Related papers: Solving Packing and Covering LPs in $\tilde{O}(\fr…
The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
In this paper, we study a class of set cover problems that satisfy a special property which we call the {\em small neighborhood cover} property. This class encompasses several well-studied problems including vertex cover, interval cover,…
In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
In this paper, we give a faster width-dependent algorithm for mixed packing-covering LPs. Mixed packing-covering LPs are fundamental to combinatorial optimization in computer science and operations research. Our algorithm finds a $1+\eps$…
We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…
Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…
In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…