Related papers: Near Optimal Line Segment Weak Visibility Queries …
Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…
We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width…
Weakly supervised learning of object detection is an important problem in image understanding that still does not have a satisfactory solution. In this paper, we address this problem by exploiting the power of deep convolutional neural…
We study the minimum vertex cover problem in the following stochastic setting. Let $G$ be an arbitrary given graph, $p \in (0, 1]$ a parameter of the problem, and let $G_p$ be a random subgraph that includes each edge of $G$ independently…
The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an $n$-point dataset $X$ lying in a metric space $\mathcal{M}$, so that given a query point $q \in \mathcal{M}$, one can quickly return a point of…
In this paper, we propose a new approach to applying point-level annotations for weakly-supervised panoptic segmentation. Instead of the dense pixel-level labels used by fully supervised methods, point-level labels only provide a single…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {\em…
The geodesic Voronoi diagram of m point sites inside a simple polygon of n vertices is a subdivision of the polygon into m cells, one to each site, such that all points in a cell share the same nearest site under the geodesic distance. The…
A Variable Parameter (VP) analysis, that we introduce here, aims to give a precise algorithm time complexity expression in which an exponent appears solely in terms of a variable parameter. A variable parameter is the number of objects with…
We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
Weakly supervised semantic segmentation is a challenging task as it only takes image-level information as supervision for training but produces pixel-level predictions for testing. To address such a challenging task, most recent…
We consider the watchman route problem for a $k$-transmitter watchman: standing at point $p$ in a polygon $P$, the watchman can see $q\in P$ if $\overline{pq}$ intersects $P$'s boundary at most $k$ times -- $q$ is $k$-visible to $p$.…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
We study the problem of computing a shortest tour that visits a sequence of $k$ polygons $P_1,\dots, P_k$ with a total number of $n$ vertices. A tour is an oriented curve such that there exist points $p_i\in P_i$ for all $i$ where $p_i$…
We present an accurate and rapid solution of Poisson's equation for space-filling, arbitrarily- shaped, convex Voronoi polyhedra (VP); the method is O(NVP), where NVP is the number of distinct VP representing the system. In effect, we…
We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…