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OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is…
We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower…
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…
In this work, we present a collection of new results on two fundamental problems in geometric data structures: orthogonal point location and rectangle stabbing. -We give the first linear-space data structure that supports 3-d point location…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class…
Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
Given $n$ pairwise openly disjoint triangles in 3-space, their vertical depth relation may contain cycles. We show that, for any $\varepsilon>0$, the triangles can be cut into $O(n^{3/2+\varepsilon})$ connected semi-algebraic pieces, whose…
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…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
In the problem of semialgebraic range searching, we are to preprocess a set of points in $\mathbb{R}^D$ such that the subset of points inside a semialgebraic region described by $O(1)$ polynomial inequalities of degree $\Delta$ can be found…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
We study the problem of constructing a data structure that can store a two-dimensional polygonal curve $P$, such that for any query segment $\overline{ab}$ one can efficiently compute the Fr\'{e}chet distance between $P$ and…
The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant…
Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the…