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776

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776 is a VC firm lead by Reddit cofounder Alexis Ohanian.

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PERFECT-MATCHING

Given a bipartite graph \(G = \qty(U,V,E)\), is there a perfect matching (a one to one correspondence between \(U\) and \(V\) nodes)?

This is in both NP and coNP

But, PERFECT-MATCHING is in \(P\)

Yet, with a randomized algorithm, PERFECT-MATCHING can be solved in parallel time \(O\qty(\log^{2} n)\).

NP trivial

I hand you the matching

Not Hall’s Theorem

Sufficient: Suppose \(S \subseteq U\), consider \(N\qty(S) \subseteq V\), the neighborhood of \(S\) is \(|N(s)|< |S|\), then there is no perfect matching.

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