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We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian…
The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the…
In this paper we propose an improved approximation scheme for the Vector Bin Packing problem (VBP), based on the combination of (near-)optimal solution of the Linear Programming (LP) relaxation and a greedy (modified first-fit) heuristic.…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate `high-level' theory and glued together self-consistently by a less accurate `low-level' theory at the…
In this work we present a quadratic programming approximation of the Semi-Supervised Support Vector Machine (S3VM) problem, namely approximate QP-S3VM, that can be efficiently solved using off the shelf optimization packages. We prove that…
Sparse computations frequently appear in scientific simulations and the performance of these simulations rely heavily on the optimization of the sparse codes. The compact data structures and irregular computation patterns in sparse matrix…
Sparse matrix-vector multiplication (SpMV) is a fundamental operation with a wide range of applications in scientific computing and artificial intelligence. However, the large scale and sparsity of sparse matrix often make it a performance…
The unconstrained binary quadratic programming (UBQP) problem is a class of problems of significant importance in many practical applications, such as in combinatorial optimization, circuit design, and other fields. The positive…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
Consider the setting where a $\rho$-sparse Rademacher vector is planted in a random $d$-dimensional subspace of $R^n$. A classical question is how to recover this planted vector given a random basis in this subspace. A recent result by…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues…
Wireless baseband processing (WBP) serves as an ideal scenario for utilizing vector processing, which excels in managing data-parallel operations due to its parallel structure. However, conventional vector architectures face certain…
Recent work [BGS17,ABGS19] has shown SETH hardness of CVP in the $\ell_p$ norm for any $p$ that is not an even integer. This result was shown by giving a Karp reduction from $k$-SAT on $n$ variables to CVP on a lattice of rank $n$. In this…
We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any…
The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable…
For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…
Hyperdimensional computing (HDC) is an emerging computing paradigm with significant promise for efficient and robust learning. In HDC, objects are encoded with high-dimensional vector symbolic sequences called hypervectors. The quality of…