Code to generate "Palindrome Cover".

Palindrome.java

import java.io.*;
import java.util.*;

class Palindrome {
  public static void main(String[] args) {
    List<String> palindromes = Arrays.asList("gabbag", "baggab");
    System.out.println(getShortestCover(palindromes));
  }
  
  private static Set<String> getShortestCover(List<String> palindromes) {
    Set<String> cover = new HashSet<>();
    
    for (String p : palindromes) {
      cover.addAll(getPair(p));
    }
    return cover;
  }
  
  private static List<String> getPair(String palindrome) {
    if (palindrome == null || palindrome.length() < 2) {
      throw new IllegalArgumentException("Incorrect palindrome: " + palindrome);
    }
    
    List<String> pairs = new ArrayList<>();
    if (palindrome.length() == 2) {
      pairs.add(String.valueOf(palindrome.charAt(0)));
      pairs.add(String.valueOf(palindrome.charAt(1)));
    } else {
      pairs.add(palindrome.substring(0, palindrome.length() / 2));
      pairs.add(palindrome.substring(palindrome.length() / 2));
    }
    return pairs;
  }
}