Related papers: Distributed PCP Theorems for Hardness of Approxima…
Optimizing parameters of Two-Prover-One-Round Game (2P1R) is an important task in PCPs literature as it would imply a smaller PCP with the same or stronger soundness. While this is a basic question in PCPs community, the connection between…
We give an attribution method for neural combinatorial-optimisation (CO) policies that (i) decomposes a decision by constraint families via LP-relaxation duals, (ii) certifies counterfactuals through a combinatorial feasibility model…
Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
This work revisits the PCP Verifiers used in the works of Hastad [Has01], Guruswami et al.[GHS02], Holmerin[Hol02] and Guruswami[Gur00] for satisfiable Max-E3-SAT and Max-Ek-Set-Splitting, and independent set in 2-colorable 4-uniform…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…
A recent and active line of work achieves tight lower bounds for fundamental problems under the Strong Exponential Time Hypothesis (SETH). A celebrated result of Backurs and Indyk (STOC'15) proves that the Edit Distance of two sequences of…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
Counterfactual explanations (CFE) are being widely used to explain algorithmic decisions, especially in consequential decision-making contexts (e.g., loan approval or pretrial bail). In this context, CFEs aim to provide individuals affected…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…
We introduce a framework for robust uncertainty quantification in situations where labeled training data are corrupted, through noisy or missing labels. We build on conformal prediction, a statistical tool for generating prediction sets…
We prove a PCP theorem for the existential theory of the reals, showing that MAX-ETR-INV is $\exists\mathbb{R}$-hard to approximate to within some constant factor. The existential theory of the reals (ETR) is a decision problem asking if…
The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about…
The Small Set Expansion Hypothesis (SSEH) is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose edge expansion is almost zero and one in which all small subsets of…