Related papers: An optical solution for the set splitting problem
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…
Given a set $P$ of $n$ points and a set $S$ of $n$ weighted disks in the plane, the disk coverage problem is to compute a subset of disks of smallest total weight such that the union of the disks in the subset covers all points of $P$. The…
Several concept learning problems can be regarded as special cases of half-space separation in abstract closure systems over finite ground sets. For the typical scenario that the closure system is implicitly given via a closure operator, we…
Quantification of microscopy time-series of in vitro reconstituted motor driven microtubule (MT) transport in 'gliding assays' is typically performed using computational object tracking tools. However, these are limited to non-intersecting…
In the Maximum Independent Set of Objects problem, we are given an $n$-vertex planar graph $G$ and a family $\mathcal{D}$ of $N$ objects, where each object is a connected subgraph of $G$. The task is to find a subfamily $\mathcal{F}…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…
Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer…
We consider the problem of decomposing a given (di)graph into paths of length 2 with the additional restriction that no two such paths may have more than one vertex in common. We establish its NP-hardness by a reduction from 3-SAT,…
Split-pulse x-ray photon correlation spectroscopy has been proposed as one of the unique capabilities made possible with the x-ray free electron lasers. It enables characterization of atomic scale structural dynamics that dictates the…
The Matching Cut problem is to decide if the vertex set of a connected graph can be partitioned into two non-empty sets $B$ and $R$ such that the edges between $B$ and $R$ form a matching, that is, every vertex in $B$ has at most one…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
We show that the Temporal Graph Exploration Problem is NP-complete, even when the underlying graph has pathwidth 2 and at each time step, the current graph is connected.
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…