Related papers: Multidimensional segment trees can do range update…
In this paper, we consider the problems for covering multiple intervals on a line. Given a set $B$ of $m$ line segments (called "barriers") on a horizontal line $L$ and another set $S$ of $n$ horizontal line segments of the same length in…
Multicast data transfers occur in many distributed systems and applications (e.g. IPTV, Grids, content delivery networks). Because of this, efficient multicast data distribution optimization techniques are required. In the first part 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…
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…
Maintaining spatial data (points in two or three dimensions) is crucial and has a wide range of applications, such as graphics, GIS, and robotics. To handle spatial data, many data structures, called spatial indexes, have been proposed,…
We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…
In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…
Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…
The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…
In this paper, we present fixed-parameter tractability algorithms for both the undirected and directed versions of the Spanning Tree Isomorphism Problem, parameterized by the size $k$ of a redundant set. A redundant set is a collection of…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
In open-world scenarios, where both novel classes and domains may exist, an ideal segmentation model should detect anomaly classes for safety and generalize to new domains. However, existing methods often struggle to distinguish between…
We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
Scaling regression to large datasets is a common problem in many application areas. We propose a two step approach to scaling regression to large datasets. Using a regression tree (CART) to segment the large dataset constitutes the first…
In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families…