相关论文: A Light-Based Device for Solving the Hamiltonian P…

In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes…

We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…

We describe here an optical device, based on time-delays, for solving the set splitting problem which is well-known NP-complete problem. The device has a graph-like structure and the light is traversing it from a start node to a destination…

A quantum computing scheme that uses a single photon and multiple-slit gratings is suggested for the Hamiltonian path problem on a simple graph G of N vertices. The photon is input to an N-slit grating followed by an N x N matrix of…

A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then…

We study the Hamiltonian path problem in C-shaped grid graphs, and present the necessary and sufficient conditions for the existence of a Hamiltonian path between two given vertices in these graphs. We also give a linear-time algorithm for…

Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable…

We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus…

The Hamiltonian Path Problem is formulated as a continuous minimization problem on conductances assigned to an Ohmic network associated with the given graph. The objective function is a sum of two penalty terms that collectively enforce a…

In this paper we present a technique that improves rendering performance for real-time scenes with ray traced lighting in the presence of dynamic lights and objects. In particular we verify photon paths from the previous frame against…

Unidirectional light transport in one-dimensional nanomaterials at the quantum level is a crucial goal to achieve for upcoming computational devices. We here employ a full-quantum mechanical approach based on master equation to describe…

In design of optical systems based on LED (Light emitting diode) technology, a crucial task is to handle the unstructured data describing properties of optical elements in standard formats. This leads to the problem of data fitting within…

In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the…

An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying graph. In this note we demonstrate that, for difficult…

In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph G=(V,E) and a subset T of V of so-called terminal vertices, the problem is to find a minimum number of vertex-disjoint simple…

In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…

We address a fundamental question of quantum optics: Can a beam of light mediate coherent Hamiltonian interactions between two distant quantum systems? This is an intriguing question whose answer is not a priori clear, since the light…

A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…