Zhang-Shasha: Tree edit distance in Python

The zss module provides a function (zss.distance) that computes the edit distance between the two given trees, as well as a small set of utilities to make its use convenient.

If you'd like to learn more about how it works, see References below.

Brought to you by Tim Henderson ([email protected]) and Steve Johnson ([email protected]).

Read the full documentation for more information.

Installation

You can get zss and its soft requirements ( editdist and numpy >= 1.7) from PyPI:

pip install zss

Both modules are optional. editdist uses string edit distance to compare node labels rather than a simple equal/not-equal check, and numpy significantly speeds up the library. The only reason version 1.7 of numpy is required is that earlier versions have trouble installing on current versions of Mac OS X.

You can install zss from the source code without dependencies in the usual way:

python setup.py install

If you want to build the docs, you'll need to install Sphinx >= 1.0.

Usage

To compare the distance between two trees, you need:

1. A tree.
2. Another tree.
3. A node-node distance function. By default, zss compares the edit distance between the nodes' labels. zss currently only knows how to handle nodes with string labels.
4. Functions to let zss.distance traverse your tree.

Here is an example using the library's built-in default node structure and edit distance function

from zss import simple_distance, Node

A = (
    Node("f")
        .addkid(Node("a")
            .addkid(Node("h"))
            .addkid(Node("c")
                .addkid(Node("l"))))
        .addkid(Node("e"))
    )
B = (
    Node("f")
        .addkid(Node("a")
            .addkid(Node("d"))
            .addkid(Node("c")
                .addkid(Node("b"))))
        .addkid(Node("e"))
    )
assert simple_distance(A, B) == 2

Specifying Custom Tree Formats

Specifying custom tree formats and distance metrics is easy. The zss.simple_distance function takes 3 extra parameters besides the two tree to compare:

1. get_children - a function to retrieve a list of children from a node.
2. get_label - a function to retrieve the label object from a node.
3. label_dist - a function to compute the non-negative integer distance between two node labels.

Example

#!/usr/bin/env python

import zss

try:
    from editdist import distance as strdist
except ImportError:
    def strdist(a, b):
        if a == b:
            return 0
        else:
            return 1

def weird_dist(A, B):
    return 10*strdist(A, B)

class WeirdNode(object):

    def __init__(self, label):
        self.my_label = label
        self.my_children = list()

    @staticmethod
    def get_children(node):
        return node.my_children

    @staticmethod
    def get_label(node):
        return node.my_label

    def addkid(self, node, before=False):
        if before:  self.my_children.insert(0, node)
        else:   self.my_children.append(node)
        return self

A = (
WeirdNode("f")
    .addkid(WeirdNode("d")
    .addkid(WeirdNode("a"))
    .addkid(WeirdNode("c")
        .addkid(WeirdNode("b"))
    )
    )
    .addkid(WeirdNode("e"))
)
B = (
WeirdNode("f")
    .addkid(WeirdNode("c")
    .addkid(WeirdNode("d")
        .addkid(WeirdNode("a"))
        .addkid(WeirdNode("b"))
    )
    )
    .addkid(WeirdNode("e"))
)

dist = zss.simple_distance(
    A, B, WeirdNode.get_children, WeirdNode.get_label, weird_dist)

print dist
assert dist == 20

References

The algorithm used by zss is taken directly from the original paper by Zhang and Shasha. If you would like to discuss the paper, or the the tree edit distance problem (we have implemented a few other algorithms as well) please email the authors.

approxlib by Dr. Nikolaus Augstent contains a good Java implementation of Zhang-Shasha as well as a number of other useful tree distance algorithms.

Kaizhong Zhang and Dennis Shasha. Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal of Computing, 18:1245–1262, 1989. (the original paper)

Slide deck overview of Zhang-Shasha

Another paper describing Zhang-Shasha