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The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…
We devise an algorithm that approximately computes the number of paths of length $k$ in a given directed graph with $n$ vertices up to a multiplicative error of $1 \pm \varepsilon$. Our algorithm runs in time $\varepsilon^{-2} 4^k(n+m)…
Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is \NP-hard. One way to allow for fewer crossings in practice are…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the complete building envelope. The validation process involves…
In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
3D non-Cartesian trajectories offer several advantages over rectilinear trajectories for rapid volumetric imaging, including improved sampling efficiency and greater robustness to motion, flow, and aliasing artifacts. In this paper, we…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
The exact path length problem is to determine if there is a path of a given fixed cost between two vertices. This paper focuses on the exact path problem for costs $-1,0$ or $+1$ between all pairs of vertices in an edge-weighted digraph.…
Knitted fabrics are two-dimensional-like structures formed by stitching one-dimensional yarn into three-dimensional curves. Plain stitch or stockinette stitch, one of the most fundamental knitting stitches, consists of periodic lattices of…