Data structure for Euler circles?

Question

Algorithms

There are entities united in sets by tags. One entity can be marked with several tags. Suggest a data structure that allows making requests Tag1+Teg2-Teg3 in constant time (possibly with structure balancing out_of_process).
If such a structure is possible, then its approximate memory_layout (on paper, Euler circles look attractive, but how to fit them into a one-dimensional sequential memory / file)
Load profile - 1000 elements, 100 tags, read more often than write.
For key-value store for example:

• data structure - dictionary/associative_array
  
• memory layout - sparse_array
  

what about tags-values?

Answer 1

bit fields

Answer 2

The classic approach to solving this problem is a boolean index:
map[tag]set[id]