:py:mod:`cotengra.pathfinders.treedecomp`
=========================================

.. py:module:: cotengra.pathfinders.treedecomp

.. autoapi-nested-parse::

   The following functions are adapted from the repository:

       https://github.com/TheoryInPractice/ConSequences

   associated with the paper:

       https://arxiv.org/abs/1807.04599

   under the following license:


   BSD 3-Clause License

   Copyright (c) 2018,  Allison L. Fisher, Timothy D. Goodrich, Blair D. Sullivan,
   Andrew L. Wright
   All rights reserved.

   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions are met:

   * Redistributions of source code must retain the above copyright notice, this
     list of conditions and the following disclaimer.

   * Redistributions in binary form must reproduce the above copyright notice,
     this list of conditions and the following disclaimer in the documentation
     and/or other materials provided with the distribution.

   * Neither the name of the copyright holder nor the names of its
     contributors may be used to endorse or promote products derived from
     this software without specific prior written permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
   AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
   FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
   SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
   CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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   OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.



Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   cotengra.pathfinders.treedecomp.TreeDecomposition
   cotengra.pathfinders.treedecomp.EliminationOrdering



Functions
~~~~~~~~~

.. autoapisummary::

   cotengra.pathfinders.treedecomp._increment_eo
   cotengra.pathfinders.treedecomp.td_to_eo
   cotengra.pathfinders.treedecomp.td_str_to_tree_decomposition



.. py:class:: TreeDecomposition


   A named struct for convenience.


.. py:class:: EliminationOrdering


   A named struct for convenience.


.. py:function:: _increment_eo(td, eo)

   Given a TreeDecomposition and a (partial) PerfectEliminationOrdering, add
   one more vertex to the eo or recognize that we're
   already done.
   Input:
       td (TreeDecomposition): A tree decomposition.
       eo (PerfectEliminationOrdering): The perfect elimination ordering
       currently being constructed.
   Output:
       The final eo


.. py:function:: td_to_eo(td)

   Generates a perfect elimination ordering from a tree decomposition. The
   algorithm is taken from Markov and Shi Proof of Prop 4.2
   (https://arxiv.org/pdf/quant-ph/0511069.pdf).
   Input:
       td (TreeDecomposition): A tree decomposition for a graph.
   Output:
       eo (PerfectEliminationOrdering): A perfect elimination ordering
       corresponding to the tree decomposition (Note: There may be multiple
       valid eo for a given td).


.. py:function:: td_str_to_tree_decomposition(td_str)

   Reads in a .td file contents in PACE format into a TreeDecomposition object
   Input:
       td_filename (str): .td file contents
   Output:
       td (TreeDecomposition): A populated TreeDecomposition object