Related papers: On the Approximation Ratio of Ordered Parsings
A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End…
A $t$-spanner of a graph $G$ is a subgraph $H$ in which all distances are preserved up to a multiplicative $t$ factor. A classical result of Alth\"ofer et al. is that for every integer $k$ and every graph $G$, there is a $(2k-1)$-spanner of…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Compression techniques that support fast random access are a core component of any information system. Current state-of-the-art methods group documents into fixed-sized blocks and compress each block with a general-purpose adaptive…
We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently…
Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…
Consider a channel with a given input distribution. Our aim is to degrade it to a channel with at most L output letters. One such degradation method is the so called "greedy-merge" algorithm. We derive an upper bound on the reduction in…
In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…
At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…
We present a new algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length $N$ in linear time, that utilizes only $N\log N + O(1)$ bits of working space, i.e., a single integer array, for constant size integer…
Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove…
Random reshuffling, which randomly permutes the dataset each epoch, is widely adopted in model training because it yields faster convergence than with-replacement sampling. Recent studies indicate greedily chosen data orderings can further…
Set Cover is a classic NP-hard problem; as shown by Slav\'{i}k (1997) the greedy algorithm gives an approximation ratio of $\ln n - \ln \ln n + \Theta(1)$. A series of works by Lund \& Yannakakis (1994), Feige (1998), Moshkovitz (2015) have…
We examine the minimum entropy coupling problem, where one must find the minimum entropy variable that has a given set of distributions $S = \{p_1, \dots, p_m \}$ as its marginals. Although this problem is NP-Hard, previous works have…
The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes $z$ and $r$ closely related to the amount of text…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts. We adapt the information-theoretic perspective of \cite{RvR16} to the contextual setting…
Zipf's law of abbreviation, the tendency of more frequent words to be shorter, is one of the most solid candidates for a linguistic universal, in the sense that it has the potential for being exceptionless or with a number of exceptions…
In this work, we study the limits of compressed data structures, i.e., structures that support various queries on an input text $T\in\Sigma^n$ using space proportional to the size of $T$ in compressed form. Nearly all fundamental queries…