diff --git a/lib/dereference.js b/lib/dereference.js
index 35eb4196..0a4c919a 100644
--- a/lib/dereference.js
+++ b/lib/dereference.js
@@ -16,7 +16,7 @@ module.exports = dereference;
  */
 function dereference (parser, options) {
   // console.log('Dereferencing $ref pointers in %s', parser.$refs._root$Ref.path);
-  let dereferenced = crawl(parser.schema, parser.$refs._root$Ref.path, "#", [], [], {}, parser.$refs, options);
+  let dereferenced = crawl(parser.schema, parser.$refs._root$Ref.path, "#", new Set(), new Set(), new Map(), parser.$refs, options);
   parser.$refs.circular = dereferenced.circular;
   parser.schema = dereferenced.value;
 }
@@ -27,9 +27,9 @@ function dereference (parser, options) {
  * @param {*} obj - The value to crawl. If it's not an object or array, it will be ignored.
  * @param {string} path - The full path of `obj`, possibly with a JSON Pointer in the hash
  * @param {string} pathFromRoot - The path of `obj` from the schema root
- * @param {object[]} parents - An array of the parent objects that have already been dereferenced
- * @param {object[]} processedObjects - An array of all the objects that have already been processed
- * @param {object} dereferencedCache - An map of all the dereferenced objects
+ * @param {Set<object>} parents - An array of the parent objects that have already been dereferenced
+ * @param {Set<object>} processedObjects - An array of all the objects that have already been processed
+ * @param {Map<string,object>} dereferencedCache - An map of all the dereferenced objects
  * @param {$Refs} $refs
  * @param {$RefParserOptions} options
  * @returns {{value: object, circular: boolean}}
@@ -41,10 +41,10 @@ function crawl (obj, path, pathFromRoot, parents, processedObjects, dereferenced
     circular: false
   };
 
-  if (options.dereference.circular === "ignore" || processedObjects.indexOf(obj) === -1) {
+  if (options.dereference.circular === "ignore" || !processedObjects.has(obj)) {
     if (obj && typeof obj === "object" && !ArrayBuffer.isView(obj)) {
-      parents.push(obj);
-      processedObjects.push(obj);
+      parents.add(obj);
+      processedObjects.add(obj);
 
       if ($Ref.isAllowed$Ref(obj, options)) {
         dereferenced = dereference$Ref(obj, path, pathFromRoot, parents, processedObjects, dereferencedCache, $refs, options);
@@ -52,7 +52,7 @@ function crawl (obj, path, pathFromRoot, parents, processedObjects, dereferenced
         result.value = dereferenced.value;
       }
       else {
-        for (let key of Object.keys(obj)) {
+        for (const key of Object.keys(obj)) {
           let keyPath = Pointer.join(path, key);
           let keyPathFromRoot = Pointer.join(pathFromRoot, key);
           let value = obj[key];
@@ -67,7 +67,7 @@ function crawl (obj, path, pathFromRoot, parents, processedObjects, dereferenced
             }
           }
           else {
-            if (parents.indexOf(value) === -1) {
+            if (!parents.has(value)) {
               dereferenced = crawl(value, keyPath, keyPathFromRoot, parents, processedObjects, dereferencedCache, $refs, options);
               circular = dereferenced.circular;
               // Avoid pointless mutations; breaks frozen objects to no profit
@@ -85,7 +85,7 @@ function crawl (obj, path, pathFromRoot, parents, processedObjects, dereferenced
         }
       }
 
-      parents.pop();
+      parents.delete(obj);
     }
   }
 
@@ -98,9 +98,9 @@ function crawl (obj, path, pathFromRoot, parents, processedObjects, dereferenced
  * @param {{$ref: string}} $ref - The JSON Reference to resolve
  * @param {string} path - The full path of `$ref`, possibly with a JSON Pointer in the hash
  * @param {string} pathFromRoot - The path of `$ref` from the schema root
- * @param {object[]} parents - An array of the parent objects that have already been dereferenced
- * @param {object[]} processedObjects - An array of all the objects that have already been dereferenced
- * @param {object} dereferencedCache - An map of all the dereferenced objects
+ * @param {Set<object>} parents - An array of the parent objects that have already been dereferenced
+ * @param {Set<object>} processedObjects - An array of all the objects that have already been dereferenced
+ * @param {Map<string,object>} dereferencedCache - An map of all the dereferenced objects
  * @param {$Refs} $refs
  * @param {$RefParserOptions} options
  * @returns {{value: object, circular: boolean}}
@@ -110,9 +110,8 @@ function dereference$Ref ($ref, path, pathFromRoot, parents, processedObjects, d
 
   let $refPath = url.resolve(path, $ref.$ref);
 
-  if (dereferencedCache[$refPath]) {
-    const cache = dereferencedCache[$refPath];
-
+  const cache = dereferencedCache.get($refPath);
+  if (cache) {
     const refKeys = Object.keys($ref);
     if (refKeys.length > 1) {
       const extraKeys = {};
@@ -142,7 +141,7 @@ function dereference$Ref ($ref, path, pathFromRoot, parents, processedObjects, d
 
   // Check for circular references
   let directCircular = pointer.circular;
-  let circular = directCircular || parents.indexOf(pointer.value) !== -1;
+  let circular = directCircular || parents.has(pointer.value);
   circular && foundCircularReference(path, $refs, options);
 
   // Dereference the JSON reference
@@ -175,7 +174,7 @@ function dereference$Ref ($ref, path, pathFromRoot, parents, processedObjects, d
 
   // only cache if no extra properties than $ref
   if (Object.keys($ref).length === 1) {
-    dereferencedCache[$refPath] = dereferencedObject;
+    dereferencedCache.set($refPath, dereferencedObject);
   }
 
   return dereferencedObject;