Related papers: A Simple Deterministic Reduction for the Gap Minim…
In this paper we present a new gap-creating randomized self-reduction for parameterized Maximum Likelihood Decoding problem over $\mathbb{F}_p$ ($k$-MLD$_p$). The reduction takes a $k$-MLD$_p$ instance with $k\cdot n$ vectors as input, runs…
The current paper studies the problem of minimizing a loss $f(\boldsymbol{x})$ subject to constraints of the form $\boldsymbol{D}\boldsymbol{x} \in S$, where $S$ is a closed set, convex or not, and $\boldsymbol{D}$ is a matrix that fuses…
The problem of combinatorial filter reduction arises from questions of resource optimization in robots; it is one specific way in which automation can help to achieve minimalism, to build better, simpler robots. This paper contributes a new…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…
Today's massively-sized datasets have made it necessary to often perform computations on them in a distributed manner. In principle, a computational task is divided into subtasks which are distributed over a cluster operated by a…
The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially…
Dvorak (2013) gave a bound on the minimum size of a distance r dominating set in the terms of the maximum size of a distance 2r independent set and generalized coloring numbers, thus obtaining a constant factor approximation algorithm for…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
Combinatorial reconfiguration is a growing research field studying problems on the transformability between a pair of solutions of a search problem. We consider the approximability of optimization variants of reconfiguration problems; e.g.,…
In 1996, Karger [Kar96] gave a startling randomized algorithm that finds a minimum-cut in a (weighted) graph in time $O(m\log^3n)$ which he termed near-linear time meaning linear (in the size of the input) times a polylogarthmic factor. In…
Minimizing empirical risk subject to a set of constraints can be a useful strategy for learning restricted classes of functions, such as monotonic functions, submodular functions, classifiers that guarantee a certain class label for some…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Goppa code is a difficult problem. In this paper, we provide a…
In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with…
Finding sparse vectors is a fundamental problem that arises in several contexts including codes, subspaces, and lattices. In this work, we prove strong inapproximability results for all these variants using a novel approach that even…
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…