Related papers: Multidimensional segment trees can do range update…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
We introduce dynamic smooth (a.k.a. balanced) compressed quadtrees with worst-case constant time updates in constant dimensions. We distinguish two versions of the problem. First, we show that quadtrees as a space-division data structure…
Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…
We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given $n$ points and $n$ lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…
Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
The advent of parameter-efficient fine-tuning methods has significantly reduced the computational burden of adapting large-scale pretrained models to diverse downstream tasks. However, existing approaches often struggle to achieve robust…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
An associative memory (AM) enables cue-response recall, and it has recently been recognized as a key mechanism underlying modern neural architectures such as Transformers. In this work, we introduce the concept of distributed dynamic…
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…
LiDAR sensor is essential to the perception system in autonomous vehicles and intelligent robots. To fulfill the real-time requirements in real-world applications, it is necessary to efficiently segment the LiDAR scans. Most of previous…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…
Motion Planning is necessary for robots to complete different tasks. Rapidly-exploring Random Tree (RRT) and its variants have been widely used in robot motion planning due to their fast search in state space. However, they perform not well…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
We consider the following problem: given an unsorted array of $n$ elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space…