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HW 1 solutions

# HW 1 solutions - Vertex Cover Data Structure n number of...

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Vertex Cover: Data Structure: n: number of vertices m[1..n][1..n]: Adjacency matrix, B: number giving target length of dominating set Length O(n^2) elements We don’t need the exact number. We just need a polynomially-related estimate. Witness w: Finite but unbounded list of labels for vertices. Note that this structure will be stored on the left of our Turing machine’s tape by the oracle. In our model, our verification algorithm must treat this as an essentially random string of symbols from the tape alphabet we will assume that all such strings will map to some instance of our witness data structure in an efficient (read: polynomial time) manner, and that there is an oracle string for every instance of our witness data structure. In short, just give a simple data structure and let the oracle fill in the fields. Do not put any preconditions on the witness, such as “the length of the set is less than k.” If the oracle does too much work, we could have a polynomial verification algorithm for a problem that is not NP!

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HW 1 solutions - Vertex Cover Data Structure n number of...

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