In this review paper, we present a development of parts of rate-distortion theory and pattern-matching algorithms for lossy data compression, centered around a lossy version of the asymptotic equipartition property (AEP). This treatment closely parallels the corresponding development in lossless compression, a point of view that was advanced in an important paper of Wyner and Ziv in 1989. In th...

Binary unlabeled ordered trees (further called binary trees) were studied at least since Euler, who enumerated them. The number of such trees with n nodes is now known as the Catalan number. Over the years various interesting questions about the statistics of such trees were investigated (e.g., height and path length distributions for a randomly selected tree). Binary trees find an abundance of...

Software developers may write a number of similar source code fragments including the same mistake in software products. To remove such faulty fragments, inspect clones if they found bug their code. While various clone detection methods have been proposed to identify either blocks or functions, those tools do not always fit inspection task because fragment be much smaller than blocks, e.g. sing...

This paper describes the STAC resource, a corpus of multi-party chats annotated for discourse structure in the style of SDRT (Asher and Lascarides, 2003; Lascarides and Asher, 2009). The main goal of the STAC project is to study the discourse structure of multi-party dialogues in order to understand the linguistic strategies adopted by interlocutors to achieve their conversational goals, especi...

In this paper, we generalize the permutation entropy (PE) measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other random...

For decades the Lempel-Ziv (LZ77) factorization has been a cornerstone of data compression and string processing algorithms, and uses for it are still being uncovered. For example, LZ77 is central to several recent text indexing data structures designed to search highly repetitive collections. However, in many applications computation of the factorization remains a bottleneck in practice. In th...

Using the Lempel-Ziv-78 compression algorithm to compress a string yields a dictionary of substrings, i.e. an edge-labelled tree with an order-compatible enumeration, here called an LZ-trie. Queries about strings translate to queries about LZ-tries and hence can in principle be answered without decompression. We compare notions of automata accepting LZ-tries and consider the relation between ac...

Relative Lempel-Ziv (RLZ) is a popular algorithm for compressing databases of genomes from individuals of the same species when fast random access is desired. With Kuruppu et al.’s (SPIRE 2010) original implementation, a reference genome is selected and then the other genomes are greedily parsed into phrases exactly matching substrings of the reference. Deorowicz and Grabowski (Bioinformatics, ...