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Parameterized Inapproximability Hypothesis under ETH Open
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to s…
Parameterized Inapproximability Hypothesis under Exponential Time Hypothesis Open
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to s…
Almost Optimal Time Lower Bound for Approximating Parameterized Clique, CSP, and More, under ETH Open
The Parameterized Inapproximability Hypothesis (PIH), which is an analog of the PCP theorem in parameterized complexity, asserts that, there is a constant $\varepsilon> 0$ such that for any computable function $f:\mathbb{N}\to\mathbb{N}$, …
Parameterized Inapproximability Hypothesis under ETH Open
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to s…
Synthesizing Efficient Memoization Algorithms Open
In this paper, we propose an automated approach to finding correct and efficient memoization algorithms from a given declarative specification. This problem has two major challenges: (i) a memoization algorithm is too large to be handled b…
Automated Tail Bound Analysis for Probabilistic Recurrence Relations Open
Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $κ$, we consider the classical concept of tail probability $\Pr[T \ge κ]$, i.e., the prob…
Improved Hardness of Approximating k-Clique under ETH Open
In this paper, we prove that assuming the exponential time hypothesis (ETH), there is no $f(k)\cdot n^{k^{o(1/\log\log k)}}$-time algorithm that can decide whether an $n$-vertex graph contains a clique of size $k$ or contains no clique of …
Automated Tail Bound Analysis for Probabilistic Recurrence Relations Open
Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $$\kappa $$ , we consider the tail probability $$\Pr [T \ge \kappa ]$$ , i.e., the probab…
Constant Approximating Parameterized $k$-SetCover is W[2]-hard Open
In this paper, we prove that it is W[2]-hard to approximate k-SetCover within any constant ratio. Our proof is built upon the recently developed threshold graph composition technique. We propose a strong notion of threshold graphs and use …
On Lower Bounds of Approximating Parameterized $k$-Clique Open
Given a simple graph $G$ and an integer $k$, the goal of $k$-Clique problem is to decide if $G$ contains a complete subgraph of size $k$. We say an algorithm approximates $k$-Clique within a factor $g(k)$ if it can find a clique of size at…
Automated Concentration Bound Analysis for Probabilistic Recurrence Relations Open
Probabilistic recurrence relations (PRRs) are a standard formalism to analyze the runtime of randomized algorithms. In this work, we consider the classical problem of obtaining concentration bounds on the runtime of randomized algorithms m…
Quantitative Analysis of Assertion Violations in Probabilistic Programs Open
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on …
Guiding dynamic programing via structural probability for accelerating programming by example Open
Programming by example (PBE) is an important subproblem of program synthesis, and PBE techniques have been applied to many domains. Though many techniques for accelerating PBE systems have been explored, the scalability remains one of the …
Concentration-Bound Analysis for Probabilistic Programs and Probabilistic Recurrence Relations Open
Analyzing probabilistic programs and randomized algorithms are classical problems in computer science. The first basic problem in the analysis of stochastic processes is to consider the expectation or mean, and another basic problem is to …