High-Performance TopSort/Dependency resolving algorithm

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1.1.0 2016-11-19 14:58 UTC

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Last update: 2020-07-07 14:23:18 UTC


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This library provides several implementations of a Topological Sort (topSort). In additional to the plain sorting algorithm it provides several implementations of a Grouped Topological Sort, means you can pass items with a type which will be grouped together in the sorting. With its implementation of using strings instead of arrays its over 20x faster than regular implementations.

What is it?

A topological sort is useful for determining dependency loading. It tells you which elements need to be proceeded first in order to fulfill all dependencies in the correct order.

Example usage: Unit of Work (relations), simple Package manager, Dependency Injection, ...


$sorter = new StringSort();

$sorter->add('car1', ['owner1', 'brand1']);
$sorter->add('owner1', ['brand1']);
$sorter->add('owner2', ['brand2']);

$result = $sorter->sort();
// output would be:

Sometimes you want to group equal types together (imagine a UnitOfWork which wants to combine all elements from the same type to stored those in one batch):

$sorter = new GroupedStringSort();

$sorter->add('car1', 'car', ['owner1', 'brand1']);
$sorter->add('brand1', 'brand');
$sorter->add('brand2', 'brand');
$sorter->add('owner1', 'user', ['brand1']);
$sorter->add('owner2', 'user', ['brand2']);

$result = $sorter->sort();
// output would be:

$groups = $sorter->getGroups();
   {type: 'brand', level: 0, position: 0, length: 2},
   {type: 'user', level: 1, position: 2, length: 2},
   {type: 'car', level: 2, position: 4, length: 1},
//of course there may be several groups with the same type, if the dependency graphs makes this necessary.

foreach ($groups as $group) {
   $firstItem = $result[$group->position];
   $allItemsOfThisGroup = array_slice($result, $group->position, $group->length);

You can only store strings as elements. To sort PHP objects you can stored its hash instead. $sorter->add(spl_object_hash($obj1), [spl_object_hash($objt1Dep)]).


Use composer package: [marcj/topsort)[]

    "require": {
        "marcj/topsort": "~0.1"
include 'vendor/autoload.php';

$sorter = new GroupedStringSort;

$result = $sorter->sort();


tl;dr: Use FixedArraySort for normal topSort or GroupedStringSort for grouped topSort since its always the fastest and has a good memory footprint.


This is the most basic, most inefficient implementation of topSort using plain php arrays.


This uses \SplFixedArray of php and is therefore much more memory friendly.


This uses a string as storage and has therefore no array overhead. It's thus a bit faster and has almost equal memory footprint like FixedArraySort. Small drawback: You can not store element ids containing a null byte.


This is the most basic, not so efficient implementation of grouped topSort using plain php arrays.


This uses a string as storage and has therefore no array operations overhead. It's extremely faster and has better memory footprint than GroupedArraySort. Small drawback: You can not store element ids containing a null byte.

Benchmarks with PHP 7.0.9

Test data: 1/3 has two edges, 1/3 has one edge and 1/3 has no edges. Use the benchmark command in ./bin/console to play with it.

Count Implementation Memory Duration
50 FixedArraySort 0b 0.0001s
50 ArraySort 0b 0.0001s
50 StringSort 0b 0.0001s
1,000 FixedArraySort 53,432b 0.0013s
1,000 ArraySort 37,720b 0.0012s
1,000 StringSort 89,112b 0.0013s
10,000 FixedArraySort 692,464b 0.0141s
10,000 ArraySort 529,240b 0.0138s
10,000 StringSort 1,080,472b 0.0154s
100,000 FixedArraySort 5,800,200b 0.1540s
100,000 ArraySort 4,199,280b 0.1499s
100,000 StringSort 10,124,000b 0.1645s
1,000,000 FixedArraySort 49,561,888b 1.5456s
1,000,000 ArraySort 33,559,408b 1.5597s
1,000,000 StringSort 95,480,848b 1.7942s
Count Implementation Memory Duration
50 GroupedArraySort 0b 0.0002s
50 GroupedStringSort 0b 0.0002s
1,000 GroupedArraySort 112,280b 0.0090s
1,000 GroupedStringSort 99,440b 0.0025s
10,000 GroupedArraySort 1,431,320b 0.8385s
10,000 GroupedStringSort 1,176,304b 0.0267s
100,000 GroupedArraySort 12,318,072b 132.9709s
100,000 GroupedStringSort 11,129,144b 0.2788s
1,000,000 GroupedArraySort - too long
1,000,000 GroupedStringSort 106,488,496b 3.0879s