2-D Tucker is PPA complete

doi:10.1016/j.jcss.2019.09.002

Journal of Computer and System Sciences

Volume 108, March 2020, Pages 92-103

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Abstract

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all $k \geq 2$ . This corrects a claim in the literature that the Tucker search problem is in PPAD.

Keywords

Tucker lemma

NP search problems

Parity principle

PPA

TFNP

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¹: Supported in part by NSF grants DMS-1101228 and CCF-1213151.

²: Supported in part by MINECO project grant TIN2013-48031-C4-1.

³: Supported in part by Simons Foundation awards 306202 and 578919.