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In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…
We design and implement an efficient parallel algorithm for finding a perfect matching in a weighted bipartite graph such that weights on the edges of the matching are large. This problem differs from the maximum weight matching problem,…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…
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,…