A Library of Languages
Last edited: August 8, 2025PERFECT-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)?
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.
AAA
Last edited: August 8, 2025AAAI Talk Contacts
Last edited: August 8, 2025AAAI2024 Index
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About
Last edited: August 8, 2025Welcome to the personal site of Houjun “Jack” Liu.
I’m on the blaggosphere as u/jemoka and @jemoka.
Who’s this guy?
I am a human interested in linguistic analysis, NLP, and user interfaces. I think AGI & Emacs are cool. I run Shabang, do research in NLP and model-based RL, and am working for TalkBank on the intersection between speech and language.
I’m currently doing my undergrad at Stanford, where I write some code for Stanza, a NLP package for many human languages, and a rover that we are sending to Antarctica.