Related papers: ikd-Tree: An Incremental K-D Tree for Robotic Appl…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Path planning in high-dimensional spaces poses significant challenges, particularly in achieving both time efficiency and a fair success rate. To address these issues, we introduce a novel path-planning algorithm, Zonal RL-RRT, that…
The M-tree is a paged, dynamically balanced metric access method that responds gracefully to the insertion of new objects. To date, no algorithm has been published for the corresponding Delete operation. We believe this to be non-trivial…
We present a dynamic data structure that maintains a tree decomposition of width at most $9k+8$ of a dynamic graph with treewidth at most $k$, which is updated by edge insertions and deletions. The amortized update time of our data…
Querying cohesive subgraphs in temporal graphs is essential for understanding the dynamic structure of real-world networks, such as evolving communities in social platforms, shifting hyperlink structures on the Web, and transient…
Dust properties, such as mass and porosity, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, available ways to calculate the…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
We present an algorithm for the Merkle tree traversal problem which combines the efficient space-time trade-off from the fractal Merkle tree [3] and the space efficiency from the improved log space-time Merkle trees traversal [8]. We give…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
The B-tree is a fundamental secondary index structure that is widely used for answering one-dimensional range reporting queries. Given a set of $N$ keys, a range query can be answered in $O(\log_B \nm + \frac{K}{B})$ I/Os, where $B$ is the…
The Web of Data has been gaining momentum and this leads to increasingly publish more semi-structured datasets following the RDF model, based on atomic triple units of subject, predicate, and object. Although it is a simple model,…
The original description of the k-d tree recognized that rebalancing techniques, such as are used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to…
Many modern programming languages are shifting toward a functional style for collection interfaces such as sets, maps, and sequences. Functional interfaces offer many advantages, including being safe for parallelism and providing simple and…
Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
We present a novel method for efficiently searching top-k neighbors for documents represented in high dimensional space of terms based on the cosine similarity. Mostly, documents are stored as bag-of-words tf-idf representation. One of the…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
Edge computing is a distributed computing paradigm that brings computation and data storage closer to the user's geographical location to improve response times and save bandwidth. It also helps to power a variety of applications requiring…
A kernel-independent treecode (KITC) is presented for fast summation of particle interactions. The method employs barycentric Lagrange interpolation at Chebyshev points to approximate well-separated particle-cluster interactions. The KITC…