Related papers: Dynamic Convex Hulls under Window-Sliding Updates
Modeling object dynamics with a neural network is an important problem with numerous applications. Most recent work has been based on graph neural networks. However, physics happens in 3D space, where geometric information potentially plays…
In the field of indoor robotics, accurately localizing and mapping in dynamic environments using point clouds can be a challenging task due to the presence of dynamic points. These dynamic points are often represented by people in indoor…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
In machine learning, concept drift is an evolution of information that invalidates the current data model. It happens when the statistical properties of the input data change over time in unforeseen ways. Concept drift detection is crucial…
We consider the task of performing Jaccard similarity queries over a large collection of items that are dynamically updated according to a streaming input model. An item here is a subset of a large universe $U$ of elements. A well-studied…
We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
For $d\in\mathbb{N}$, let $S$ be a set of points in $\mathbb{R}^d$ in general position. A set $I$ of $k$ points from $S$ is a $k$-island in $S$ if the convex hull $\mathrm{conv}(I)$ of $I$ satisfies $\mathrm{conv}(I) \cap S = I$. A…
An external memory data structure is presented for maintaining a dynamic set of $N$ two-dimensional points under the insertion and deletion of points, and supporting 3-sided range reporting queries and top-$k$ queries, where top-$k$ queries…
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
We present a simple randomized scheme for triangulating a set $P$ of $n$ points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of $P$ move continuously along piecewise algebraic…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which…
In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated…
Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. The aggregations of interest can usually be expressed as binary operators that are associative but not necessarily…
This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
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,…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…