Related papers: Towards the sampling Lov\'asz Local Lemma
In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…
We reduce non-deterministic time $T \ge 2^n$ to a 3SAT instance $\phi$ of quasilinear size $|\phi| = T \cdot \log^{O(1)} T$ such that there is an explicit circuit $C$ that on input an index $i$ of $\log |\phi|$ bits outputs the $i$th…
Schoening presents a simple randomized algorithm for (d,k)-CSP problems with running time (d(k-1)/k)^n poly(n). Here, d is the number of colors, k is the size of the constraints, and n is the number of variables. A derandomized version of…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained…
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the…
We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
We present a new algorithm for the exact uniform sampling of proper \(k\)-colorings of a graph on \(n\) vertices with maximum degree~\(\Delta\). The algorithm is based on partial rejection sampling (PRS) and introduces a soft relaxation of…
We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…
We present a deterministic distributed algorithm, in the LOCAL model, that computes a $(1+o(1))\Delta$-edge-coloring in polylogarithmic-time, so long as the maximum degree $\Delta=\tilde{\Omega}(\log n)$. For smaller $\Delta$, we give a…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fixed $k\ge 3$ and $\varepsilon>0$, a randomised…
We consider a design problem where experimental conditions (design points $X_i$) are presented in the form of a sequence of i.i.d.\ random variables, generated with an unknown probability measure $\mu$, and only a given proportion…
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…
Traditionally, robust statistics has focused on designing estimators tolerant to a minority of contaminated data. Robust list-decodable learning focuses on the more challenging regime where only a minority $\frac 1 k$ fraction of the…
We show that the uniform Constraint Satisfaction Problem (CSP) parameterized by the size of the solution is in W[1] (the problem is W[1]-hard and it is easy to place it in W[3]). Given a single "free" element of the domain, denoted by $0$,…
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…