SQL Indexing when full joining two tables on columns that might be NULL

I have two tables table1 and table2, both with columns group, element_id1, element_id2, date.For every date and every group, there are multiple elements in the group. Each element has 2 ids (every element_id1 is mapped to exactly one element_id2 as vice versa, but sometimes one of them can be NULL [exists but not recorded in our table for that row]).I want to find elements that are in one table per each group and date but not in the other. For checking if two elements are equal, I match them either on element_id1 or element_id2 (depending on which one is non-NULL).For example let the tables be:

• table1:

• table2:

I want the outcome to be

I want to set INDEX in the tables. What are the good indices here? Should I index on the combination of (group, date, element_id1, element_id2)? But the problem is sometimes one of the elemet_ids is NULL. Sould I index only on group and date in both tables?

The SQL that I use is as follows but is VERY slow:

SELECT COALESCE(t1.group, t2.group) as [Group],       COALESCE(t1.element_id1, t2.element_id1) as element_id1,       COALESCE(t1.element_id2, t2.element_id2) as element_id2,       COALESCE(t1.[date], t2.[date]) as [date],       CASE WHEN t1.[date] IS NULL THEN 'Missing from table1'            ELSE 'Missing from table2'       END AS [Status]FROM       table1 t1FULL JOIN       table2 t2ON     t1.[group] = t2.[group]       AND t1.[date] = t2.[date]       AND (t1.element_id1 = t2.element_id1 OR t1.element_id2 = t2.element_id2)WHERE t1.[date] IS NULL OR t2.[date] IS NULL