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PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion ManuscriptsAug 20 2019In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as lemmas/corollaries/claims whenever ... More
Verification of Flat FIFO SystemsAug 20 2019The decidability and complexity of reachability problems and model-checking for flat counter systems have been explored in detail. However, only few results are known for flat FIFO systems, only in some particular cases (a single loop or a single bounded ... More
Two-variable logic revisitedAug 20 2019In this paper we present another proof for the well-known small model property of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is combinatorial in nature and uses only ... More
Decoding Downset codes over a finite gridAug 20 2019In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid. We show that their algorithm can be adapted to solve the unique ... More
Freezing, Bounded-Change and Convergent Cellular AutomataAug 19 2019This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded ... More
Safe sets in digraphsAug 19 2019A non-empty subset $S$ of the vertices of a digraph $D$ is called a {\it safe set} if \begin{itemize} \item[(i)] for every strongly connected component $M$ of $D-S$, there exists a strongly connected component $N$ of $D[S]$ such that there exists an arc ... More
A New Fast Computation of a PermanentAug 18 2019This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been ... More
Majorana fermions and the Sensitivity ConjectureAug 17 2019Recently, Hao Huang proved the Sensitivity Conjecture, an important result about complexity measures of Boolean functions. We will discuss how this simple and elegant proof turns out to be closely related to physics concepts of the Jordan-Wigner transformation ... More
Revisiting the Graph Isomorphism Problem with Semidefinite ProgrammingAug 17 2019We present a new algorithm for the graph isomorphism problem which solves an equivalent maximum clique formulation via semidefinite programming. Following previous results, we show that graph isomorphism is equivalent to determining whether an auxiliary ... More
Finding Hamiltonian and Longest (s, t)-paths of C-shaped Supergrid Graphs in Linear TimeAug 17 2019A supergrid graph is a finite vertex-induced subgraph of the infinite graph whose vertex set consists of all points of the plane with integer coordinates and in which two vertices are adjacent if the difference of their x or y coordinates is not larger ... More
LaserTank is NP-completeAug 16 2019We show that the classical game LaserTank is $\mathrm{NP}$-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing $3$-SAT instances to LaserTank ... More
Algorithms and Complexity for Functions on General DomainsAug 16 2019Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the approximation ... More
Placing quantified variants of 3-SAT and Not-All-Equal 3-SAT in the polynomial hierarchyAug 14 2019The complexity of variants of 3-SAT and Not-All-Equal 3-SAT is well studied. However, in contrast, very little is known about the complexity of the problems' quantified counterparts. In the first part of this paper, we show that $\forall \exists$ 3-SAT ... More
The sum-of-squares hierarchy on the sphere, and applications in quantum information theoryAug 14 2019We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of Sum-of-Squares (SOS) relaxations. Exploiting the polynomial kernel technique, we obtain a quadratic improvement of the known convergence rate by Reznick ... More
Type-two Iteration with Bounded Query RevisionAug 14 2019Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we consider functionals ... More
Pointers in Recursion: Exploring the TropicsAug 14 2019We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual ... More
On the Elementary Affine Lambda-Calculus with and Without Fixed PointsAug 14 2019The elementary affine lambda-calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type fixpoints (a.k.a. ... More
Proceedings Third Joint Workshop on Developments in Implicit Computational complExity and Foundational & Practical Aspects of Resource AnalysisAug 13 2019These proceedings present the accepted regular papers and some selected extended abstracts from the 3rd joint DICE-FOPARA workshop, which was held in Prague, Czech Republic on April 6-7, 2019, as a part of ETAPS. The joint workshop provides synergies ... More
Span Programs and Quantum Space ComplexityAug 12 2019While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a function f with ... More
On simplified NP-complete variants of Not-All-Equal 3-Sat and 3-SatAug 12 2019We consider simplified, monotone versions of Not-All-Equal 3-Sat and 3-Sat, variants of the famous Satisfiability Problem where each clause is made up of exactly three distinct literals. We show that Not-All-Equal 3-Sat remains NP-complete even if (1) ... More
Coded trace reconstruction in a constant number of tracesAug 12 2019The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate $1-\varepsilon$ ... More
Graph Motif Problems Parameterized by DualAug 11 2019Let $G=(V,E)$ be a vertex-colored graph, where $C$ is the set of colors used to color $V$. The Graph Motif (or GM) problem takes as input $G$, a multiset $M$ of colors built from $C$, and asks whether there is a subset $S\subseteq V$ such that (i) $G[S]$ ... More
EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 2: EXPSPACE-HardnessAug 09 2019It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 are NEXPTIME-hard and that the satisfiability problem of the logic SSL of subset spaces is PSPACE-hard. We improve these lower bounds for the complexity of these problems ... More
EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 1: ESPACE-AlgorithmsAug 09 2019It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 and of the logic SSL of subset spaces are in N2EXPTIME. We improve this upper bound for the complexity of these problems by presenting ESPACE-algorithms for these problems. ... More
Cyclic Oritatami Systems Cannot Fold Infinite Fractal CurvesAug 09 2019RNA cotranscriptional folding is the phenomenon in which an RNA transcript folds upon itself while being synthesized out of a gene. The oritatami system (OS) is a computation model of this phenomenon, which lets its sequence (transcript) of beads (abstract ... More
Trade-offs in Distributed Interactive ProofsAug 09 2019The study of interactive proofs in the context of distributed network computing is a novel topic, recently introduced by Kol, Oshman, and Saxena [PODC 2018]. In the spirit of sequential interactive proofs theory, we study the power of distributed interactive ... More
Average-Case Lower Bounds for Learning Sparse Mixtures, Robust Estimation and Semirandom AdversariesAug 08 2019This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality ... More
Finite determination of accessibility and geometric structure of singular points for nonlinear systemsAug 08 2019Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The results are ... More
Maximal Spectral Efficiency of OFDM with Index Modulation under Polynomial Space ComplexityAug 07 2019In this letter we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling \emph{all OFDM-IM waveforms} maximizes the spectral efficiency (SE) ... More
Maximal Spectral Efficiency of OFDM with Index Modulation under Polynomial Space ComplexityAug 07 2019Aug 18 2019In this letter we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling \emph{all OFDM-IM waveforms} maximizes the spectral efficiency (SE) ... More
A Constraint Model for the Tree Decomposition of a GraphAug 07 2019We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that decomposition. ... More
Testing convexity of functions over finite domainsAug 07 2019We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the upper bound $O(\frac{\log(\epsilon ... More
The Argument against Quantum ComputersAug 07 2019We give a computational complexity argument against the feasibility of quantum computers. We identify a very low complexity class of probability distributions described by noisy intermediate-scale quantum computers, and explain why it will allow neither ... More
A Universality Theorem for Nested PolytopesAug 06 2019In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope $X$ on $k$ vertices ... More
Optimal Separation and Strong Direct Sum for Randomized Query ComplexityAug 02 2019We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $\epsilon$-error randomized query complexity satisfies ... More
Exact and Fast Inversion of the Approximate Discrete Radon TransformAug 02 2019We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J. Comput., 27(1), 107--119] that is of cost $O(N \log N)$ for a square 2D image with N pixels.
On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear ForestAug 01 2019A graph is $H$-free if it contains no induced subgraph isomorphic to $H$. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in polynomial time ... More
Sublinear Subwindow SearchJul 31 2019We propose an efficient approximation algorithm for subwindow search that runs in sublinear time and memory. Applied to object localization, this algorithm significantly reduces running time and memory usage while maintaining competitive accuracy scores ... More
FaVeST: Fast Vector Spherical Harmonic TransformsJul 31 2019Vector spherical harmonics on $\mathbb{S}^{2}\subset \mathbb{R}^3$ have wide applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent field, one needs to evaluate the expansion and the Fourier coefficients of ... More
FaVeST: Fast Vector Spherical Harmonic TransformsJul 31 2019Aug 06 2019Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ have wide applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients ... More
Monotonic and Non-Monotonic Solution Concepts for Generalized CircuitsJul 30 2019Generalized circuits are an important tool in the study of the computational complexity of equilibrium approximation problems. However, in this paper, we reveal that they have a conceptual flaw, namely that the solution concept is not monotonic. By this ... More
Lecture Notes on Automata, Languages, and GrammarsJul 30 2019These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these notes in a course. ... More
Non-Locality and Zero-Knowledge MIPsJul 29 2019The foundation of zero-knowledge is the simulator: a weak machine capable of pretending to be a weak verifier talking with all-powerful provers. To achieve this, simulators need some kind of advantage such as the knowledge of a trapdoor. In existing zero-knowledge ... More
Parameterized Valiant's ClassesJul 29 2019We define a theory of parameterized algebraic complexity classes in analogy to parameterized Boolean counting classes. We define the classes VFPT and VW[t], which mirror the Boolean counting classes #FPT and #W[t], and define appropriate reductions and ... More
On the Robustness of Median Sampling in Noisy Evolutionary OptimizationJul 28 2019In real-world optimization tasks, the objective (i.e., fitness) function evaluation is often disturbed by noise due to a wide range of uncertainties. Evolutionary algorithms (EAs) have been widely applied to tackle noisy optimization, where reducing the ... More
Parameterized Pre-coloring Extension and List Coloring ProblemsJul 28 2019Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose removal results ... More
Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood RatioJul 26 2019These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a certain quantity ... More
Subexponential-Time Algorithms for Sparse PCAJul 26 2019We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from the Gaussian ... More
On maximal isolation sets in the uniform intersection matrixJul 26 2019Let $A_{k,t}$ be the matrix that represents the adjacency matrix of the intersection bipartite graph of all subsets of size $t$ of $\{1,2,...,k\}$. We give constructions of large isolation sets in $A_{k,t}$, where, for a large enough $k$, our constructions ... More
Generalized Liar's Dominating Set in GraphsJul 26 2019In this article, we study generalized liar's dominating set problem in graphs. Let $G=(V,E)$ be a simple undirected graph. The generalized liar's dominating set, called as the distance-$d$ $(m,\ell)$-liar's dominating set, is a subset $L\subseteq V$ such ... More
A note on the complexity of integer programming gamesJul 26 2019Jul 29 2019In this brief note, we prove that the existence of Nash equilibria on integer programming games is $\Sigma^p_2$-complete.
Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-MaxJul 25 2019Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$ denotes the ... More
Deciding Fast Termination for Probabilistic VASS with NondeterminismJul 25 2019A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter ... More
The Complexity of Computational Problems about Nash Equilibria in Symmetric Win-Lose GamesJul 24 2019We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that ${\mathcal{NP}}$-hardness ... More
Anti-unification in Constraint Logic ProgrammingJul 24 2019Anti-unification refers to the process of generalizing two (or more) goals into a single, more general, goal that captures some of the structure that is common to all initial goals. In general one is typically interested in computing what is often called ... More
The Expressive Power of Higher-Order DatalogJul 23 2019Jul 24 2019A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases. In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate ... More
The $k$-Dimensional Weisfeiler-Leman AlgorithmJul 22 2019In this note, we provide details of the $k$-dimensional Weisfeiler-Leman Algorithm and its analysis from Immerman-Lander (1990). In particular, we present an optimized version of the algorithm that runs in time $O(n^{k+1}\log n)$, where $k$ is fixed (not ... More
Between the deterministic and non-deterministic query complexityJul 22 2019We consider problems that can be solved by asking certain queries. The deterministic query complexity $D(P)$ of a problem $P$ is the smallest number of queries needed to ask in order to find the solution (in the worst case), while the non-deterministic ... More
A note on the complexity of a phaseless polynomial interpolationJul 22 2019Jul 23 2019In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a ... More
A note on the complexity of a phaseless polynomial interpolationJul 22 2019In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a ... More
Optimal In-place Algorithms for Basic Graph ProblemsJul 22 2019We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity problems (like biconnectivity, ... More
The Complexity of Online Bribery in Sequential Elections (Extended Abstract)Jul 22 2019Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters' votes. But neither of those assumptions always holds. In many real-world settings, votes come in sequentially, ... More
Complexity of Modification Problems for Reciprocal Best Match GraphsJul 20 2019Reciprocal best match graphs (RBMGs) are vertex colored graphs whose vertices represent genes and the colors the species where the genes reside. Edges identify pairs of genes that are most closely related with respect to an underlying evolutionary tree. ... More
Quantum Computing: Lecture NotesJul 19 2019This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. ... More
Imperfect Gaps in Gap-ETH and PCPsJul 18 2019We study the role of perfect completeness in probabilistically checkable proof systems (PCPs) and give a new way to transform a PCP with imperfect completeness to a PCP with perfect completeness when the initial gap is a constant. In particular, we show ... More
Metric Dimension Parameterized by TreewidthJul 18 2019A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size ... More
Counting single-qubit Clifford equivalent graph states is #P-CompleteJul 18 2019Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit ... More
Transforming graph states to Bell-pairs is NP-CompleteJul 18 2019Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of ... More
On the $\text{AC}^0[\oplus]$ complexity of Andreev's ProblemJul 18 2019Andreev's Problem states the following: Given an integer $d$ and a subset of $S \subseteq \mathbb{F}_q \times \mathbb{F}_q$, is there a polynomial $y = p(x)$ of degree at most $d$ such that for every $a \in \mathbb{F}_q$, $(a,p(a)) \in S$? We show an ... More
Approximate counting CSP seen from the other sideJul 18 2019In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an arbitrary structure ... More
Approximating Constraint Satisfaction Problems on High-Dimensional ExpandersJul 18 2019We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also highly expanding, ... More
Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group TheoryJul 17 2019The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a lower bound ... More
Almost tight bound on the query complexity of generalized Simon's problemJul 17 2019Simon's problem played an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's problem has been ... More
Almost tight bound on the query complexity of generalized Simon's problemJul 17 2019Jul 18 2019Simon's problem played an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's problem has been ... More
Computing Nested Fixpoints in Quasipolynomial TimeJul 16 2019It is well known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $n^{\lceil\frac{k}{2}\rceil+1}$ iterations ... More
Computing Nested Fixpoints in Quasipolynomial TimeJul 16 2019Jul 18 2019It is well known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $n^{\lceil\frac{k}{2}\rceil+1}$ iterations ... More
Lower Bounding the AND-OR Tree via SymmetrizationJul 15 2019We prove a nearly tight lower bound on the approximate degree of the two-level $\mathsf{AND}$-$\mathsf{OR}$ tree using symmetrization arguments. Specifically, we show that $\widetilde{\mathrm{deg}}(\mathsf{AND}_m \circ \mathsf{OR}_n) = \widetilde{\Omega}(\sqrt{mn})$. ... More
Inapproximability within W[1]: the case of Steiner OrientationJul 15 2019In the $k$-Steiner Orientation problem we are given a mixed graph, that is, with both directed and undirected edges, and a set of $k$ terminal pairs. The goal is to find an orientation of the undirected edges that maximizes the number of terminal pairs ... More
Inapproximability within W[1]: the case of Steiner OrientationJul 15 2019Jul 28 2019In the $k$-Steiner Orientation problem we are given a mixed graph, that is, with both directed and undirected edges, and a set of $k$ terminal pairs. The goal is to find an orientation of the undirected edges that maximizes the number of terminal pairs ... More
More Supervision, Less Computation: Statistical-Computational Tradeoffs in Weakly Supervised LearningJul 14 2019We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1- {\alpha}$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the statistical accuracies ... More
Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexityJul 13 2019In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibility ... More
Coloring invariants of knots and links are often intractableJul 13 2019Let $G$ be a nonabelian, simple group with a nontrivial conjugacy class $C \subseteq G$. Let $K$ be a diagram of an oriented knot in $S^3$, thought of as computational input. We show that for each such $G$ and $C$, the problem of counting homomorphisms ... More
The Projection Games Conjecture and the Hardness of Approximation of SSAT and related problemsJul 12 2019The Super-SAT or SSAT problem was introduced by Dinur, Kindler, Raz and Safra[2002,2003] to prove the NP-hardness of approximation of two popular lattice problems - Shortest Vector Problem (SVP) and Closest Vector Problem (CVP). They conjectured that ... More
Spherical Discrepancy Minimization and Algorithmic Lower Bounds for Covering the SphereJul 11 2019Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x, v_i\rangle$. ... More
Computational Concentration of Measure: Optimal Bounds, Reductions, and MoreJul 11 2019Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is different from ... More
Simplification of Polyline BundlesJul 11 2019We propose and study generalizations to the well-known problem of polyline simplification. Instead of a single polyline, we are given a set of polylines possibly sharing some line segments and bend points. The simplification of those shared parts has ... More
Optimal Space-Depth Trade-Off of CNOT Circuits in Quantum Logic SynthesisJul 11 2019Due to the decoherence of the state-of-the-art physical implementations of quantum computers, it is essential to parallelize the quantum circuits to reduce their depth. Two decades ago, Moore et al. demonstrated that additional qubits (or ancillae) could ... More
Approximately counting and sampling small witnesses using a colourful decision oracleJul 10 2019In this paper, we prove "black box" results for turning algorithms which decide whether or not a witness exists into algorithms to approximately count the number of witnesses, or to sample from the set of witnesses approximately uniformly, with essentially ... More
On the Complexity of Completing Binary PredicatesJul 10 2019Given a binary predicate P, the length of the smallest program that computes a complete extension of P is less than the size of the domain of P plus the amount of information that P has with the halting sequence. This result is derived from a theorem ... More
Smoothed Analysis of Order TypesJul 10 2019Consider an ordered point set $P = (p_1,\ldots,p_n)$, its order type (denoted by $\chi_P$) is a map which assigns to every triple of points a value in $\{+,-,0\}$ based on whether the points are collinear(0), oriented clockwise(-) or counter-clockwise(+). ... More
Polytopes, lattices, and spherical codes for the nearest neighbor problemJul 10 2019We study locality-sensitive hash methods for the nearest neighbor problem for the angular distance, focusing on the approach of first projecting down onto a low-dimensional subspace, and then partitioning the projected vectors according to Voronoi cells ... More
On the Approximability of Presidential Type PredicatesJul 09 2019Given a predicate $P: \{-1, 1\}^k \to \{-1, 1\}$, let $CSP(P)$ be the set of constraint satisfaction problems whose constraints are of the form $P$. We say that $P$ is approximable if given a nearly satisfiable instance of $CSP(P)$, there exists a probabilistic ... More
SNAP: Finding Approximate Second-Order Stationary Solutions Efficiently for Non-convex Linearly Constrained ProblemsJul 09 2019This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first ... More
A complexity dichotomy for hitting connected minors on bounded treewidth graphs: the chair and the banner draw the boundaryJul 09 2019For a fixed connected graph $H$, the $\{H\}$-M-DELETION problem asks, given a graph $G$, for the minimum number of vertices that intersect all minor models of $H$ in $G.$ It is known that this problem can be solved in time $f(tw)\cdot n^{O(1)}$, where ... More
Symmetric Polymorphisms and Efficient Decidability of Promise CSPsJul 09 2019In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between ... More
Interactive Verifiable Polynomial EvaluationJul 09 2019Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks to strong but untrusted servers. Verifiable computing algorithms help build trust in such interactions by enabling the server to provide ... More
On the relationships between Z-, C-, and H-local unitariesJul 09 2019Quantum walk algorithms can speed up search of physical regions of space in both the discrete-time [arXiv:quant-ph/0402107] and continuous-time setting [arXiv:quant-ph/0306054], where the physical region of space being searched is modeled as a connected ... More
Linear MIM-Width of TreesJul 09 2019We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.
Santha-Vazirani sources, deterministic condensers and very strong extractorsJul 08 2019The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i'th bit on the previous i-1 bits is limited for every $i\in[n]$. If the dependence of the i'th bit on the remaining ... More
Counting and Finding Homomorphisms is Universal for Parameterized Complexity TheoryJul 08 2019Counting homomorphisms from a graph $H$ into another graph $G$ is a fundamental problem of (parameterized) counting complexity theory. In this work, we study the case where \emph{both} graphs $H$ and $G$ stem from given classes of graphs: $H\in \mathcal{H}$ ... More