Related papers: Parallel approximation of min-max problems
We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE. This relationship is obtained by means of an efficient parallel algorithm, based on the multiplicative weights update…
We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…
In this paper, we study the communication complexity for the problem of computing a conjunctive query on a large database in a parallel setting with $p$ servers. In contrast to previous work, where upper and lower bounds on the…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
In this paper we present an equilibrium value based framework for solving SDPs via the multiplicative weight update method which is different from the one in Kale's thesis \cite{Kale07}. One of the main advantages of the new framework is…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…
We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other…
We provide an alternative proof of \class{QIP}=\class{PSPACE} to the recent breakthrough result. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
The simulation of large ensembles of particles is usually parallelized by partitioning the domain spatially and using message passing to communicate between the processes handling neighboring subdomains. The particles are represented as…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
We study parallel comparison-based algorithms for finding all equivalence classes of a set of $n$ elements, where sorting according to some total order is not possible. Such scenarios arise, for example, in applications, such as in…
Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
We present a parallel approximation algorithm for a class of mixed packing and covering semidefinite programs which generalize on the class of positive semidefinite programs as considered by Jain and Yao [2011]. As a corollary we get a…