ﻻ يوجد ملخص باللغة العربية
We develop a polynomial time $Omegaleft ( frac 1R log R right)$ approximate algorithm for Max 2CSP-$R$, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of size $R$, and we want to find an assignment to the variables that maximizes the number of satisfied constraints. Assuming the Unique Games Conjecture, this is the best possible approximation up to constant factors. Previously, a $1/R$-approximate algorithm was known, based on linear programming. Our algorithm is based on semidefinite programming (SDP) and on a novel rounding technique. The SDP that we use has an almost-matching integrality gap.
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it, we obtain t
MAX CLIQUE problem (MCP) is an NPO problem, which asks to find the largest complete sub-graph in a graph $G, G = (V, E)$ (directed or undirected). MCP is well known to be $NP-Hard$ to approximate in polynomial time with an approximation ratio of $1 +
An ordering constraint satisfaction problem (OCSP) is given by a positive integer $k$ and a constraint predicate $Pi$ mapping permutations on ${1,ldots,k}$ to ${0,1}$. Given an instance of OCSP$(Pi)$ on $n$ variables and $m$ constraints, the goal is
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A in mathbb{R}^{n times n}$ and $b in mathbb{R}^n$, we wish to find a vector $x in mathbb{R}^n$ s
The minimum linear ordering problem (MLOP) seeks to minimize an aggregated cost $f(cdot)$ due to an ordering $sigma$ of the items (say $[n]$), i.e., $min_{sigma} sum_{iin [n]} f(E_{i,sigma})$, where $E_{i,sigma}$ is the set of items that are mapped b