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A theorem of Ding, Oporowski, Oxley, and Vertigan implies that any sufficiently large twin-free graph contains a large matching, a co-matching, or a half-graph as a semi-induced subgraph. The sizes of these unavoidable patterns are measured…

Computational Complexity · Computer Science 2026-02-10 Jan Dreier , Nikolas Mählmann , Sebastian Siebertz

Finding a cycle of lowest weight that represents a homology class in a simplicial complex is known as homology localization (HL). Here we address this NP-complete problem using parameterized complexity theory. We show that it is W[1]-hard…

Computational Geometry · Computer Science 2020-12-01 Nello Blaser , Erlend Raa Vågset

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not…

Computational Complexity · Computer Science 2007-05-23 Scott Aaronson

A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…

Data Structures and Algorithms · Computer Science 2013-08-19 Rajesh Chitnis , MohammadTaghi Hajiaghayi , Guy Kortsarz

The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…

Computational Complexity · Computer Science 2012-07-30 Luke Mathieson

We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…

Computational Complexity · Computer Science 2013-08-23 Amer E. Mouawad , Naomi Nishimura , Venkatesh Raman , Narges Simjour , Akira Suzuki

We establish a connection between non-deterministic communication complexity and instance complexity, a measure of information based on algorithmic entropy. Let $\overline{x}$, $\overline{y}$ and $Y_1(\overline{x})$ be respectively the…

Computational Complexity · Computer Science 2009-01-20 Armando Matos , Andreia Teixeira , Andre Souto

Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP}…

Quantum Physics · Physics 2026-04-15 Scott Aaronson , Anand Natarajan , Avishay Tal , Agi Villanyi

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…

Data Structures and Algorithms · Computer Science 2020-06-09 Andreas Emil Feldmann , Karthik C. S. , Euiwoong Lee , Pasin Manurangsi

The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…

Logic in Computer Science · Computer Science 2018-04-06 Paul Gainer , Ernst Moritz Hahn , Sven Schewe

This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…

Symbolic Computation · Computer Science 2013-10-04 Tatsuya Akutsu , Takeyuki Tamura , Atsuhiro Takasu

We investigate the following longstanding open questions raised by Kraj\'i\v{c}ek and Pudl\'ak (J. Symb. L. 1989), Sadowski (FCT 1997), K\"obler and Messner (CCC 1998) and Messner (PhD 2000). Q1: Does TAUT have (p-)optimal proof systems?…

Computational Complexity · Computer Science 2026-02-03 Fabian Egidy

The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…

Machine Learning · Computer Science 2022-05-11 Todd Wareham

Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…

Data Structures and Algorithms · Computer Science 2023-08-23 Robert Ganian , Liana Khazaliya , Kirill Simonov

We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…

Data Structures and Algorithms · Computer Science 2024-07-26 Tim Randolph , Karol Węgrzycki

A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…

Computational Complexity · Computer Science 2026-05-05 Christian Komusiewicz , Nils Morawietz , Frank Sommer , Luca Pascal Staus

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-08 Marius Bozga , Javier Esparza , Radu Iosif , Joseph Sifakis , Christoph Welzel

Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…

Quantum Physics · Physics 2015-08-25 Harumichi Nishimura , Tomoyuki Yamakami

This work analyses the so-called "Relativization Barrier" with respect to the Baker-Gill-Solovay oracle Turing machine. We show that the {\em diagonalization} technique is a valid mathematical proof technique, but it has some prerequisites…

Computational Complexity · Computer Science 2023-11-14 Tianrong Lin