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On graph-theoretic lemmata and complexity classes

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C. H. PapadimitriouAuthors Info & Claims

SFCS '90: Proceedings of the 31st Annual Symposium on Foundations of Computer Science

Pages 794 - 801 vol.2

https://doi.org/10.1109/FSCS.1990.89602

Published: 22 October 1990 Publication History

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Abstract

Several new complexity classes of search problems that lie between the classes FP and FNP are defined. These classes are contained in the class TFNP of search problems that always have a solution. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph, very much like PLS (polynomial local search). The existence of the solution sought is established by means of a simple graph-theoretic lemma with an inefficiently constructive proof. Several class containments and collapses, resulting in the two new classes PDLF contained in PLF are shown; the relation of either class of PLS is open. PLF contains several important problems for which no polynomial-time algorithm is presently known.

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SFCS '90: Proceedings of the 31st Annual Symposium on Foundations of Computer Science

October 1990

ISBN:081862082X

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IEEE Computer Society

United States

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Published: 22 October 1990

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Belovs AIvanyos GQiao YSantha MYang S(2017)On the polynomial parity argument complexity of the combinatorial NullstellensatzProceedings of the 32nd Computational Complexity Conference10.5555/3135595.3135625(1-24)Online publication date: 9-Jul-2017
https://dl.acm.org/doi/10.5555/3135595.3135625
Beckmann ABuss S(2017)The NP Search Problems of Frege and Extended Frege ProofsACM Transactions on Computational Logic10.1145/306014518:2(1-19)Online publication date: 2-Jun-2017
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Feige UJozeph SRoughgarden T(2015)Separation between Estimation and ApproximationProceedings of the 2015 Conference on Innovations in Theoretical Computer Science10.1145/2688073.2688101(271-276)Online publication date: 11-Jan-2015
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Chen XDeng X(2009)On the complexity of 2D discrete fixed point problemTheoretical Computer Science10.1016/j.tcs.2009.07.052410:44(4448-4456)Online publication date: 1-Oct-2009
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Friedl KIvanyos GSantha MVerhoeven Y(2006)Locally 2-dimensional sperner problems complete for the polynomial parity argument classesProceedings of the 6th Italian conference on Algorithms and Complexity10.1007/11758471_36(380-391)Online publication date: 29-May-2006
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Chen XDeng XGabow HFagin R(2005)On algorithms for discrete and approximate brouwer fixed pointsProceedings of the thirty-seventh annual ACM symposium on Theory of computing10.1145/1060590.1060638(323-330)Online publication date: 22-May-2005
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Separating Complexity Classes Using Autoreducibility

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