计算复杂性

In this paper we present a graph property with sensitivity $\Theta(\sqrt{n})$, where $n={v\choose2}$ is the number of variables, and generalize it to a $k$-uniform hypergraph property with sensitivity $\Theta(\sqrt{n})$, where $n={v\choose…

We prove upper bounds on deterministic communication complexity in terms of log of the rank and simple versions of the corruption bound. Our bounds are a simplified version of the results of Gavinsky and Lovett, using the same set of tools.…

In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all…

The problems of Permutation Routing via Matching and Token Swapping are reconfiguration problems on graphs. This paper is concerned with the complexity of those problems and a colored variant. For a given graph where each vertex has a…

In this paper, we investigate property testing whether or not a degree d multivariate poly- nomial is a sum of squares or is far from a sum of squares. We show that if we require that the property tester always accepts YES instances and…

Let $\mathcal{F}$ be a finite alphabet and $\mathcal{D}$ be a finite set of distributions over $\mathcal{F}$. A Generalized Santha-Vazirani (GSV) source of type $(\mathcal{F}, \mathcal{D})$, introduced by Beigi, Etesami and Gohari (ICALP…

The paper is concerned with the computational complexity of the initial value problem (IVP) for a system of ordinary dynamical equations. Formal problem statement is given, containing a Turing machine with an oracle for getting the initial…

We show that the conjugacy problem in a wreath product $A \wr B$ is uniform-$\mathsf{TC}^0$-Turing-reducible to the conjugacy problem in the factors $A$ and $B$ and the power problem in $B$. If $B$ is torsion free, the power problem for $B$…

Let $F$ be a connected graph with $\ell$ vertices. The existence of a subgraph isomorphic to $F$ can be defined in first-order logic with quantifier depth no better than $\ell$, simply because no first-order formula of smaller quantifier…

For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…

We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of…

We construct uniquely satisfiable $k$-CNF formulas that are hard for the algorithm PPSZ. Firstly, we construct graph-instances on which "weak PPSZ" has savings of at most $(2 + \epsilon) / k$; the saving of an algorithm on an input formula…

Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this…

We prove that for a triangulated plane graph it is NP-complete to determine its domination number and its power domination number.

We introduce a temporal Steiner network problem in which a graph, as well as changes to its edges and/or vertices over a set of discrete times, are given as input; the goal is to find a minimal subgraph satisfying a set of $k$…

We derive upper and lower bounds on the degree $d$ for which the Lov\'asz $\vartheta$ function, or equivalently sum-of-squares proofs with degree two, can refute the existence of a $k$-coloring in random regular graphs $G_{n,d}$. We show…

A constraint satisfaction problem (CSP) is a problem of computing a homomorphism ${\bf R} \rightarrow {\bf \Gamma}$ between two relational structures. Analyzing its complexity has been a very fruitful research direction, especially for…

Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…

Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…