diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index 4cacac98164..cf42511b01a 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -327,6 +327,9 @@ Optimizations
   Always use MethodHandles to create AttributeImpl classes.
   (Uwe Schindler)
 
+* LUCENE-5960: Use a more efficient bitset, not a Set<Integer>, to
+  track visited states.  (Markus Heiden via Mike McCandless)
+
 Bug Fixes
 
 * LUCENE-5796: Fixes the Scorer.getChildren() method for two combinations 
diff --git a/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java b/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
index 58d9e78e5ed..98c1113a914 100644
--- a/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
+++ b/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
@@ -21,6 +21,7 @@ import java.io.IOException;
 import java.nio.file.Files;
 import java.nio.file.Path;
 import java.util.ArrayList;
+import java.util.BitSet;
 import java.util.Collections;
 import java.util.Comparator;
 import java.util.HashSet;
@@ -42,26 +43,24 @@ import org.apache.lucene.util.Accountables;
 import org.apache.lucene.util.ArrayUtil;
 import org.apache.lucene.util.BytesRef;
 import org.apache.lucene.util.BytesRefBuilder;
-import org.apache.lucene.util.CharsRef;
 import org.apache.lucene.util.CharsRefBuilder;
 import org.apache.lucene.util.IOUtils;
 import org.apache.lucene.util.IntsRef;
 import org.apache.lucene.util.IntsRefBuilder;
 import org.apache.lucene.util.OfflineSorter;
-import org.apache.lucene.util.UnicodeUtil;
-import org.apache.lucene.util.automaton.Operations;
 import org.apache.lucene.util.automaton.Automaton;
+import org.apache.lucene.util.automaton.Operations;
 import org.apache.lucene.util.automaton.Transition;
 import org.apache.lucene.util.fst.Builder;
 import org.apache.lucene.util.fst.ByteSequenceOutputs;
-import org.apache.lucene.util.fst.FST.BytesReader;
 import org.apache.lucene.util.fst.FST;
-import org.apache.lucene.util.fst.PairOutputs.Pair;
+import org.apache.lucene.util.fst.FST.BytesReader;
 import org.apache.lucene.util.fst.PairOutputs;
+import org.apache.lucene.util.fst.PairOutputs.Pair;
 import org.apache.lucene.util.fst.PositiveIntOutputs;
+import org.apache.lucene.util.fst.Util;
 import org.apache.lucene.util.fst.Util.Result;
 import org.apache.lucene.util.fst.Util.TopResults;
-import org.apache.lucene.util.fst.Util;
 
 /**
  * Suggester that first analyzes the surface form, adds the
@@ -270,11 +269,12 @@ public class AnalyzingSuggester extends Lookup {
   }
 
   private int[] topoSortStates(Automaton a) {
-    int[] states = new int[a.getNumStates()];
-    final Set<Integer> visited = new HashSet<>();
+    int numStates = a.getNumStates();
+    int[] states = new int[numStates];
+    final BitSet visited = new BitSet(numStates);
     final LinkedList<Integer> worklist = new LinkedList<>();
     worklist.add(0);
-    visited.add(0);
+    visited.set(0);
     int upto = 0;
     states[upto] = 0;
     upto++;
@@ -284,8 +284,8 @@ public class AnalyzingSuggester extends Lookup {
       int count = a.initTransition(s, t);
       for (int i=0;i<count;i++) {
         a.getNextTransition(t);
-        if (!visited.contains(t.dest)) {
-          visited.add(t.dest);
+        if (!visited.get(t.dest)) {
+          visited.set(t.dest);
           worklist.add(t.dest);
           states[upto++] = t.dest;
         }