diff --git a/include/dsu.h b/include/dsu.h
index d59c0b12..ef38d451 100644
--- a/include/dsu.h
+++ b/include/dsu.h
@@ -1,13 +1,13 @@
 #pragma once
-#include <vector>
 #include <atomic>
 #include <cassert>
+#include <vector>
 
-template<class T>
+template <class T>
 struct DSUMergeRet {
-  bool merged; // true if a merge actually occured
-  T root; // new root
-  T child; // new child of root
+  bool merged;  // true if a merge actually occured
+  T root;       // new root
+  T child;      // new child of root
 };
 
 template <class T>
@@ -18,7 +18,24 @@ class DisjointSetUnion {
   // parent and size arrays
   T* parent;
   T* size;
-public:
+
+  // Order based on size and break ties with
+  // a simple fixed ordering of the edge
+  // if sum even, smaller first
+  // if sum odd, larger first
+  inline void order_edge(T& a, T& b) {
+    if (size[a] < size[b])
+      std::swap(a, b);
+    else if (size[a] == size[b]) {
+      if ((a + b) % 2 == 0 && a > b) {
+        std::swap(a, b);
+      } else if ((a + b) % 2 == 1 && a < b) {
+        std::swap(a, b);
+      }
+    }
+  }
+
+ public:
   DisjointSetUnion(T n) : n(n), parent(new T[n]), size(new T[n]) {
     for (T i = 0; i < n; i++) {
       parent[i] = i;
@@ -32,7 +49,7 @@ class DisjointSetUnion {
   }
 
   // make a copy of the DSU
-  DisjointSetUnion(const DisjointSetUnion &oth) : n(oth.n), parent(new T[n]), size(new T[n]) {
+  DisjointSetUnion(const DisjointSetUnion& oth) : n(oth.n), parent(new T[n]), size(new T[n]) {
     for (T i = 0; i < n; i++) {
       parent[i] = oth.parent[i];
       size[i] = oth.size[i];
@@ -40,17 +57,17 @@ class DisjointSetUnion {
   }
 
   // move the DSU to a new object
-  DisjointSetUnion(DisjointSetUnion &&oth) : n(oth.n), parent(oth.parent), size(oth.size) {
+  DisjointSetUnion(DisjointSetUnion&& oth) : n(oth.n), parent(oth.parent), size(oth.size) {
     oth.n = 0;
     oth.parent = nullptr;
     oth.size = nullptr;
   }
 
-  DisjointSetUnion operator=(const DisjointSetUnion &oth) = delete;
+  DisjointSetUnion operator=(const DisjointSetUnion& oth) = delete;
 
   inline T find_root(T u) {
     assert(0 <= u && u < n);
-    while(parent[parent[u]] != u) {
+    while (parent[parent[u]] != u) {
       parent[u] = parent[parent[u]];
       u = parent[u];
     }
@@ -64,7 +81,7 @@ class DisjointSetUnion {
     assert(0 <= b && b < n);
     if (a == b) return {false, 0, 0};
 
-    if (size[a] < size[b]) std::swap(a,b);
+    order_edge(a, b);
     parent[b] = a;
     size[a] += size[b];
     return {true, a, b};
@@ -82,14 +99,31 @@ class DisjointSetUnion {
 // thus is a little slower for single threaded use cases
 template <class T>
 class DisjointSetUnion_MT {
-private:
+ private:
   // number of items in the DSU
   T n;
 
   // parent and size arrays
   std::atomic<T>* parent;
   std::atomic<T>* size;
-public:
+
+  // Order based on size and break ties with
+  // a simple fixed ordering of the edge
+  // if sum even, smaller first
+  // if sum odd, larger first
+  inline void order_edge(T& a, T& b) {
+    if (size[a] < size[b])
+      std::swap(a, b);
+    else if (size[a] == size[b]) {
+      if ((a + b) % 2 == 0 && a > b) {
+        std::swap(a, b);
+      } else if ((a + b) % 2 == 1 && a < b) {
+        std::swap(a, b);
+      }
+    }
+  }
+
+ public:
   DisjointSetUnion_MT(T n) : n(n), parent(new std::atomic<T>[n]), size(new std::atomic<T>[n]) {
     for (T i = 0; i < n; i++) {
       parent[i] = i;
@@ -103,7 +137,7 @@ class DisjointSetUnion_MT {
   }
 
   // make a copy of the DSU
-  DisjointSetUnion_MT(const DisjointSetUnion_MT &oth) : n(oth.n), parent(new T[n]), size(new T[n]) {
+  DisjointSetUnion_MT(const DisjointSetUnion_MT& oth) : n(oth.n), parent(new T[n]), size(new T[n]) {
     for (T i = 0; i < n; i++) {
       parent[i] = oth.parent[i].load();
       size[i] = oth.size[i].load();
@@ -111,7 +145,7 @@ class DisjointSetUnion_MT {
   }
 
   // move the DSU to a new object
-  DisjointSetUnion_MT(DisjointSetUnion_MT &&oth) : n(oth.n), parent(oth.parent), size(oth.size) {
+  DisjointSetUnion_MT(DisjointSetUnion_MT&& oth) : n(oth.n), parent(oth.parent), size(oth.size) {
     oth.n = 0;
     oth.parent = nullptr;
     oth.size = nullptr;
@@ -131,8 +165,7 @@ class DisjointSetUnion_MT {
     while ((a = find_root(a)) != (b = find_root(b))) {
       assert(0 <= a && a < n);
       assert(0 <= b && b < n);
-      if (size[a] < size[b])
-        std::swap(a, b);
+      order_edge(a, b);
 
       // if parent of b has not been modified by another thread -> replace with a
       if (parent[b].compare_exchange_weak(b, a)) {