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Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with…
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…
We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by…
We present algorithms for topic modeling based on the geometry of cross-document word-frequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novel-words that…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
The dispersion problem has received much attention recently in the distributed computing literature. In this problem, $k\leq n$ agents placed initially arbitrarily on the nodes of an $n$-node, $m$-edge anonymous graph of maximum degree…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…
In the Equal Maximum Flow Problem (EMFP), we aim for a maximum flow where we require the same flow value on all edges in some given subsets of the edge set. In this paper, we study the closely related Almost Equal Maximum Flow Problems…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…
With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…
In this paper, we focus on the problem of identifying semantic factors of variation in large image datasets. By training a convolutional Autoencoder on the image data, we create encodings, which describe each datapoint at a higher level of…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Given a set $V$ of $n$ elements and a distance matrix $[d_{ij}]_{n\times n}$ among elements, the max-mean dispersion problem (MaxMeanDP) consists in selecting a subset $M$ from $V$ such that the mean dispersion (or distance) among the…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
The broadcast throughput in a network is defined as the average number of messages that can be transmitted per unit time from a given source to all other nodes when time goes to infinity. Classical broadcast algorithms treat messages as…