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ACM Transactions on Computation Theory (TOCT), Volume 5 Issue 1, May 2013

On the usefulness of predicates
Per Austrin, Johan Håstad
Article No.: 1
DOI: 10.1145/2462896.2462897

Motivated by the pervasiveness of strong inapproximability results for Max-CSPs, we introduce a relaxed notion of an approximate solution of a Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to replace the constraints...

Verifying proofs in constant depth
Olaf Beyersdorff, Samir Datta, Andreas Krebs, Meena Mahajan, Gido Scharfenberger-Fabian, Karteek Sreenivasaiah, Michael Thomas, Heribert Vollmer
Article No.: 2
DOI: 10.1145/2462896.2462898

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask...

On multiway cut parameterized above lower bounds
Marek Cygan, Marcin Pilipczuk, Michał Pilipczuk, Jakub Onufry Wojtaszczyk
Article No.: 3
DOI: 10.1145/2462896.2462899

We introduce a concept of parameterizing a problem above the optimum solution of its natural linear programming relaxation and prove that the node multiway cut problem is fixed-parameter tractable (FPT) in this setting. As a consequence we...