Related papers: Maintaining the cycle structure of dynamic permuta…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
A merge tree is a fundamental topological structure used to capture the sub-level set (and similarly, super-level set) topology in scalar data analysis. The interleaving distance is a theoretically sound, stable metric for comparing merge…
While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…
We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$,…
Efficient text indexing data structures have enabled large-scale genomic sequence analysis and are used to help solve problems ranging from assembly to read mapping. However, these data structures typically assume that the underlying…
We propose a data structure that stores, in a compressed way, object trajectories, which at the same time, allow to efficiently response queries without the need to decompress the data. We use a data structure, called $k^{2}$-tree, to store…
Permutation $\sigma$ appears in permutation $\pi$ if there exists a subsequence of $\pi$ that is order-isomorphic to $\sigma$. The natural question is to check if $\sigma$ appears in $\pi$, and if so count the number of occurrences. We know…
We show how a collection of Euler-tour trees for a forest on $n$ vertices can be stored in $2 n + o (n)$ bits such that simple queries take constant time, more complex queries take logarithmic time and updates take polylogarithmic amortized…
A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in "as few moves as possible", using a given set of allowed operations, or…
This article introduces the Event based Prediction Suffix Tree (EPST), a biologically inspired, event-based prediction algorithm. The EPST learns a model online based on the statistics of an event based input and can make predictions over…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Let $T$ be a tree on $n$ vertices. We can regard the edges of $T$ as transpositions of the vertex set; their product (in any order) is a cyclic permutation. All possible cyclic permutations arise (each exactly once) if and only if the tree…
Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
Crystal-structure match (CSM), the atom-to-atom correspondence between two crystalline phases, is used extensively to describe solid-solid phase transition (SSPT) mechanisms. However, existing computational methods cannot account for all…
Tree-based models are increasingly popular due to their ability to identify complex relationships that are beyond the scope of parametric models. Survival tree methods adapt these models to allow for the analysis of censored outcomes, which…
Open Answer Set Programming (OASP) is an attractive framework for integrating ontologies and rules. In general OASP is undecidable. In previous work we provided a tableau-based algorithm for satisfiability checking w.r.t. forest logic…
We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of…
Prediction suffix trees (PST) provide an effective tool for sequence modelling and prediction. Current prediction techniques for PSTs rely on exact matching between the suffix of the current sequence and the previously observed sequence. We…