To design an algorithm to find the longest increasing subsequence in an array of integers, you can follow the steps below:

```html

Algorithm: Longest Increasing Subsequence

To find the longest increasing subsequence in an array of integers:

1. Initialize an array to store the length of longest increasing subsequence ending at each index.
2. Initialize the maximum length to 1.
3. Iterate over the array starting from the second element.
4. For each element, compare it with the previous elements to find the longest increasing subsequence ending at the current index.
5. Update the length of longest increasing subsequence at the current index.
6. Update the maximum length if necessary.
7. Return the maximum length as the result.

```

This algorithm is efficient with a time complexity of O(n^2) and can be further optimized using dynamic programming for a time complexity of O(n log n).