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Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…
Huffman coding is a widely used method for lossless data compression because it optimally stores data based on how often the characters occur in Huffman trees. An $n$-ary Huffman tree is a connected, cycle-lacking graph where each vertex…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…
We present a novel lossless universal source coding algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other…
For some applications where the speed of decoding and the fault tolerance are important, like in video storing, one of the successful answers is Fix-Free Codes. These codes have been applied in some standards like H.263+ and MPEG-4. The…
For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum…
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…
Large Language Models (LLMs) have advanced Verilog code generation significantly, yet face challenges in data quality, reasoning capabilities, and computational efficiency. This paper presents ReasoningV, a novel model employing a hybrid…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
We utilize machine learning models which are based on recurrent neural networks to optimize dynamical decoupling (DD) sequences. DD is a relatively simple technique for suppressing the errors in quantum memory for certain noise models. In…
FDTD codes, such as Sophie developed at CEA/DAM, no longer take advantage of the processor's increased computing power, especially recently with the raising multicore technology. This is rooted in the fact that low order numerical schemes…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
Huffman compression is a statistical, lossless, data compression algorithm that compresses data by assigning variable length codes to symbols, with the more frequently appearing symbols given shorter codes than the less. This work is a…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Diffusion Large Language Models (DLLMs) have emerged as a new paradigm of language modeling beyond autoregressive next-token prediction. Taking advantage of their inherent modeling foundations, DLLMs have the great potential of efficient…
We consider integer programming problems $\max \{ c^T x : \mathcal{A} x = b, l \leq x \leq u, x \in \mathbb{Z}^{nt}\}$ where $\mathcal{A}$ has a (recursive) block-structure generalizing "$n$-fold integer programs" which recently received…
We report on recent advances in rule-based graph programming, which allow us to match the time complexity of some fundamental imperative graph algorithms. In general, achieving the time complexity of graph algorithms implemented in…
Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and unbounded domains. Existing deep learning approaches, such as…
In this letter, we propose a joint resource allocation algorithm for an OFDM-based multi-user system assisted by an improved Decode-and-Forward (DF) relay. We aim at maximizing the sum rate of the system by jointly optimizing subcarrier…