Related papers: Dynamic Convex Hulls under Window-Sliding Updates

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…

We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…

We revisit the S-procedure for general functions with "geometrical glasses". We thus delineate a necessary condition, and almost a sufficient condition, to have the S-procedure valid. Everything is expressed in terms of convexity of…

We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii)…

Let $S \subseteq \mathbb{R}^2$ be a set of $n$ \emph{sites} in the plane, so that every site $s \in S$ has an \emph{associated radius} $r_s > 0$. Let $D(S)$ be the \emph{disk intersection graph} defined by $S$, i.e., the graph with vertex…

Truss was proposed to study social network data represented by graphs. A k-truss of a graph is a cohesive subgraph, in which each edge is contained in at least k-2 triangles within the subgraph. While truss has been demonstrated as superior…

How can one quickly answer the most and top popular objects at any time, given a large log stream in a system of billions of users? It is equivalent to find the mode and top-frequent elements in a dynamic array corresponding to the log…

We present an algorithm to perform fuel-optimal stationkeeping for spacecraft in unstable halo orbits with additional constraints to ensure safety in the event of a control failure. We formulate a convex trajectory-optimization problem to…

While traditional data-management systems focus on evaluating single, ad-hoc queries over static data sets in a centralized setting, several emerging applications require (possibly, continuous) answers to queries on dynamic data that is…

In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed a compact topological space for the combinatorics of "A regular pentagonal tiling of the plane", which we…

Half-space depth (also called Tukey depth or location depth) is one of the most commonly studied data depth measures because it possesses many desirable properties for data depth functions. The data depth contours bound regions of…

We revisit the complexity of the classical Interval Scheduling in the dynamic setting. In this problem, the goal is to maintain a set of intervals under insertions and deletions and report the size of the maximum size subset of pairwise…

In this paper we study the problem of fully dynamic maximal matching with lookahead. In a fully dynamic $n$-vertex graph setting, we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph,…

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…

A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…

We devise the following dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and/or deletions to the simple polygon. * A fully-dynamic algorithm for maintaining…

Computationally efficient and automated generation of convex hulls is desirable for high throughput materials discovery of thermodynamically stable multi-species crystal structures. A convex hull genetic algorithm is proposed that uses…

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…

We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…

In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…