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We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…
We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared…
We introduce a new notion of acyclicity representation in labeled graphs, and present three applications thereof. Our main result is an algorithm that, given a graph $G$ and a $k$-clique expression of $G$, in time $O(6^kn^c)$ counts modulo…
We study perfect error-correcting codes in $\mathbb{Z}^n$ for the symmetric limited-magnitude error channel, where at most $e$ coordinates of an integer vector may be altered by a value whose magnitude is at most $s$. Geometrically, such…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
In this paper, we propose the first continuous optimization algorithms that achieve a constant factor approximation guarantee for the problem of monotone continuous submodular maximization subject to a linear constraint. We first prove that…
Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…