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An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of 3/2 and the time order…
We introduce the NP-complete problem 3SAT_N and extend Tovey's results to a classification theorem for this problem. This theorem leads us to generalize the concept of truth assignments for SAT to aggressive truth assignments for 3SAT_N. We…
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
We give simple deterministic reductions demonstrating the NP-hardness of approximating the nearest codeword problem and minimum distance problem within arbitrary constant factors (and almost-polynomial factors assuming NP cannot be solved…