Related papers: Another virtue of wavelet forests?
A weighted random survival forest is presented in the paper. It can be regarded as a modification of the random forest improving its performance. The main idea underlying the proposed model is to replace the standard procedure of averaging…
We investigate properties of the bijective Burrows-Wheeler transform (BBWT). We show that for any string $w$, a bidirectional macro scheme of size $O(r_B)$ can be induced from the BBWT of $w$, where $r_B$ is the number of maximal character…
We study Witten's open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
Splay trees (Sleator and Tarjan) satisfy the so-called access lemma. Many of the nice properties of splay trees follow from it. What makes self-adjusting binary search trees (BSTs) satisfy the access lemma? After each access, self-adjusting…
We show how to merge two run-length compressed Burrows-Wheeler Transforms (RLBWTs) into a run-length compressed extended Burrows-Wheeler Transform (eBWT) in $O (r)$ space and $O ((r + L) \log (m + n))$ time, where $m$ and $n$ are the…
Given a string $T$, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with $e_T$ arcs, taking overall $O(e_T+e_{{\overline{T}}})$ words of space, where ${\overline{T}}$ is the reverse…
The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalization to weighted trees, a.k.a. the weighted ancestor problem, has been extensively…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…
Parameterized strings are a generalization of strings in that their characters are drawn from two different alphabets, where one is considered to be the alphabet of static characters and the other to be the alphabet of parameter characters.…
It is shown how wavelets may be used to analyse the absorption properties of the Lya forest. The Discrete Wavelet Transform of a QSO spectrum is used to decompose the light fluctuations that comprise the forest into orthogonal wavelets. It…
Indexing of very large collections of strings such as those produced by the widespread sequencing technologies, heavily relies on multi-string generalizations of the Burrows-Wheeler Transform (BWT), and for this problem various in-memory…
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…
We present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees. It takes O(n^{1.5} log n) time for trees with unbounded degrees, matching the best known time complexity for the rooted case. Our…
Constructing the Burrows-Wheeler transform (BWT) for long strings poses significant challenges regarding construction time and memory usage. We use a prefix of the suffix array to partition a long string into shorter substrings, thereby…
Wavelet transforms, a powerful mathematical tool, have been widely used in different domains, including Signal and Image processing, to unravel intricate patterns, enhance data representation, and extract meaningful features from data.…
Binary relations are commonly used in Computer Science for modeling data. In addition to classical representations using matrices or lists, some compressed data structures have recently been proposed to represent binary relations in compact…
We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of…
We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…
We propose a $O(\log k \log n)$-competitive randomized algorithm for online node-weighted Steiner forest. This is essentially optimal and significantly improves over the previous bound of $O(\log^2 k \log n)$ by Hajiaghayi et al. [2017]. In…