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Or How to Untangle Closed Planar Curves
Computing the Strength of a Graph
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accepting algebra algorithm apply assigned assume bound called column complexity components computation Computer Science condition connected consider consists constant construct contains data structure defined definition denote determine distribution edge elements equal equations equivalent example exists fact final finite function give given graph grid Hence holds implies initial input integer labels least Lemma length lower machine matrix measure method node Note O(log obtain operations optimal oracle output pair parallel partition path performed polynomial position PRAM probability problem procedure processors Proof prove queries random reduce respectively result root running satisfies segment sequence SIAM simple sort space sparse specification stage step string structure subset takes Theorem theory tree Turing University upper variables vertex vertices visible