Related papers: A Light-Based Device for Solving the Hamiltonian P…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…
For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
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…
The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given graph, and of the existence of a truth assignment satisfying a given Boolean formula $C$, are well-known {\it NP}-complete problems. Here we…
In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…
Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…
A configuration of light pulses is generated, together with emitters and receptors, that allows computing. The computing is extraordinarily high in number of flops per second, exceeding the capability of a quantum computer for a given size…
We develop a new algebraic technique that solves the following problem: Given a black box that contains an arithmetic circuit $f$ over a field of characteristic $2$ of degree~$d$. Decide whether $f$, expressed as an equivalent multivariate…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
Illumination effects cause problems for many computer vision algorithms. We present a user-friendly interactive system for robust illumination-invariant image generation. Compared with the previous automated illumination-invariant image…
The most efficient known method for solving certain computational problems is to construct an iterated map whose fixed points are by design the problem's solution. Although the origins of this idea go back at least to Newton, the clearest…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
An $r$-simple $k$-path is a {path} in the graph of length $k$ that passes through each vertex at most $r$ times. The $r$-SIMPLE $k$-PATH problem, given a graph $G$ as input, asks whether there exists an $r$-simple $k$-path in $G$. We first…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
We proposed an algorithm for solving Hamilton-Jacobi equation associated to an optimal trajectory problem for a vehicle moving inside the pre-specified domain with the speed depending upon the direction of the motion and current position of…
Consider the random graph process where we start with an empty graph on n vertices, and at time t, are given an edge e_t chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…