given.
The post-processing of data in the experiment*.sh scripts has been greatly enhanced.
The rlfap/celar/scen11 directory contains subproblems of RLFAP SCEN11 useful for benchmarking and fail-firstness analysis.
The Basic decomposition has been renamed to K-Way.
The Solo examples have been removed. Not useful anymore.
Support for computing the backdoor has been added, as described in "Backdoors To Typical Case Complexity" by Ryan Williams, Carla P. Gomes and Bart Selman, and in "The Backdoor Key: A Path to Understanding Problem Hardness" by Yongshao Ruan, Henry Kautz and Eric Horvitz. The command line option is --backdoor.
Support for computing the list of branching variables (on the way to a solution) and their assignment. The command line option is --branching-assignments.
Support for drawing graphs of subproblems has been added. See the --problem-graph-depth command line option for details. The library now generates 2 graphs, one as soon as search reaches the given depth, and another right before search backtracks from that depth. The purpose of the first is to allow the visualization of very difficult problems for which search times out. The purpose of the second is to incorporate information gathered when a solution is found (i.e. backdoors).
Support for averaging the number of loose constraints per depth has been added. Such constraints (tightness=0) are interesting because they may artificially and unnecessarily connect otherwise disconnected subproblems, making it harder to make ordering decisions during search.
Constraints that become loose (tightness=0) can now be optionally disabled. This may speed up things, mostly because certain heuristics (like min-domain/degree) become more accurate, taking into account only those constraints that matter in computing the degree. The removal of loose constraints is not on by default, but can be turned on with the --deactivate-loose-constraints command line flag.
Added support for printing the exact variables and values selected on the last path traversed (usually the one containing the solution). This includes the wrong selections that led to failure points. The commad line option is --last-path-selections.
Changed the computation of the number of heuristic failures to account for failed propagations.
The Jumper class has been renamed "Retraction" to better follow existing CSP terminology.
Some code cleanups:
- the flags controlling decomposition statistics and those that control decomposition features are grouped into separate BitFlags objects.
- printing statistics is no longer done by the library, but rather by the code using it; the library now provides the outside world read-only access to the statistics so that they can be processed in any way (rather than just printed).
The value ordering heuristic mistakes are reported after each solution if --heuristic-mistakes is given.
The total and per depth number of backtracks, as well as the number of backtracks per mistake point are reported after each solution if --backtracks is given.
The --graph command line option has been renamed to --problem-graph.
The code can now generate a plot of the search tree in AT&T's Graphviz format. Nodes are properly labeled with the corresponding decision if the --last-path-selections command line option is given. The corresponding command line options are --search-tree and --search-tree-depth.
The bell-flattening technique has been removed from the code, as better understanding of search made clear its uselessness.

Version 0.4.1 (April 20th, 2004):

Support for generating problem graphs using AT&T's Graphviz DOT format has been added. To generate the graphs, first use the --graph=FILE command line option, then run one of these commands to lay out the graph:
dot FILE.dot -Tpng -oFILE.png
fdp FILE.dot -Tpng -oFILE.png
neato FILE.dot -Tpng -oFILE.png
circo FILE.dot -Tpng -oFILE.png
twopi FILE.dot -Tpng -oFILE.png
twopi is the only one that processed the RLFAP SCEN11 problem in a reasonable amount of time, but dot generates nicer layouts. dot needed 400Mb of RAM to generate the RLFAP SCEN11 graph, but GIMP could not load the resulting PNG file.
The greedy processing of variables whose domains have been reduced to a single value it's now off by default. It can be turned on by calling Decomposition::setGreedyVariableProcessing() or with the --greedy command line flag. Greedy variable processing improves performance most of the time by significantly reducing the depth of the search tree, but I think having it on by default adds another factor to the complexity of the search, making an accurate performance analysis more difficult.
Added code to compute the number of times a variable is selected at each depth. The command line option is --variable-selection-counters.
Due to the fact that some of the statistics gathered by the library are really expensive to compute (notably the average constrainedness and average tightness), the Decomposition object and the corresponding command line options have been changed to allow different statistics to be computed independently. The corresponding command line flags are:
--average-uninstantiated-variables
--average-modified-variables
--average-domain-size
--average-active-constraints
--average-degree
--average-constrainedness
--average-density
--average-tightness
--extra-propagation-statistics
--variable-selection-counters
The Decomposition object now supports a concept called "optimistic search", in both static and dynamic form. The corresponding command line options are --static-optimism and --dynamic-optimism. They both specify a percentage of values to be removed from the domain of a variable, either before search (in the static version), or during search. Each variable's domain of values will be sorted according to the main value ordering heuristic, and a percentage of the values will be discarded (i.e. not considered during search), with the idea that they're not really useful. This is based on a study of the quality of the MinInconsistency heuristic that proved experimentally that if the current domain of a variable is sorted according to the heuristic preference, most of the time the value suggested by the heuristic is very close to one or more values that are perfect choices (i.e. they lead to a solution). Discarding values that are considered "bad" by the heuristic may generate a problem that still contains at least one of the solutions of the original problem while being smaller and thus easier to solve. The only decompositions currently supporting dynamic optimism are MC and Basic.
A new variable ordering heuristic called "domain wipeout" has been implemented. It can select variables in the order of the number of times they have caused propagation failures because of the fact that their domain has been wiped out. The command line flags are -h max-dwos and -h min-dwos (for the anti-heuristic).
Added support for calculating the number of search tree nodes per depth as well as the number of failures of the value ordering heuristic.
Added support for Radio Link Frequency Assignment Benchmarks, as provided by the Centre d'Electronique de l'Armement (France). See B. Cabon, S. de Givry, L. Lobjois, T. Schiex and J.P. Warners, CONSTRAINTS journal, 1998. A copy of the RLFAP CELAR SCEN11 data files has been included in the examples/rlfap/celar/scen11 directory. To run the tests, try:
./csp_rlfap -d mc -f ac3 -q --greedy -h min-domain/degree -h rand-var -h min-dynamic-inconsistency -h rand-var -h rand-val --data-directory=rlfap/celar/scen11
All variable and value ordering heuristics have now access to the decomposition they're plugged into so that more information is available to them for the purpose of making a selection.
A new script (peak-experiment.sh) has been added to draw a 3-D graph of a problem's peak of difficulty.
The experiment.sh script now compresses the log so that experiments take significantly less disk space.
Various new search statistics can now be computed during search. They are the average domain size per depth, the average number of active constraints per depth, the average variable degree per depth, the average constrainedness per depth and the average constraint density and tightness per depth. The can be turned on by specifying the --statistics command line option. Note that constrainedness is computed as defined in "The Constrainedness of Search" by Ian P. Gent, Patrick Prosser and Toby Walsh, 1999, for constraint satisfaction problems.
Random problems can now be saved and reloaded. The corresponding command line options are --save-problem and --load-problem.
The quality of certain value ordering heuristics can now be analyzed (random problems only). This works by running the search twice. The first time we calculate all the solutions to the problem, and store them in a file (using the --save-solutions command line option). The second time we run the search we load the saved solutions using the --load-solutions command line option and turn the analysis on by invoking the heuristic with "on" as the third option in its colon-separated list of flags:
./csp_random --load-problem=p.txt --load-solutions=s.txt -d mc -f ac3 -h min-domain -hmin-inconsistency:1::on -h rand-var -h rand-val --fancy
The Minimum Inconsistency heuristic has now a dynamic version. The command line flags are:
-h min-static-inconsistency
-h min-dynamic-inconsistency
-h max-static-inconsistency
-h max-dynamic-inconsistency
Some heuristics have been changed so that their logic can be reversed. As a result, several new heuristics are now available: Maximum Domain, Minimum Degree, Maximum Domain/Degree, Maximum Inconsistency, etc.
A new variable ordering heuristic has been implemented: "Maximum Solution Probability". This heuristic selects a variable based on the probability of a solution being found in the subproblem that would remain to be solved if that variable were to be selected. The heuristic comes in both static (constraint probabilities are computed only once, before search) and dynamic versions. Both are very expensive. The command line options to activate them are:
-h max-static-sp-var
-h max-dynamic-sp-var
-h min-static-sp-var
-h min-dynamic-sp-var
The "Maximum Solution Probability" concept has also been implemented as a value ordering heuristic. This value ordering heuristic returns the list of values that, when selected, maximize the probability of finding a solution in the remaining subproblem after consistency is restored. The anti-heuristic is also available. The command line options are -h max-sp-val and -h min-sp-val.
It is now possible to set a certain quality for each heuristic. For instance, specifying the min-domain heuristic with -h min-domain:0.5 instead of just -h min-domain will cause the heuristic to sort the variables according to their domain size, identify the groups of variables that have equal values, create another vector with just one variable from each such group, pick the one in the middle (consistent with our 0.5 quality selection) and then passing its entire group to the next heuristic for tie-breaking. This can be useful in studying the impact of a good or bad heuristic on the performance of various algorithms.
Heuristics can now be made active only at certain depths of the search tree. The depths are specified in terms of the percentage of instantiated variables, and the intervals where a heuristic is to become active is specified after the quality, as a comma separated list, for example -h min-domain:0.7:10-20,85-95 specifies that the minimum domain heuristic is to be applied with a quality of 0.7 at depths where the percentage of instantiated variables is between 10 and 20% or between 85 and 95%.
The Goldilocks code as well as the related experiment script have been updated, making it possible to reproduce the experiments in the paper. See the examples/goldilocks-experiment.sh script and the .config files in the examples/experiments/goldilocks directory.
The random problem generator used a slightly different definition of constraint density than the one used by other researchers in the field. Specifically, it was using the definition found in "Understanding and Improving the MAC Algorithm" - Daniel Sabin & Eugene Freuder, CP97: "the fraction of the possible constraints beyond the minimum n-1, that the problem has". A CSP with n variables requires at least n-1 constraints for its graph to be connected. If the graph is not connected, the subgraphs can be treated as independent problems and solved separately - which was the rationale behind the old definition. It seems however that most researchers have standardized on a density definition that is the fraction of all possible constraints that the problem has. The random number generator has been changed to use this standard definition by default, but can still use the old one if the --non-standard-density command line option is given.
All the examples (including the random problem generator) now use by default a new pseudo-random number generator, as presented in William H. Press, et al.'s "Numerical Recipes in C", Second Edition with corrections (1994) page 282. This should make it easier for other researchers to reproduce our results (as well as for us to reproduce theirs), and will also make sure that given a set of parameters the same problem is generated on all supported platforms. The system's pseudo-random number generator is still available as an option (through --system-prng).
The random problem generator we used in so far was "model B". In order to be able to easier reproduce other people's experiments, models "A, C, and D" were implemented. The models are explained in examples/Random.cc. A command line option (--model) can be used to select a particular model. See "Random Constraint Satisfaction: Flaws and Structure" by Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith and Toby Walsh for an in-depth discussion of these models.
The random number generator now defaults to generating flawless problem instances. See "Random Constraint Satisfaction: Flaws and Structure" by Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith and Toby Walsh for a discussion on this topic. Briefly, the models currently used by random problem generators are asymptotically uninteresting because they start generating trivially insoluble problems. The random problem generator can still be forced to create flawed problem instances by using the --flawed command line option.
Improved the experiment.sh script to be able to average results over several runs of the same problem created with different seeds. Random problems now have MD5 signatures, for comparison purposes.
Implemented AC-3d. See M.R.C. van Dongen's paper "AC-3d an Efficient Arc-Consistency Algorithm with a Low Space-Complexity", which is available online from his web page.
Implemented AC-8. Same as AC-3, but keeping a queue of variables rather than constraints. See A. Chmeiss and P. Jegou: "Efficient path-consistency propagation", International Journal on Artificial Intelligence Tools, 7(2):121-142, 1998.
Implemented AC-2000. Based on AC-8, but improves slightly upon it by keeping track of the most recently pruned values and only checking for supports for value if at least one such support has been removed from the other variable involved in the constraint. See "Refining the Basic Constraint Propagation Algorithm" by Christian Bessiere and Jean-Charles Regin.
Implemented AC-2001. Based on AC-8, but improves slightly upon it by keeping an extra integer to remember the last support checked. See "Refining the Basic Constraint Propagation Algorithm" by Christian Bessiere and Jean-Charles Regin.
A command line option that controls the debug level has been added to all examples (-V). It defaults to "notice".
A command line option that allows the user to verify the problem's consistency without running a search has been added to all examples (--consistency-only).
Added support for plotting the number of constraint checks.
Added support for plotting the average total number of backtracks.
Added support for plotting the value ordering heuristic failures.
Added support for plotting 3D graphs of the average number of backtracks per depth.
Added support for plotting 3D graphs of the number of value ordering heuristic failures per depth.
Fixed a bug in the random problem generator that was causing the bit array used by constraints to represent valid pairs to be incorrectly resized.
Renamed AC-3p (again) - that name seems to be used too. It's now called AC-3x.
Added a "Dummy" filter that can be combined with the "Basic" decomposition to create a "Generate And Test" search algorithm.
Added support for building under KDE's KDevelop 3.0.x.
Loads of other minor fixes and improvements.

Version 0.4.0 (December 11th, 2003):

The library now uses wide characters/strings everywhere.
Small fixes throughout the library, too many to mention.
The API documentation can now be generated with Doxygen.
Implemented a mechanism for restricting the search to a subset of the original problem. See the Decomposition object for details.
Added an implementation of the Local Changes (LC) algorithm, as presented in "Solution Reuse in Dynamic Constraint Satisfaction Problems" by Gerard Verfaillie and Thomas Schiex.
Added an implementation of the Local Changes (LC) algorithm combined with MAC-like additional constraint propagation and the ability to select a new variable after removing failed values from the domain of the current variable.
The MinInconsistency value ordering heuristic has been fixed.
AC-5 was renamed AC-3 Plus as it was really just an attempt at improving AC-3 rather than an AC-5 filter.
AC-3 and AC-3p have been fixed so that they do not assume there is at most one constraint between any pair of variables.
Made the strategy for instantiating variables more flexible, allowing both propagate() and propagateAndSearch() to mark only certain variables as instantiables. Previously both these functions would automatically instantiate any variable that had its domain reduced to a single value. Very useful for LC. See the Decomposition::propagateAndSearch() for details.
Improved the variable selection mechanism. Reselecting a variable that has already been selected at the current depth is now optionally possible. It is also possible to specify a set of variables whose selection is to be avoided. See Decomposition::selectVariable() for details.
Floating point variables (single & double precision) have been implemented as variables with discrete domains.
Reorganized a bit the way header files are included, eliminating unnecessary dependencies and reducing compilation time.
--enable-predictable is no longer a compile time option, but rather a runtime option.
Better logging, can be activated separately for each library component, decomposition, filter, jumper, etc. Should be very helpful in tracking down problems and following the algorithm's logic. See the -l flag in the examples, it takes a comma-separated list of patterns matching logging categories. All messages logged by a CSP library component use the component's C++ namespace as the category. The -i/--indentation command line option will cause the logging to be indented consistent with the search depth, making it even easier to follow the flow of the decomposition algorithms.
The code now compiles with the upcoming version of GCC (3.4).
make pch: new target that builds the precompiled headers supported in GCC 3.4. Still needs some work for a better integration in the dependency system. Hopefully new versions of the GNU tools will automate that.
The library has been ported to Microsoft Visual C++ .Net 7.0. It has not been tested under 7.1, but with a bit of luck it should just work :-). Note that since GCC and Visual C++ use different STL implementations, the library's search algorithm may follow a different path on one platform than it does on the other for the same exact problem and configuration. This is normal. One way to minimize such differences would be to always add the lexical variable and value ordering heuristics as the last heuristics in their respective lists.
A bug in Cygwin's C++ compiler (GCC) prevents code using wcout/wcerr from compiling for now. Hopefully some future update to Cygwin's compiler will fix this.
A lot of effort has been put into making the library work better with the latest versions of GNU Autoconf, GNU Automake and GNU Libtool. Many cosmetic and installation-related changes.
A better explanation of the naming scheme used for decompositions, filters and search algorithms is now being used and can be found in doc/NamingScheme.txt. As part of cleaning up the naming scheme, the MAC, IDCMAC and LCMAC decompositions have been renamed to MC, IDCMC and LCMC. When combined with filters like FP that do not restore arc consistency, the name was confusing as it was suggesting that the resulting search algorithm was maintaining arc consistency, which was false.
The AIEDAM 2003 version of the Goldilocks paper is now included with the distribution.

Documentation

This description of the library is a bit out-of-date. The general structure of the library has not changed, but a lot more classes and algorithms have been added, and they're completely described in the API documentation. Reading the News might also be a good idea.

API

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