Related papers: Computation of Spatial Skyline Points
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
Versions of the following problem appear in several topics such as Gamma Knife radiosurgery, studying objects with the X-ray transform, the 3SUM problem, and the $k$-linear degeneracy testing. Suppose there are $n$ points on a plane whose…
Top-$k$ queries and skylines are the two most common approaches to finding the most interesting entries in a homogeneous multi-dimensional dataset. However, both of these strategies have some shortcomings. Top-$k$ queries are very…
The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…
This paper addresses an inconsistency in various definitions of supported non-dominated points within multi-objective combinatorial problems (MOCO). MOCO problems are known to contain supported and unsupported non-dominated points, with the…
Many web databases are "hidden" behind proprietary search interfaces that enforce the top-$k$ output constraint, i.e., each query returns at most $k$ of all matching tuples, preferentially selected and returned according to a proprietary…
In this paper, we consider a coverage problem for uncertain points in a tree. Let T be a tree containing a set P of n (weighted) demand points, and the location of each demand point P_i\in P is uncertain but is known to appear in one of m_i…
Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
Dominant features of spatial data are connected structures or patterns that emerge from location-based variation and manifest at specific scales or resolutions. To identify dominant features, we propose a sequential application of…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
Let $G=(V,E)$ be a simple graph without isolated vertices. A set $S\subseteq V$ is a paired-dominating set if every vertex in $V-S$ has at least one neighbor in $S$ and the subgraph induced by $S$ contains a perfect matching. In this paper,…
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…
In a simple connected graph $G=(V,E)$, a subset of vertices $S \subseteq V$ is a dominating set if any vertex $v \in V\setminus S$ is adjacent to some vertex $x$ from this subset. A number of real-life problems can be modeled using this…
A dominating set of a graph is a set of vertices such that every vertex not in the set has at least one neighbor in the set. The problem of counting dominating sets is #P-complete for chordal graphs but solvable in polynomial time for its…
Detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
We consider the problem of computing Shapley values for points in the plane, where each point is interpreted as a player, and the value of a coalition is defined by the area of usual geometric objects, such as the convex hull or the minimum…
The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…
Skyline computation aims at looking for the set of tuples that are not worse than any other tuples in all dimensions from a multidimensional database. In this paper, we present SDI (Skyline on Dimension Index), a dimension indexing…