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accepted Efficiently construct unique pairs of sets, over and over again
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comment Efficiently construct unique pairs of sets, over and over again
I think this will only work if I use all sets (not having my constraint). e.g. let's say I start with 3 sets $$T_1 = {a_1}, T_2 = {a_2}, T_3 = {a_3}$$ When pairing the three sets, I will get, $$T_1 \bigvee T_2 = \{a_1, a_2\}, T_1 \bigvee T_3 = \{a_1, a_3\}, T_2 \bigvee T_3 = \{a_2, a_3\}$$ Now let's say $$T_1 \bigvee T_2$$ does not satisfy my constraint. The final family: $$(T_1 \bigvee T_3) \bigvee (T_2 \bigvee T_3)$$ Will be $$p_1 \bigvee p_2 \bigvee p_3$$ Which, if we enumerate, will give us all possible pairs. But $$T_1 \bigvee T_2$$ is wrong...
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comment Efficiently construct unique pairs of sets, over and over again
Ok. So are you suggesting that I have one family for each specific number of elements? And then I construct all possible pairs, and for each pair, I check whether it exists or not (based on the level of pairing), if it does exist, ignore it, and if it doesn't exist add it. Is this what's on your mind? Another (interesting) question would be, can you go from the family of subsets to the subsets themselves? Like can you re-construct $$T_1 \bigvee ... \bigvee T_k \mbox{ from } \psi_{{T_1, ..., T_k}}$$ Is this by any chance related to something called representative sets? If Yes, any references?
Apr
20
comment Efficiently construct unique pairs of sets, over and over again
I deleted my last comment (third question); I figured out it doesn't really make sense...
Apr
20
comment Efficiently construct unique pairs of sets, over and over again
Clever answer, but I still have three questions; 1) What if my data is not intrinsically sorted. Each element (a or b) is actually a pair of values read from a database, so like <name, id> or <age, id> (age would be replaced with the actual value of age, like 22, same goes for name or id, so it won't be trivial to sort those, especially if their different attributes. Like <name(Bob), id(9)> and <hairColor(black), age(22)>. My second question is that why "one Trie for each possible set size" it seems that there should be one Trie, and the length from the root to the leaf would be the length.
Apr
19
comment Efficiently construct unique pairs of sets, over and over again
@Aryabhata: Your answer helped. A lot. I'm currently thinking of all my option. I want to observe all the knowledge. I might have some questions, and I will be commenting on the answers when I make sure I fully understand them, or when I give up and need more help. I will work on this problem tonight. Thanks a bunch