The "ay-o" bit in particular always made me think of "day-o" as in Harry Belafonte's The Banana Boat Song.
Specifically an algorithm of bit complexity O(n2log3nloglogn) where n="|y| is the number of digits in y.
These slots are for FL, O (the "bit" that falls out early in the narrative), OR, and MAT, spelling the answer FLOORMAT.
Known indexes take O(nlogn) bits or O(nlog1+ϵn) bits space, and answer this query in O(p+logn+occℓ,rlogn) time or in optimal O(p+occℓ,r) time respectively, where ϵ is any positive constant.
These shift distances can then be used to pack the extracted bits of each integer to O(n) bits.
We then improve our second construction and show that we can reduce the entropy loss to 2log(1/epsilon)+O(1) bits, while still using O log3n) truly random bits (where entropy loss is defined as [(source min-entropy)+ (# truly random bits used)- (# output bits)], and epsilon is the statistical difference from uniform achieved).
We then improve our second construction and show that we can reduce the entropy loss to 2 log(1/ε)+O(1) bits, while still using O log3 n) truly random bits (where entropy loss is defined as [(source min−entropy)+(#truly random bits used)−(#output bits)], and ε is the statistical difference from uniform achieved).
The dictionary (i.e., plaintext space) is necessarily very small, since processing ℓ-bit words requires lookup tables of size O(2 ℓ )×O(2 ℓ )=O(22ℓ ) bits.2 Thus, to remain feasible, we are bound to processing chunks of up to 8 bits (and hardly more).
Then, the node assembles a data packet by adding an overhead with length of L o bits to the payload.
Building on a recent O(n -bits implemen -bits of DFS due to Elmasry et al. (STACS 2015) we provimplementationmplementatiofs for all these applications of DFS.
