pgRouting · wifiBlack · Aug 26, 2025 · Aug 26, 2025 · Aug 26, 2025 · Aug 26, 2025
diff --git a/NEWS.md b/NEWS.md
@@ -156,6 +156,10 @@ Summary of changes by function
 
   * Combinations signature promoted to official.
 
+* pgr_minDegreeOrdering
+
+    * New experimental function.
+
 * pgr_pushRelabel
 
   * Combinations signature promoted to official.

diff --git a/doc/_static/page_history.js b/doc/_static/page_history.js
@@ -15,7 +15,7 @@ var titles = [
 
 
 var newpages = [
-    {v: '4.0', pages: ['pgr_bandwidth', 'pgr_kingOrdering', 'pgr_sloanOrdering']},
+    {v: '4.0', pages: ['pgr_bandwidth', 'pgr_kingOrdering', 'pgr_minDegreeOrdering', 'pgr_sloanOrdering']},
 
     {v: '3.8', pages: ['pgr_contractionDeadEnd', 'pgr_contractionLinear', 'pgr_separateCrossing',
         'pgr_separateTouching']},

diff --git a/doc/ordering/CMakeLists.txt b/doc/ordering/CMakeLists.txt
@@ -2,8 +2,9 @@ SET(LOCAL_FILES
     ordering-family.rst
     pgr_cuthillMckeeOrdering.rst
     pgr_topologicalSort.rst
-    pgr_sloanOrdering.rst
     pgr_kingOrdering.rst
+    pgr_minDegreeOrdering.rst
+    pgr_sloanOrdering.rst
     )
 
 foreach (f ${LOCAL_FILES})

diff --git a/doc/ordering/ordering-family.rst b/doc/ordering/ordering-family.rst
@@ -22,10 +22,10 @@ Ordering - Family of functions
 .. official-start
 
 * :doc:`pgr_cuthillMckeeOrdering` - Return reverse Cuthill-McKee ordering of an undirected graph.
-* :doc:`pgr_topologicalSort` - Linear ordering of the vertices for directed
-  acyclic graph.
-* :doc:`pgr_sloanOrdering` - Returns the sloan ordering of an undirected graph.
+* :doc:`pgr_topologicalSort` - Linear ordering of the vertices for directed acyclic graph.
 * :doc:`pgr_kingOrdering` - Returns the King ordering of an undirected graph.
+* :doc:`pgr_minDegreeOrdering` - Returns the Minimum Degree ordering of an undirected graph.
+* :doc:`pgr_sloanOrdering` - Returns the Sloan ordering of an undirected graph.
 
 .. official-end
 
@@ -34,8 +34,9 @@ Ordering - Family of functions
 
     pgr_cuthillMckeeOrdering
     pgr_topologicalSort
-    pgr_sloanOrdering
     pgr_kingOrdering
+    pgr_minDegreeOrdering
+    pgr_sloanOrdering
 
 See Also
 -------------------------------------------------------------------------------

diff --git a/doc/ordering/pgr_minDegreeOrdering.rst b/doc/ordering/pgr_minDegreeOrdering.rst
@@ -0,0 +1,110 @@
+..
+   ****************************************************************************
+    pgRouting Manual
+    Copyright(c) pgRouting Contributors
+
+    This documentation is licensed under a Creative Commons Attribution-Share
+    Alike 3.0 License: http://creativecommons.org/licenses/by-sa/3.0/
+   ****************************************************************************
+
+.. index::
+   single: Ordering Family ; pgr_minDegreeOrdering
+   single: minDegreeOrdering - Experimental on v4.0
+
+|
+
+``pgr_minDegreeOrdering`` - Experimental
+===============================================================================
+
+``pgr_minDegreeOrdering`` — Returns the minimum degree ordering of an undirected graphs
+
+.. include:: experimental.rst
+   :start-after: warning-begin
+   :end-before: end-warning
+
+.. rubric:: Version 4.0.0 
+
+  * New experimental function.
+
+Description
+-------------------------------------------------------------------------------
+
+In numerical linear algebra, the MinDegree ordering is a heuristic used to
+reduce the amount of fill-in during sparse matrix factorization, such as
+Cholesky decomposition for symmetric matrices.
+
+When eliminating variables in a sparse system, new nonzero entries—called
+fill-ins—can appear in positions that were originally zero, increasing storage
+and computation costs. The minimum degree approach attempts to reorder the
+vertices (or equivalently, the rows and columns of the matrix) so that,
+at each elimination step, the vertex with the smallest degree is removed first,
+thereby reducing potential fill-in.
+
+The main characteristics are:
+
+- The implementation works on undirected graphs.
+- The algorithm is a heuristic; finding the true optimal ordering is NP-complete.
+- The time complexity is: :math:`O(|V| \log |V| + |E|)`
+
+   - where :math:`|V|` is the number of vertices,
+   - :math:`|E|` is the number of edges.
+
+|Boost| Boost Graph Inside
+
+Signatures
+------------------------------------------------------------------------------
+
+.. index::
+    single: minDegreeOrdering - Experimental on v4.0
+
+.. admonition:: \ \
+   :class: signatures
+
+   | pgr_minDegreeOrdering(`Edges SQL`_)
+
+   | Returns set of |result_node_order|
+   | OR EMPTY SET
+
+:Example: Graph ordering of pgRouting :doc:`sampledata`
+
+.. literalinclude:: minDegreeOrdering.queries
+   :start-after: -- q1
+   :end-before: -- q2
+
+Parameters
+-------------------------------------------------------------------------------
+
+.. include:: pgRouting-concepts.rst
+   :start-after: only_edge_param_start
+   :end-before: only_edge_param_end
+
+Inner Queries
+-------------------------------------------------------------------------------
+
+Edges SQL
+...............................................................................
+
+.. include:: pgRouting-concepts.rst
+   :start-after: basic_edges_sql_start
+   :end-before: basic_edges_sql_end
+
+Result columns
+-------------------------------------------------------------------------------
+
+.. include:: pgr_cuthillMckeeOrdering.rst
+   :start-after: node_ordering_start
+   :end-before: node_ordering_end
+
+See Also
+-------------------------------------------------------------------------------
+
+* :doc:`sampledata`
+* `Boost: King Ordering
+  <https://www.boost.org/libs/graph/doc/minimum_degree_ordering.html>`__
+
+.. rubric:: Indices and tables
+
+* :ref:`genindex`
+* :ref:`search`
+
+
diff --git a/doc/src/pgRouting-introduction.rst b/doc/src/pgRouting-introduction.rst
@@ -66,6 +66,7 @@ This Release Contributors
 Individuals in this release v4.0.0 (in alphabetical order)
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
+Aurélie Bousquet,
 Bipasha Gayary,
 Fan Wu,
 Regina Obe,

diff --git a/doc/src/release_notes.rst b/doc/src/release_notes.rst
@@ -232,6 +232,12 @@ Summary of changes by function
      :start-after: Version 4.0.0
      :end-before: .. rubric
 
+* pgr_minDegreeOrdering
+
+  .. include:: pgr_minDegreeOrdering.rst
+     :start-after: Version 4.0.0
+     :end-before: Description
+
 * pgr_pushRelabel
 
   .. include:: pgr_pushRelabel.rst

diff --git a/docqueries/ordering/CMakeLists.txt b/docqueries/ordering/CMakeLists.txt
@@ -2,8 +2,9 @@
 SET(LOCAL_FILES
     cuthillMckeeOrdering
     topologicalSort
-    sloanOrdering
     kingOrdering
+    minDegreeOrdering
+    sloanOrdering
     )
 
 foreach (f ${LOCAL_FILES})

diff --git a/docqueries/ordering/minDegreeOrdering.pg b/docqueries/ordering/minDegreeOrdering.pg
@@ -0,0 +1,7 @@
+-- CopyRight(c) pgRouting developers
+-- Creative Commons Attribution-Share Alike 3.0 License : https://creativecommons.org/licenses/by-sa/3.0/
+/* -- q1 */
+SELECT * FROM pgr_minDegreeOrdering(
+  'SELECT id, source, target, cost, reverse_cost FROM edges'
+  );
+/* -- q2 */
diff --git a/docqueries/ordering/minDegreeOrdering.result b/docqueries/ordering/minDegreeOrdering.result
@@ -0,0 +1,32 @@
+BEGIN;
+BEGIN
+SET client_min_messages TO NOTICE;
+SET
+/* -- q1 */
+SELECT * FROM pgr_minDegreeOrdering(
+  'SELECT id, source, target, cost, reverse_cost FROM edges'
+  );
+ seq | node
+-----+------
+   1 |    8
+   2 |   12
+   3 |    1
+   4 |    9
+   5 |   16
+   6 |    1
+   7 |   15
+   8 |    1
+   9 |    4
+  10 |   10
+  11 |    8
+  12 |   14
+  13 |    3
+  14 |    4
+  15 |    1
+  16 |    2
+  17 |    6
+(17 rows)
+
+/* -- q2 */
+ROLLBACK;
+ROLLBACK
diff --git a/docqueries/ordering/test.conf b/docqueries/ordering/test.conf
@@ -3,11 +3,11 @@
 %main::tests = (
     'any' => {
         'files' => [qw(
-            sloanOrdering.pg
             cuthillMckeeOrdering.pg
             topologicalSort.pg
-            sloanOrdering.pg
             kingOrdering.pg
+            minDegreeOrdering.pg
+            sloanOrdering.pg
             )]
     },
 

diff --git a/include/ordering/minDegreeOrdering.hpp b/include/ordering/minDegreeOrdering.hpp
@@ -0,0 +1,96 @@
+/*PGR-GNU*****************************************************************
+File: minDegreeOrdering.hpp
+
+Generated with Template by:
+Copyright (c) 2015 pgRouting developers
+Mail: project@pgrouting.org
+
+Developer:
+Copyright (c) 2025 Fan Wu
+Mail: wifiblack0131 at gmail.com
+
+------
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+ ********************************************************************PGR-GNU*/
+
+#ifndef INCLUDE_ORDERING_MINDEGREEORDERING_HPP_
+#define INCLUDE_ORDERING_MINDEGREEORDERING_HPP_
+#pragma once
+
+#include <vector>
+#include <limits>
+#include <iterator>
+#include <utility>
+#include <string>
+
+#include <boost/config.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/property_map/property_map.hpp>
+
+
+#include "cpp_common/base_graph.hpp"
+#include "cpp_common/interruption.hpp"
+#include <boost/graph/minimum_degree_ordering.hpp>
+
+
+namespace pgrouting  {
+
+template <class G>
+std::vector<int64_t>
+minDegreeOrdering(G &graph) {
+    using V = typename G::V;
+
+    size_t n = boost::num_vertices(graph.graph);
+    std::vector<int64_t> results(n);
+
+    auto index_map = boost::get(boost::vertex_index, graph.graph);
+
+    std::vector<V> degrees(n);
+    auto degree_map = boost::make_iterator_property_map(degrees.begin(), index_map);
+
+    std::vector<V> supernode_sizes(n, 1);
+    auto supernode_map = boost::make_iterator_property_map(supernode_sizes.begin(), index_map);
+
+    std::vector<V> permutation(n);
+    std::vector<V> inv_permutation(n);
+
+    for (V v = 0; v < n; ++v) {
+        degree_map[v] = boost::degree(v, graph.graph);
+    }
+
+    CHECK_FOR_INTERRUPTS();
+
+    boost::minimum_degree_ordering(
+        graph.graph,
+        degree_map,
+        inv_permutation.begin(),
+        permutation.begin(),
+        supernode_map,
+        0,
+        index_map);
+
+    size_t j = 0;
+    for (auto i = inv_permutation.begin(); i != inv_permutation.end(); ++i, ++j) {
+        results[j] = static_cast<int64_t>(graph.graph[index_map[*i]].id);
+    }
+
+    return results;
+}
+
+}  // namespace pgrouting
+
+#endif  // INCLUDE_ORDERING_ORDERING_HPP_