cotengra.tree#

The following functions are adapted from the repository:

associated with the paper:

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:

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Module Contents#

Classes#

TreeDecomposition

A named struct for convenience.

EliminationOrdering

A named struct for convenience.

Functions#

_increment_eo(td, eo)

Given a TreeDecomposition and a (partial) PerfectEliminationOrdering, add

td_to_eo(td)

Generates a perfect elimination ordering from a tree decomposition. The

td_str_to_tree_decomposition(td_str)

Reads in a .td file contents in PACE format into a TreeDecomposition object

class cotengra.tree.TreeDecomposition#

A named struct for convenience.

class cotengra.tree.EliminationOrdering#

A named struct for convenience.

cotengra.tree._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

cotengra.tree.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).

cotengra.tree.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