相关论文: A Birthday Repetition Theorem and Complexity of Ap…

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 $f:\mathbb{N}\to\mathbb{N}$,…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

Probabilistically checkable proofs of proximity (PCPP) are proof systems where the verifier is given a 3SAT formula, but has only oracle access to an assignment and a proof. The verifier accepts a satisfying assignment with a valid proof,…

We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…

In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…

We design approximation algorithms for Unique Games when the constraint graph admits good low diameter graph decomposition. For the ${\sf Max2Lin}_k$ problem in $K_r$-minor free graphs, when there is an assignment satisfying $1-\varepsilon$…

We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…

In this paper, we present a randomized polynomial-time approximation algorithm for k-CSPd. In k-CSPd, we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of…

We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…

We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in time $n^{O(k)}$, where $k$ is the treewidth of the graph. This improves on the previous $2^{2^k}$-approximation in time $\poly(n) 2^{O(k)}$ due to Chlamt\'a\v{c}…

We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\delta \cdot…

We revisit the Strong Birthday Problem (SBP) introduced by DasGupta'05, which asks for the minimum population n required such that, with a probability of at least 1/2, every individual in the group shares a birthday with at least one other…

Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…

We introduce a fun problem that can be considered as a variant of the classic birthday problem, the Bottleneck Birthday Problem (BBP). It is stated as: what is the maximum number of people we have to choose so that no day of the year has…

Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…

Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…

We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…

The Super-SAT or SSAT problem was introduced by Dinur et al.(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 SSAT is…

We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are `unique' constraints (i.e., permutations), the value of the game can be well…

We present a family of algorithms to solve random planted instances of any $k$-ary Boolean constraint satisfaction problem (CSP). A randomly planted instance of a Boolean CSP is generated by (1) choosing an arbitrary planted assignment…