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Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion codes. The other is azinv codes which are known as single balanced…
We present Dv2v, a new dynamic (one-pass) variable-to-variable compressor. Variable-to-variable compression aims at using a modeler that gathers variable-length input symbols and a variable-length statistical coder that assigns shorter…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the…
Quantum low-density parity-check (QLDPC) codes have been proven to achieve higher minimum distances at higher code rates than surface codes. However, this family of codes imposes stringent latency requirements and poor performance under…
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not…
In this paper, we consider tree decompositions, branch decompositions, and clique decompositions. We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of…
Recent developments in storage -- especially in the area of resistive random access memory (ReRAM) -- are attempting to scale the storage density by regarding the information data as two-dimensional (2D), instead of one-dimensional (1D).…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
In-loop filtering (ILF) is a key technology for removing the artifacts in image/video coding standards. Recently, neural network-based in-loop filtering methods achieve remarkable coding gains beyond the capability of advanced video coding…
Priority encoders are typically considered expensive hardware components in terms of complexity, especially at high bit precisions or input lengths (e.g., above 512 bits). However, if the complexity can be reduced, priority encoders can…
The present work attempts to integrate the independent efforts in the fast N-body community to create the fastest N-body library for many-core and heterogenous architectures. Focus is placed on low accuracy optimizations, in response to the…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
In Wireless Multi-hop Networks (WMhNs), routing protocols with energy efficient and delay reduction techniques are needed to fulfill users demands. In this paper, we present Linear Programming models (LP_models) to assess and enhance…
The stochastic finite volume method (SFV method) is a high-order accurate method for uncertainty quantification (UQ) in hyperbolic conservation laws. However, the computational cost of SFV method increases for high-dimensional stochastic…