Geometric Routing Research Articles

Развитие узловой терминально-складской инфраструктуры: модификация методов исследования и прогнозы

Purpose: Development of an economic-geographical method in finding the optimal locations of logistics freight distribution centers in the territory under consideration and its application to the construction of a geometric routing model for the distribution of cargo flows. Methods: The economic-geographic method of dividing the ‘areas of influence’ of transportation process participants. Statistical methods for processing empirical data. Monte Carlo method. Results: A geometric routing model has been developed for the distribution of cargo flows generated by participants in the transportation process competing in a territorial oligopolistic freight transportation market. Practical significance: The constructed model allows for a proper assessment of the existing transportation network to identify the ‘areas of influence’ of transportation process participants, considered as oligopolists in the regional freight transportation market.

Geometric routing model as a new approach in mathematical modeling of wagon flows rational distribution

In the ongoing transport and logistics researches, a coefficient of railway line non-straightness is introduced, by means of which, for the considered loading stations, the specifics of the location of the railway network in a given region are taken into account. The use of this coefficient makes it possible to increase the efficiency and practical expediency of applying the method of economic and geographical delimitation of the «influence areas» of the loading stations. As a result, it is possible to construct a mathematically substantiated geometric routing model of the territorial oligopolistic market for freight transportation formed by the considered loading stations. As an effective tool in the research process, a system of analytical calculations is used.

Multi-shuttle crane scheduling in automated storage and retrieval systems

We study a shared-storage automated storage and retrieval system (AS/RS) with one crane capable of carrying multiple unit loads. In a shared-storage system, items to be stored are not pre-assigned to dedicated shelf spaces. Therefore, given a set of storage and retrieval requests, the crane scheduling problem consists of deciding which requests are processed together in the same tour, determining the sequence in which the requests are processed, and assigning each storage request to an available slot on the shelf. We reformulate the problem as a special type of capacitated vehicle routing problem, which we use to close some open questions regarding the time complexity of related geometric routing problems. The reformulation allows us to tap into the rich and mature vehicle routing toolbox from the literature to propose a new exact solution approach. We show that this method is capable of solving large instances to optimality, outperforming previous methods from the literature. We use our new approach to derive multiple insights. Specifically, we show that system throughput can be predicted from the capacity of the crane via a simple rule. We also determine the optimal shape of a shelf and investigate the value of having knowledge of multiple requests when planning the crane schedule. Finally, we demonstrate that our approach can easily be extended to solve a whole family of multi-shuttle crane scheduling problems.

Fast high-fidelity geometric quantum control with quantum brachistochrones

We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over $99.2%$ on the spin state of the nitrogen-vacancy center are realized with average durations shortened by $21.5%$ compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds $96.5%$ on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.

Geometrical link aware geocast routing for energy balancing in wireless sensor networks

Efficient use of sensor’s available energy is one of prime issues to be solved for wireless sensor network (WSN) alive and functional as long as possible. Appropriate relay sensor selection to forward packets to sink have been recommended as an encouraging solution to overcome the aforesaid challenge in WSN. However, the literature lacks towards link quality-oriented relay sensor selection to equalize energy consumption for longevity of the network. In this context, this paper proposes a geometrical link aware geocast routing for energy balancing (GeoLE) in WSN. Each time, GeoLE selects different sets of relay sensors based on a proposed predicted relay selection (PRS) metric to fairy equalize energy consumption of the sensors. The PRS metric is designed based on expected transmission count, forward progress, delay and residual energy. It is evident from simulation results that the proposed GeoLE approach outperforms the state of the art routing approaches in the terms of network lifetime, packet delivery ratio, average energy consumption, and energy balance factor.

Geometric greedy router in Quantum-dot Cellular Automata

This paper describes the first Geometric Greedy Router using the Quantum-dot Cellular Automata (QCA) paradigm based on a spanning-tree of the network. This type of router is a revolution for communications as it works without IP address lookups. It uses only local information and can be employed in numerous communication devices. When combined with QCA technology, a proper alternative to replace conventional circuits (CMOS), the desired results can be achieved on a nanometric scale and with very low-power consumption. In a top-down approach, we first describe the main components of the router and later present their QCA architecture. We implemented the router in the QCADesigner simulator to validate and demonstrate the functionality of the design, testing with many examples. With both technologies, geometric routing and QCA, combined and being substitutes of current paradigms, this study can be another step towards new types of digital nanocommunications systems and devices.

Local Routing in Convex Subdivisions

In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required [Formula: see text] state bits to be stored and passed with the message. We present the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and, when the algorithm has knowledge of the incoming port (the preceding node on the route), the first stateless local geometric routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions). We also show that [Formula: see text] state bits are necessary in planar subdivisions in which faces may have three or more reflex vertices.

A Review on Routing in Internet of Things

Recently, internet of things has drawn attention among the academicians, governments and engineers from various sectors. There are many critical issues in IoT such as security, scalability, big data analytics. Availability, interoperability, performance, mobility. This paper focus on providing optimal routing among the various networking environment such as wired wireless and sensors in the IoT. In this paper the major research issues involved in the existing routing protocols to meet the requirements of internet of things are reviewed the major issues involved in the design of a routing protocol and the different classification of routing protocols are studied. The major challenges of the internet of things, must address the problem of dynamic topology, scalability, mobility of nodes and limited bandwidth. The review covers different kinds of routing protocols such as reactive, proactive, hybrid, location aware, hybrid, multicast, multipath, Geocast, power aware and hierarchical existing geometric routing protocols have been sensibly studied which involves discussion on routing techniques, the advantages and disadvantages of the existing work area analysed in order to help the future researchers. The analysis of existing routing protocols is carried out based on shortest path, least transmission time. Finally, a research open challenge in routing which needs to be addressed by the research and academic community are discussed.

String Method for Protein-Protein Binding Free-Energy Calculations.

A powerful computational strategy to determine the equilibrium association constant of two macromolecules with explicit-solvent molecular dynamics (MD) simulations is the "geometric route", which considers the reversible physical separation of the bound complex in solution. Nonetheless, multiple challenges remain to render this type of methodology reliable and computationally efficient in practice. In particular, in one, formulation of the geometric route relies on the potential of mean force (PMF) for physically separating the two binding partners restrained along a straight axis, which must be selected prior to the calculation. However, practical applications indicate that the calculation of the separation PMF along the predefined rectilinear pathway may be suboptimal and slowly convergent. Recognizing that a rectilinear straight separation pathway is generally not representative of how the protein complex physically separates in solution, we put forth a novel theoretical framework for binding free-energy calculations, leaning on the optimal curvilinear minimum free-energy path (MFEP) determined from the string method. The proposed formalism is validated by comparing the results obtained using both rectilinear and curvilinear pathways for a prototypical host-guest complex formed by cucurbit[7]uril (CB[7]) binding benzene, and for the barnase-barstar protein complex. On the basis of multi-microsecond MD calculations, we find that the calculations following the traditional rectilinear pathway and the string-based curvilinear pathway agree quantitatively, but convergence is faster with the latter.

Secure Data Sharing Framework via Hierarchical Greedy Embedding in Darknets

Geometric routing, which combines greedy embedding and greedy forwarding, is a promising approach for efficient data sharing in darknets. However, the security of data sharing using geometric routing in darknets is still an issue that has not been fully studied. In this paper, we propose a Secure Data Sharing framework (SeDS) for future darknets via hierarchical greedy embedding. SeDS adopts a hierarchical topology and uses a set of secure nodes to protect the whole topology. To support geometric routing in the hierarchical topology, a two-level bit-string prefix embedding approach (Prefix-T) is first proposed, and then a greedy forwarding strategy and a data mapping approach are combined with Prefix-T for data sharing. SeDS guarantees that the publication or request of a data item can always pass through the corresponding secure node, such that security strategies can be performed. The experimental results show that SeDS provides scalable and efficient end-to-end communication and data sharing.

Lightweight Anonymous Geometric Routing for Internet of Things

Mobile service computing relies on efficient and secure data transfer. Geometric routing, which guarantees scalability, efficiency, and mobility, is a promising routing scheme for mobile services in the resource-constrained Internet of Things (IoT). However, the private data transmitted by geometric routing may be eavesdropped by the malicious node and the privacy-preserving becomes one of the important issues for the mobile service in IoTs. Due to the resource constrains, approaches using encryption or hashing are not suitable for geometric routing. In this paper, we propose a lightweight anonymous geometric routing (LAGER) to protect the node-related private data. Instead of using the encryption or hashing approach, LAGER adopts a coordinate confusion mechanism which provides each node an anonymous coordinate of virtual node, such that the private data is decoupled from the node coordinate. The malicious node cannot determine which node the data belongs to even if it obtains the private data. To support the data transmission with anonymous coordinates, LAGER adopts a hybrid routing scheme by combining the greedy routing and a source routing. The experiment results show that LAGER provides effective anonymity with acceptable costs of scalability and efficiency.

Estimation of geometric route distance from its topological distance: application to narrow road networks in Tokyo

The structure of road networks has been investigated in accordance with the development of GIScience. By classifying road networks into wide and narrow ones, we can define the route as the path from the route’s origin (also called the root) on a wide road network to a narrow road segment which consists of the sequence of narrow road segments arranged by ascending order of the number of steps of adjacency to its root. The length of the route can be defined with the following geometric and topological terms: the route distance, measuring the length along the route and the depth, counting the number of road segments on the route. The depth plays the important role of being a substitute for the route distance in modelling road networks as a planar graph. Since road networks clearly exhibit irregular patterns and road segment lengths are non-uniform, it is considered appropriate to adopt a stochastic approach rather than a deterministic one to analyse the route distance. However, the relationship between the route distance and its depth has not been sufficiently investigated stochastically. Therefore, the research question is how can we estimate the route distance from its depth? Based on an empirical study in the Tokyo metropolitan region, it was found that (1) the statistical distribution of the route distance can be formulated as an Erlang distribution whose parameters are its depth and the inverse of the mean length of narrow road segments, and (2) this length is constant and close to 40 m. Therefore, we can estimate the route distance from only one parameter, the depth. Also, as a practical application, accessibility to the kth depth link in terms of firefighting was evaluated because the maximum length of the extension of fire hoses is approximately 200 m. It was found that (1) even if k ≤ 5, the probability that the route distance to the kth depth link is equal to or longer than 200 m ranges from 0 to 0.45; and (2) if k ≥ 8, the probability is approximately 1. These indicate the limitation of the deterministic approach because, on the basis of complete grid patterns (with intervals of 40 m between intersections), k = 5 corresponds to a distance of 200 m from wide road networks and the route to the 5th depth link can be covered with fire hoses. Moreover, it was found that the connectivity of wide road networks is higher than that of narrow ones in terms of the smaller ratio of cul-de-sacs and the larger ratio of four-way intersections. These answers contribute substantially not only to constructing a science of cities that provides a simple model and specifies the most important parameter, but also to our understanding of the structure of narrow road networks within several hundred metres of wide road networks.

Ehrenfest Statistical Dynamics in Chemistry: Study of Decoherence Effects.

In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to nonadiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.

On Planar Greedy Drawings of 3-Connected Planar Graphs

A graph drawing is greedy if, for every ordered pair of vertices (x, y), there is a path from x to y such that the Euclidean distance to y decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing scheme, in which any node that has to send a packet to a destination “greedily” forwards the packet to any neighbor that is closer to the destination than itself, according to the Euclidean distance in the drawing. In a greedy drawing such a neighbor always exists and hence this routing scheme is guaranteed to succeed. In 2004 Papadimitriou and Ratajczak stated two conjectures related to greedy drawings. The greedy embedding conjecture states that every 3-connected planar graph admits a greedy drawing. The convex greedy embedding conjecture asserts that every 3-connected planar graph admits a planar greedy drawing in which the faces are delimited by convex polygons. In 2008 the greedy embedding conjecture was settled in the positive by Leighton and Moitra. In this paper we prove that every 3-connected planar graph admits a planar greedy drawing. Apart from being a strengthening of Leighton and Moitra’s result, this theorem constitutes a natural intermediate step towards a proof of the convex greedy embedding conjecture.

On the performance of greedy forwarding on Yao and Theta graphs

Greedy Forwarding algorithm is an important geometric routing algorithm for wireless networks. However, it can fail if the network topologies contain voids, in which a packet cannot be moved closer to destination. Since Yao and Theta graphs are two types of geometric graphs exploited to construct wireless network topologies, this paper first gives theoretical results on whether these two types of graphs can contain voids with respect to their cone numbers. Then, this paper examines the performance of Greedy Forwarding on Yao and Theta graphs in terms of stretch (the ratio between the path length found by Greedy Forwarding and the shortest path length from a source to a destination). Both worst-case and average-case stretches are studied. For the worst case, this paper shows that the stretches of Greedy Forwarding on both Yao and Theta graphs do not have a constant upper bound (i.e., not competitive) in hop metric. For the average case, this paper studies the stretch experimentally by running Greedy Forwarding on a large number of Yao and Theta graphs with randomly generated node sets. The average-case stretches in both hop and Euclidean metrics are measured, and several interesting findings are revealed.

Enhanced reliable reactive routing (ER3) protocol for multimedia applications in 3D wireless sensor networks

Sensor networks designed especially for the multimedia applications require high data rate and better Quality of Service (QoS). Offering a reliable and energy efficient routing technique in a harsh and complex three-dimensional (3-D) environment for multimedia applications is a challenging job. Geo-routing and geometric routing have been efficient routing schemes for two-dimensional (2-D), but are unable to work properly for 3-D sensor networks. In order to enhance the resilience to link the dynamics in the 3-D sensor network, in this research an Enhanced Reliable Reactive Routing (ER3) is proposed. ER3 is an advancement to the existing reactive routing schemes, to provide energy efficient and reliable routing of data packets in the complex 3-D sensor networks for multimedia applications. The major attraction of ER3 is its backoff scheme, which occurs in the route discovery phase. In backoff scheme robust pilot paths formed between the source and destination are calculated to enable cooperative forwarding of the data packets. The data packets in ER3 are forwarded greedily to the destination from the source and doesn’t require any prior location information of the nodes. The encompassing simulations suggest that the ER3 outperforms the existing routing protocols on the basis of energy efficiency, low latency and high packet delivery ratio.

Routing at Large Scale: Advances and Challenges for Complex Networks

A wide range of social, technological and communication systems can be described as complex networks. Scale-free networks are one of the well known classes of complex networks in which nodes� degrees follow a power-law distribution. The design of scalable, adaptive and resilient routing schemes in such networks is very challenging. In this article we present an overview of required routing functionality, categorize the potential design dimensions of routing protocols among existing routing schemes, and analyze experimental results and analytical studies performed so far to identify the main trends/trade-offs and draw main conclusions. Besides traditional schemes such as hierarchical/shortest-path path-vector routing, the article pays attention to advances in compact routing and geometric routing since they are known to significantly improve scalability in terms of memory space. The identified trade-offs and the outcomes of this overview enable more careful conclusions regarding the (un-)suitability of different routing schemes to large-scale complex networks and provide a guideline for future routing research.

Composite Dislocations in Smectic Liquid Crystals.

Smectic liquid crystals are characterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in smectics play an important role in phase nucleation, layer reorientation, and dynamics. Typically modeled as possessing one line singularity, the layer structure of a dislocation leads to a diverging compression strain as one approaches the defect center, suggesting a large, elastically determined melted core. However, it has been observed that for large charge dislocations, the defect breaks up into two disclinations [C. E. Williams, Philos. Mag. 32, 313 (1975)PHMAA40031-808610.1080/14786437508219956]. Here we investigate the topology of the composite core. Because the smectic cannot twist, transformations between different disclination geometries are highly constrained. We demonstrate the geometric route between them and show that despite enjoying precisely the topological rules of the three-dimensional nematic, the additional structure of line disclinations in three-dimensional smectics localizes transitions to higher-order point singularities.

A 3D topological auto-routing algorithm for mechatronic products design

New technologies, like 3D-MID (Three Dimensional - Mechatronic Integrated Devices), Flex Circuits and jet-printing technology for mechatronic products, raise requirement for integrated design, in which 3D layout is crucial. However, research on 3D routing algorithm is far from enough. Current 3D auto-routing algorithms are mainly based on 2D geometry routing algorithms. Geometric routing algorithms are usually used on regular geometry, bringing limitations in routing directions. Besides, existing 3D routing algorithms did not break through geometry structures’ constraints of 3D routing bases. A 3D topological auto-routing algorithm based on rubber-band routing was proposed in this paper. First, a new dynamic 3D search graph based on a triangular mesh was established. The 3D search graph concludes adjacent relations among different surfaces, getting rid of 3D surface limitation, even for curved surface. The renewal of the search graph assures that routes won’t cross through each other. In addition, the data structure combining hash table and adjacency list was used to store the 3D search graph, which reduces the storage space and promotes the algorithm efficiency. Afterwards, the generation of rubber bands was realised on modified A* algorithm and funnel algorithm. And then, append appropriate spokes to obtain extended rubber bands, which are treated as shortest paths theoretically.

Destination unaware geometric routing for delay tolerant networks

Receiving great interest from the research community, the concept of delay/disruption tolerant networks (DTNs) is without the contemporaneous end to end connectivity to bridge communication in the challenged networks, suffering from sparse network density and frequent disruption. In this paper, our motivation is to firstly adopt geographic information instead of history encounter information to relay message. Then we argue it is unreasonable to rely on realtime location of destination to relay message due to sparse network density and high mobility. Therefore, our contribution is to propose a geographic routing algorithm for DTNs without knowing where the destination is. The key insight is to replicate message in an efficient manner rather than flooding, taking into account encounter angle between pairwise nodes. Evaluation results under the Helsinki city scenario show an improvement of our proposed.