Logical operations over matrices of sorted numbers

Our e-commerce view engine (E.V.E.) works with matrices of sorted number on the lowest level of its application logic. I’d like to describe some of the algorithms we use to combine such matrices in logic operations. Why do we keep data in matrices in sorted order? There is a price to be paid when adding new number to the matrix when sorted order is required - appending number on last position would be much faster.

What lies on background of e-commerce site

I’d like to start series of posts about problems we’re facing in e-commerce area and what algorithms we used to solve them. There are a lot of e-commerce sites on different levels of complexity in terms of feature richness, data amount, throughput requirements, consistency and realtime updates. Let me first introduce the situation we’re trying to handle and then move to the solution space. Domain Let’s look at example of some e-commerce site product listing: