Related papers: FunSeqSet: Towards a Purely Functional Data Struct…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set $S$ of $w$-bit numbers under insertions, deletions, and predecessor queries (return the largest element in $S$ no larger…
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…
The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only…
A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
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…
Reiter's HS-Tree is one of the most popular diagnostic search algorithms due to its desirable properties and general applicability. In sequential diagnosis, where the addressed diagnosis problem is subject to successive change through the…
Classic dynamic data structure problems maintain a data structure subject to a sequence S of updates and they answer queries using the latest version of the data structure, i.e., the data structure after processing the whole sequence. To…
Decision Trees have remained a popular machine learning method for tabular datasets, mainly due to their interpretability. However, they lack the expressiveness needed to handle highly nonlinear or unstructured datasets. Motivated by recent…
We consider the problem of designing a succinct data structure for {\it path graphs} (which are a proper subclass of chordal graphs and a proper superclass of interval graphs) on $n$ vertices while supporting degree, adjacency, and…
Succinct trees, such as wavelet trees and those based on, for instance, range Min-Max trees (RMMTs), are a family of practical data structures that store information close to their information-theoretic space lower bound. These structures…
Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are…
Given a system that does not work as expected, Sequential Diagnosis (SD) aims at suggesting a series of system measurements to isolate the true explanation for the system's misbehavior from a potentially exponential set of possible…
Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data…
Program comprehension is a fundamental task in software development and maintenance processes. Software developers often need to understand a large amount of existing code before they can develop new features or fix bugs in existing…
We show how to construct a dynamic ordered dictionary, supporting insert/delete/rank/select on a set of $n$ elements from a universe of size $U$, that achieves the optimal amortized expected time complexity of $O(1 + \log n / \log \log U)$,…
The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…
Most existing recursive neural network (RvNN) architectures utilize only the structure of parse trees, ignoring syntactic tags which are provided as by-products of parsing. We present a novel RvNN architecture that can provide dynamic…