diff --git a/lucene/core/src/java/org/apache/lucene/search/AbstractVectorSimilarityQuery.java b/lucene/core/src/java/org/apache/lucene/search/AbstractVectorSimilarityQuery.java
index dde9ce76ac3d..f88eabe0fcac 100644
--- a/lucene/core/src/java/org/apache/lucene/search/AbstractVectorSimilarityQuery.java
+++ b/lucene/core/src/java/org/apache/lucene/search/AbstractVectorSimilarityQuery.java
@@ -25,6 +25,7 @@
 import org.apache.lucene.index.LeafReaderContext;
 import org.apache.lucene.index.QueryTimeout;
 import org.apache.lucene.search.knn.KnnCollectorManager;
+import org.apache.lucene.util.ArrayUtil;
 import org.apache.lucene.util.BitSet;
 import org.apache.lucene.util.BitSetIterator;
 import org.apache.lucene.util.Bits;
@@ -248,9 +249,12 @@ public int nextDoc() {
 
             @Override
             public int advance(int target) {
+              assert index >= -1 : "index must >= -1 but got " + index;
               index =
-                  Arrays.binarySearch(
+                  ArrayUtil.exponentialSearch(
                       scoreDocs,
+                      Math.min(index + 1, scoreDocs.length),
+                      scoreDocs.length,
                       new ScoreDoc(target, 0),
                       Comparator.comparingInt(scoreDoc -> scoreDoc.doc));
               if (index < 0) {
diff --git a/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java b/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
index 2cd3cb63cfe5..ca88e275593c 100644
--- a/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
+++ b/lucene/core/src/java/org/apache/lucene/util/ArrayUtil.java
@@ -801,4 +801,44 @@ public static int compareUnsigned4(byte[] a, int aOffset, byte[] b, int bOffset)
     return Integer.compareUnsigned(
         (int) BitUtil.VH_BE_INT.get(a, aOffset), (int) BitUtil.VH_BE_INT.get(b, bOffset));
   }
+
+  /**
+   * Run an exponential search for the target in an array
+   *
+   * @param arr the array
+   * @param fromIndex the start index of the search (inclusive)
+   * @param toIndex the end index of the search (exclusive)
+   * @param target the target to search for
+   * @return index of the search key, if it is contained in the array; otherwise, (-(insertion
+   *     point) - 1)
+   */
+  public static int exponentialSearch(int[] arr, int fromIndex, int toIndex, int target) {
+    int bound = 1;
+    while (fromIndex + bound < toIndex && arr[fromIndex + bound] < target) {
+      bound *= 2;
+    }
+    return Arrays.binarySearch(
+        arr, fromIndex + bound / 2, Math.min(fromIndex + bound + 1, toIndex), target);
+  }
+
+  /**
+   * Run an exponential search for the target in an array
+   *
+   * @param arr the array
+   * @param fromIndex the start index of the search (inclusive)
+   * @param toIndex the end index of the search (exclusive)
+   * @param target the target to search for
+   * @param comp the comparator
+   * @return index of the search key, if it is contained in the array; otherwise, (-(insertion
+   *     point) - 1)
+   */
+  public static <T> int exponentialSearch(
+      T[] arr, int fromIndex, int toIndex, T target, Comparator<? super T> comp) {
+    int bound = 1;
+    while (fromIndex + bound < toIndex && comp.compare(arr[fromIndex + bound], target) < 0) {
+      bound *= 2;
+    }
+    return Arrays.binarySearch(
+        arr, fromIndex + bound / 2, Math.min(fromIndex + bound + 1, toIndex), target, comp);
+  }
 }
diff --git a/lucene/core/src/java/org/apache/lucene/util/IntArrayDocIdSet.java b/lucene/core/src/java/org/apache/lucene/util/IntArrayDocIdSet.java
index d44cc7839233..c1ac33d08b88 100644
--- a/lucene/core/src/java/org/apache/lucene/util/IntArrayDocIdSet.java
+++ b/lucene/core/src/java/org/apache/lucene/util/IntArrayDocIdSet.java
@@ -83,12 +83,7 @@ public int nextDoc() throws IOException {
 
     @Override
     public int advance(int target) throws IOException {
-      int bound = 1;
-      // given that we use this for small arrays only, this is very unlikely to overflow
-      while (i + bound < length && docs[i + bound] < target) {
-        bound *= 2;
-      }
-      i = Arrays.binarySearch(docs, i + bound / 2, Math.min(i + bound + 1, length), target);
+      i = ArrayUtil.exponentialSearch(docs, i, length, target);
       if (i < 0) {
         i = -1 - i;
       }
diff --git a/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java b/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
index 41f320ba0071..e0e17de10bcd 100644
--- a/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
+++ b/lucene/core/src/test/org/apache/lucene/util/TestArrayUtil.java
@@ -508,4 +508,58 @@ public void testCompareUnsigned8() {
 
     assertEquals(0, ArrayUtil.compareUnsigned8(a, aOffset, b, bOffset));
   }
+
+  public void testExponentialSearchForIntArray() {
+    final Random rnd = random();
+    final int[] arr = new int[rnd.nextInt(2000) + 1];
+    int last = 0;
+    for (int i = 0; i < arr.length; i++) {
+      arr[i] = last;
+      last += rnd.nextInt(1, 10);
+    }
+
+    // case 1: random number, may not be in the array
+    int target = random().nextInt(arr[arr.length - 1]);
+    int idx = ArrayUtil.exponentialSearch(arr, 0, arr.length, target);
+    assertEquals(Arrays.binarySearch(arr, 0, arr.length, target), idx);
+
+    // case 2: search for a number in the array
+    assertExponentialSearch(arr, random().nextInt(arr.length));
+    assertExponentialSearch(arr, 0);
+    assertExponentialSearch(arr, arr.length - 1);
+  }
+
+  private static void assertExponentialSearch(int[] arr, int expectedIndex) {
+    int idx = ArrayUtil.exponentialSearch(arr, 0, arr.length, arr[expectedIndex]);
+    assertEquals(expectedIndex, idx);
+  }
+
+  public void testExponentialSearchForObjectArray() {
+    final Random rnd = random();
+    final Integer[] arr = new Integer[rnd.nextInt(2000) + 1];
+    int last = 0;
+    for (int i = 0; i < arr.length; i++) {
+      arr[i] = last;
+      last += rnd.nextInt(1, 10);
+    }
+
+    // case 1: random number, may not be in the array
+    int target = random().nextInt(arr[arr.length - 1]);
+    int idx =
+        ArrayUtil.exponentialSearch(
+            arr, 0, arr.length, target, Comparator.comparingInt(Integer::intValue));
+    assertEquals(Arrays.binarySearch(arr, 0, arr.length, target), idx);
+
+    // case 2: search for a number in the array
+    assertExponentialSearch(arr, random().nextInt(arr.length));
+    assertExponentialSearch(arr, 0);
+    assertExponentialSearch(arr, arr.length - 1);
+  }
+
+  private static void assertExponentialSearch(Integer[] arr, int expectedIndex) {
+    int idx =
+        ArrayUtil.exponentialSearch(
+            arr, 0, arr.length, arr[expectedIndex], Comparator.comparingInt(Integer::intValue));
+    assertEquals(expectedIndex, idx);
+  }
 }