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In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
In distributed optimization and machine learning, multiple nodes coordinate to solve large problems. To do this, the nodes need to compress important algorithm information to bits so that it can be communicated over a digital channel. The…
We address the problem of delay in an arithmetic coding system. Due to the nature of the arithmetic coding process, source sequences causing arbitrarily large encoding or decoding delays exist. This phenomena raises the question of just how…
Coded caching is a technique that leverages locally cached contents at the end users to reduce the network's peak-time communication load. Coded caching has been shown to achieve significant performance gains with a centralized placement…
Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…
In this paper we present a simple linear-time algorithm constructing a context-free grammar of size O(g log(N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string.…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between…
Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
We show that the edit distance between two run-length encoded strings of compressed lengths $m$ and $n$ respectively, can be computed in $\mathcal{O}(mn\log(mn))$ time. This improves the previous record by a factor of…
We propose an approach to lossy source coding, utilizing ideas from Gibbs sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is to sample a reconstruction sequence from a Boltzmann distribution associated with an…
In this paper, we consider controlled linear dynamical systems in which the controller has only access to a compressed version of the system state. The technical problem we investigate is that of allocating compression resources over time…
In pliable index coding, we consider a server with $m$ messages and $n$ clients where each client has as side information a subset of the messages. We seek to minimize the number of broadcast transmissions, so that each client can recover…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
Recent advancements in large language models (LLMs) have enabled their successful application to a broad range of tasks. However, in information-intensive tasks, the prompt length can grow fast, leading to increased computational…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…
We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we…
We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…