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On the blackbox complexity of Sperner’s Lemma
 In FCT 2005
, 2005
"... We present several results on the complexity of various forms of Sperner’s Lemma. In the blackbox model of computing, we exhibit a deterministic algorithm for Sperner problems over pseudomanifolds of arbitrary dimension. The query complexity of our algorithm is essentially linear in the separation ..."
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Cited by 9 (1 self)
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We present several results on the complexity of various forms of Sperner’s Lemma. In the blackbox model of computing, we exhibit a deterministic algorithm for Sperner problems over pseudomanifolds of arbitrary dimension. The query complexity of our algorithm is essentially linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an O ( √ n) deterministic query algorithm for the blackbox version of the problem 2DSPERNER, a well studied member of Papadimitriou’s complexity class PPAD. This upper bound matches the Ω ( √ n) deterministic lower bound of Crescenzi and Silvestri. In another blackbox result we prove for the same problem an Ω ( 4 √ n) lower bound for its probabilistic, and an Ω ( 8 √ n) lower bound for its quantum query complexity, showing that all these measures are polynomially related. Finally we explicit Sperner problems on a 2dimensional pseudomanifold and prove that they are complete respectively for the classes PPAD, PPADS and PPA. This is the first time that a 2dimensional Sperner problem is proved to be complete for any of the polynomial parity argument classes. 1
The npcompleteness column: Finding needles in haystacks
 ACM Transactions on Algorithms
, 2007
"... Abstract. This is the 26th edition of a column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that which M. R. Garey and I used in our book “Computers and Intractability: A Guide to the Theory of NPCompleteness, ” W. H. Freeman & Co., New York, 1979, h ..."
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Cited by 7 (0 self)
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Abstract. This is the 26th edition of a column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that which M. R. Garey and I used in our book “Computers and Intractability: A Guide to the Theory of NPCompleteness, ” W. H. Freeman & Co., New York, 1979, hereinafter referred to as “[G&J]. ” Previous columns, the first 23 of which appeared in J. Algorithms, will be referred to by a combination of their sequence number and year of appearance, e.g., “Column 1 [1981]. ” Full bibliographic details on the previous columns, as well as downloadable unofficial versions of them, can be found at