Journal ArticleDOI
The complexity of the parity argument with potential
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It is shown that the problem of finding an unknown odd-degree vertex or a local optimum vertex on a graph with potential is polynomially equivalent to EndOfPotentialLine if the maximum degree is at most three, however, even if themaximum degree is 4, such a problem is PPA ∩ PLS -complete.About:
This article is published in Journal of Computer and System Sciences.The article was published on 2021-09-01. It has received 4 citations till now. The article focuses on the topics: Degree (graph theory) & Graph (abstract data type).read more
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The Complexity of Gradient Descent: CLS = PPAD $\cap$ PLS.
TL;DR: It is shown that computing a Karush-Kuhn-Tucker point of a continuously differentiable function over the domain [0,1]2 is PPAD ∩ PLS-complete, which is the first natural problem to be shown complete for this class.
Proceedings ArticleDOI
The complexity of gradient descent: CLS = PPAD ∩ PLS
TL;DR: In this article, it was shown that computing a Karush-Kuhn-Tucker (KKT) point of a continuous differentiable function over a bounded convex polytopal domain is PPAD ∩ PLS-complete.
Journal ArticleDOI
Further collapses in TFNP
Mika Goos,Alexandros Hollender,Siddhartha Jain,Gilbert Maystre,William Pires,Robert Robere,Ran Tao +6 more
TL;DR: In particular, the authors showed EOPL = PLS ∩ PPAD, which is a simpler proof of the breakthrough collapse CLS = PPAD by Fearnley et al. (JCSS 2020).
Journal ArticleDOI
The Complexity of Gradient Descent: CLS = PPAD ∩ PLS
TL;DR: In this article , it was shown that the problem of computing a Karush-Kuhn-Tucker (KKT) point of a continuous differentiable function over a bounded convex polytopal domain is PPAD ∩ PLS-complete.
References
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Journal ArticleDOI
The Complexity of Computing a Nash Equilibrium
TL;DR: It is shown that finding a Nash equilibrium in three-player games is indeed PPAD-complete; and this result is resolved by a reduction from Brouwer's problem, thus establishing that the two problems are computationally equivalent.
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On the complexity of the parity argument and other inefficient proofs of existence
TL;DR: Several new complexity classes of search problems, ''between'' the classes FP and FNP, are defined, based on lemmata such as ''every graph has an even number of odd-degree nodes.''
Journal ArticleDOI
How easy is local search
TL;DR: A natural class PLS is defined consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and it is shown that there are complete problems for this class.
Proceedings ArticleDOI
The complexity of pure Nash equilibria
TL;DR: This work focuses on congestion games, and shows that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLS-complete in general.
Journal ArticleDOI
Settling the complexity of computing two-player Nash equilibria
TL;DR: The complexity of finding a Nash equilibrium in a two-player game is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991 as discussed by the authors.