I started to read about distance oracle but I don’t understand the term ‘size’ of distance oracle. What is it?
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After digging a bit in several articles of the subject it seems that it refers to the amount of space the oracle stores to be able to efficiently answer queries of type “what is the distance between the vertices u and v in graph G.
For instance, the stretch-3 oracle of Thorp & Zwick (2005) uses memory of O(|E| + (|V|^2)/|L|). Such that |L| is number of landmark vertices.
Each oracle has it’s efficiency and hence maybe stores other elements of the graph to be able to answer those queries.