Reducing the number of link crossings in a network drawn on the plane such as a wiring board is a well-known problem, and especially the calculation of the minimum number of such crossings: this is the crossing number problem. It has been shown that finding a general solution to the crossing number problem is NP-hard. So, this problem is addressed for particular classes of graphs and this is also our approach in this paper. More precisely, we focus hereinafter on the torus topology. First, we discuss an upper bound on cr(T(2, k)) the number of crossings in a 2-dimensional k-ary torus T(2, k) where k ≥ 2: the result cr(T(2, k)) ≤ k(k - 2) and the given constructive proof lay foundations for the rest of the paper. Second, we extend this discussion to derive an upper bound on the crossing number of a 3-dimensional k-ary torus: cr(T(3, k)) ≤ 2k4 - k3 - 4k2 - 2⌈k/2⌉⌊k/2⌋(k - (k mod 2)) is obtained. Third, an upper bound on the crossing number of an n-dimensional k-ary torus is derived from the previously established results, with the order of this upper bound additionally established for more clarity: cr(T(n, k)) is O(n2k2n-2) when n ≥ k and O(nk2n-1) otherwise.

It is well known that the large-scale access of wind power to the power system will affect the economic and environmental objectives of power generation scheduling, and also bring new challenges to the traditional deterministic power generation scheduling because of the intermittency and randomness of wind power. In order to deal with these problems, a multiobjective optimization dispatch method of wind-thermal power system is proposed. The method can be described as follows: A multiobjective interval power generation scheduling model of wind-thermal power system is firstly established by describing the wind speed on wind farm as an interval variable, and the minimization of fuel cost and pollution gas emission cost of thermal power unit is chosen as the objective functions. And then, the optimistic and pessimistic Pareto frontiers of the multi-objective interval power generation scheduling are obtained by utilizing an improved normal boundary intersection method with a normal boundary intersection (NBI) combining with a bilevel optimization method to solve the model. Finally, the optimistic and pessimistic compromise solutions is determined by a distance evaluation method. The calculation results of the 16-unit 174-bus system show that by the proposed method, a uniform optimistic and pessimistic Pareto frontier can be obtained, the analysis of the impact of wind speed interval uncertainty on the economic and environmental indicators can be quantified. In addition, it has been verified that the Pareto front in the actual scenario is distributed between the optimistic and pessimistic Pareto front, and the influence of different wind power access levels on the optimistic and pessimistic Pareto fronts is analyzed.

In the age of information and communications technology (ICT), not only collecting data but also using such data is provided in various services. It is necessary to ensure data privacy in such services while providing efficient computation and communication complexity. In this paper, we propose the first interval test designed according to the notion of online and offline phases by executing our new empty-set check. Our protocol is proved to ensure both server and client privacy. Furthermore, neither the computational complexity of a client in the online phase nor the communicational complexity from a server to a client depends on the size of the set. As a result, even in a practical situation in which one server receives requests from numerous clients, the waiting time for a client to obtain the result of an interval test can be minimized.

In this paper, the performance of a vehicle information sharing (VIS) system for an intersection collision warning system (ICWS) is analyzed. The on-board unit (OBU) of the ICWS sharing obstacle detection sensor information (ICWS-ODSI) is mounted on a vehicle, and it obtains information about the surrounding vehicles, such as their position and velocity, by its in-vehicle obstacle detection sensors. These information are shared with other vehicles via an intervehicle communication network. In this analysis, a T-junction is assumed as the road environment for the theoretical analysis of the VIS performance in terms of the mean of entire vehicle information acquiring probability (MEVIAP). The MEVIAP on OBU penetration rate indicated that the ICWS-ODSI is superior to the conventional VIS system that only shares its own individual driving information via an intervehicle communication network. Furthermore, the MEVIAP on the sensing range of the ICWS-ODSI is analyzed, and it was found that the ISO15623 sensor used for the forward vehicle collision warning system becomes a candidate for the in-vehicle detection sensor of ICWS-ODSI.

In the development of inter-vehicle communication systems for a prevention of car crashes, it is important to know path loss characteristics at blind intersections in urban area. Thus field experiments and numerical simulations have been performed. By the way, transparent waves from building walls are not considered in many cases. The reason why is that it is the worst case in terms of the path loss at blind intersection surrounded by buildings in urban area. However, it would be important to know the effect of transparent wave on the path loss in actual environments. On the other hand, path loss models have been proposed to estimate easily the path loss in urban environment. In these models, the effect of transparent wave is not clear. In this paper, the effect of transparent wave from building walls on path loss characteristics at blind intersection in urban area is investigated by using the FDTD method. Additionally, the relationship between transparent wave and path loss models is also investigated.

In the development of inter-vehicle communication systems for the prevention of car crashes, it is important to know radio propagation characteristics at blind intersections. In field experiments and numerical simulations to investigate radio propagation characteristics, a half wavelength dipole antenna is assumed to be the wave source in many cases. However, a directivity of car antenna is changed by the effect of both car body and antenna position on car. In this paper, path loss characteristics considering antenna positions on car body at a blind intersection in urban area for inter-vehicle communications using 700MHz band are investigated. Additionally, simplified car models are proposed for the efficient analysis of radio propagation. Here, the hybrid method using both FDTD and ray-tracing methods is used for the radio propagation analysis.

A hinge vertex is a vertex in an undirected graph such that there exist two vertices whose removal makes the distance between them longer than before. Identifying hinge vertices in a graph can help detect critical nodes in communication network systems, which is useful for making them more stable. For finding them, an O(n3) time algorithm was developed for a simple graph, and, linear time algorithms were developed for interval and permutation graphs, respectively. Recently, the maximum detour hinge vertex problem is defined by Honma et al. For a hinge vertex u in a graph, the detour degree of u is the largest value of distance between any pair of x and y (x and y are adjacent to u) by removing u. A hinge vertex with the largest detour degree in G is defined as the maximum detour hinge vertex of G. This problem is motivated by practical applications, such as network stabilization with a limited cost, i.e., by enhancing the reliability of the maximum detour hinge vertex, the stability of the network is much improved. We previously developed an O(n2) time algorithm for solving this problem on an interval graph. In this study, we propose an algorithm that identifies the maximum detour hinge vertex on a permutation graph in O(n2) time, where n is the number of vertices in the graph.

Accessing a geo-location database is one of the approaches for a secondary user (SU) to obtain the list of available channels for its operation. Channel availability is calculated based on information stored in the geo-location database and information submitted by the SU so that primary users (PU) are protected from harmful interference. The available channel checking process is modeled as a number of intersection tests between the protected contours of PUs and the operation area of the SU regarding to all potential channels. Existing studies indicated that these intersection tests consume time and introduce overhead to the database, especially when the contours or the operation areas are represented by n-polygons and the number of vertices n is a large number. This paper presents a novel method of determining available channels which reduces the number of intersection tests. By submitting SU's preferred channels or the number of channels to be checked to the database, the calculation time and database's load will be reduced significantly. This paper also presents analysis and simulation results of the database workload and the average number of channels obtained per query on different query methods. Suitable query method can be selected based on the number of similar channels in neighbor areas and the maximum number of intersection tests.

Consider a simple undirected graph G = (V,E) with vertex set V and edge set E. Let G-u be a subgraph induced by the vertex set V-{u}. The distance δG(x,y) is defined as the length of the shortest path between vertices x and y in G. The vertex u ∈ V is a hinge vertex if there exist two vertices x,y ∈ V-{u} such that δG-u(x,y)>δG(x,y). Let U be a set consisting of all hinge vertices of G. The neighborhood of u is the set of all vertices adjacent to u and is denoted by N(u). We define d(u) = max{δG-u(x,y) | δG-u(x,y)>δG(x,y),x,y ∈ N(u)} for u ∈ U as detour degree of u. A maximum detour hinge vertex problem is to find a hinge vertex u with maximum d(u) in G. In this paper, we proposed an algorithm to find the maximum detour hinge vertex on an interval graph that runs in O(n2) time, where n is the number of vertices in the graph.

We consider the minimum feedback vertex set problem for some bipartite graphs and degree-constrained graphs. We show that the problem is linear time solvable for bipartite permutation graphs and NP-hard for grid intersection graphs. We also show that the problem is solvable in O(n2log 6n) time for n-vertex graphs with maximum degree at most three.

This paper presents an efficient algorithm for reporting all intersections among n given segments in the plane using work space of arbitrarily given size. More exactly, given a parameter s which is between Ω(1) and O(n) specifying the size of work space, the algorithm reports all the segment intersections in roughly O(n2/+ K) time using O(s) words of O(log n) bits, where K is the total number of intersecting pairs. The time complexity can be improved to O((n2/s) log s + K) when input segments have only some number of different slopes.

We have developed a dedicated onboard “sensor” utilizing wireless communication devices for collision avoidance around road intersections. The “sensor” estimates the positions of transmitters on traffic participants by comparing the strengths of signals received by four ZigBee receivers installed at the four corners of a vehicle. On-board sensors involving cameras cannot detect objects in non line-of-sight (NLOS) area caused by buildings and other vehicles. Although infrastructure sensors for vehicle-to-infrastructure (V2I) cooperative systems can detect such hidden objects, they are substantially more expensive than on-board sensors. The on-board wireless “sensor” developed in this work would function as an alternative tool for collision avoidance around intersections. Herein, we extend our previous work by considering a road surface reflection model to improve the estimation accuracy. By using this model, we succeeded in reducing the error mismatches between the observed data and the calibration data of the estimation algorithm. The proposed system will be realized on the basis of these enhancements.

Given a simple connected graph G with n vertices, the spanning tree problem involves finding a tree that connects all the vertices of G. Solutions to this problem have applications in electrical power provision, computer network design, circuit analysis, among others. It is known that highly efficient sequential or parallel algorithms can be developed by restricting classes of graphs. Circular trapezoid graphs are proper superclasses of trapezoid graphs. In this paper, we propose an O(n) time algorithm for the spanning tree problem on a circular trapezoid graph. Moreover, this algorithm can be implemented in O(log n) time with O(n/log n) processors on EREW PRAM computation model.

Secure computation of the set intersection functionality allows n parties to find the intersection between their datasets without revealing anything else about them. An efficient protocol for such a task could have multiple potential applications in commerce, health care, and security. However, all currently known secure set intersection protocols for n > 2 parties have computational costs that are quadratic in the (maximum) number of entries in the dataset contributed by each party, making secure computation of the set intersection only practical for small datasets. In this paper, we describe the first multi-party protocol for securely computing the set intersection functionality with both the communication and the computation costs that are quasi-linear in the size of the datasets. For a fixed security parameter, our protocols require O(n2k) bits of communication and Õ(n2k) group multiplications per player in the malicious adversary setting, where k is the size of each dataset. Our protocol follows the basic idea of the protocol proposed by Kissner and Song, but we gain efficiency by using different representations of the polynomials associated with users' datasets and careful employment of algorithms that interpolate or evaluate polynomials on multiple points more efficiently. Moreover, the proposed protocol is robust. This means that the protocol outputs the desired result even if some corrupted players leave during the execution of the protocol.

An inter-vehicle communication system for the 720 MHz band that is designed to prevent car crashes at intersections has recently been proposed in Japan. This paper presents an analysis of the propagation characteristics of an intersection surrounded by concrete block walls in a residential area. The propagation characteristics were analyzed for the first time using the finite-difference time-domain (FDTD) method. We investigated the influence of wall thickness and source locations on the propagation characteristics. The results of our investigation showed that the most commonly used wall thickness and source locations do not strongly affect propagation loss. Furthermore, we analyzed the power delay profile and delay spread by taking into consideration the structure of the concrete block walls.

This paper proposes a novel waveguide intersection separating two H-plane waveguide systems from each other. If a four-port network in a four-fold rotational symmetry is completely matched, it has necessarily intersection properties. The proposed waveguide intersection consists of a square H-plane waveguide planar circuit connected four input/output waveguide ports in a four-fold rotational symmetry, and several metallic posts inserted at the junction without destroying the symmetry to realize a perfect matching. By optimizing the circuit parameters, high isolation properties are obtained in a relatively wide frequency band of about 8.6% for return loss and isolation better than 20 and 30 dB, respectively, for a circuit designed at 10 GHz. The proposed waveguide intersection can be analyzed by H-plane planar circuit approach, and possess advantages of compactness, simplicity, and high-power handling capability. Furthermore, an SIW intersection is designed by applying H-plane planar circuit approach to a waveguide circuit filled with dielectric material, and high isolation properties similar to H-plane waveguide intersection can be realized. The validity of these design concepts is confirmed by em-simulations and experiments.

Inter-vehicle communication (IVC) system using 700 MHz band to prevent car crashes has been proposed recently. In this paper, we first apply the FDTD method to the analyses of propagation characteristics at an intersection for IVC. We investigate the propagation characteristics considering the electrical conductivities, thickness and windows of building wall and pedestrians. As a result, it is shown that the electrical conductivities and thickness of building wall have a slight influence. In contrast, windows and pedestrians have a great influence on the propagation characteristics. Furthermore, the azimuth delay profiles are obtained by using the MUSIC algorithm.

Ray tracing is one of the most popular techniques for generating photo-realistic images. Extensive research and development work has made interactive static scene rendering realistic. This paper deals with interactive dynamic scene rendering in which not only the eye point but also the objects in the scene change their 3D locations every frame. In order to realize interactive dynamic scene rendering, RTRPS (Ray Tracing based on Ray Plane and Bounding Sphere), which utilizes the coherency in rays, objects, and grouped-rays, is introduced. RTRPS uses bounding spheres as the spatial data structure which utilizes the coherency in objects. By using bounding spheres, RTRPS can ignore the rotation of moving objects within a sphere, and shorten the update time between frames. RTRPS utilizes the coherency in rays by merging rays into a ray-plane, assuming that the secondary rays and shadow rays are shot through an aligned grid. Since a pair of ray-planes shares an original ray, the intersection for the ray can be completed using the coherency in the ray-planes. Because of the three kinds of coherency, RTRPS can significantly reduce the number of intersection tests for ray tracing. Further acceleration techniques for ray-plane-sphere and ray-triangle intersection are also presented. A parallel projection technique converts a 3D vector inner product operation into a 2D operation and reduces the number of floating point operations. Techniques based on frustum culling and binary-tree structured ray-planes optimize the order of intersection tests between ray-planes and a sphere, resulting in 50% to 90% reduction of intersection tests. Two ray-triangle intersection techniques are also introduced, which are effective when a large number of rays are packed into a ray-plane. Our performance evaluations indicate that RTRPS gives 13 to 392 times speed up in comparison with a ray tracing algorithm without organized rays and spheres. We found out that RTRPS also provides competitive performance even if only primary rays are used.

Internet routers need to classify incoming packets quickly into flows in order to support features such as Internet security, virtual private networks and Quality of Service (QoS). Packet classification uses information contained in the packet header, and a predefined rule table in the routers. Packet classification of multiple fields is generally a difficult problem. Hence, researchers have proposed various algorithms. This study proposes a multi-dimensional encoding method in which parameters such as the source IP address, destination IP address, source port, destination port and protocol type are placed in a multi-dimensional space. Similar to the previously best known algorithm, i.e., bitmap intersection, multi-dimensional encoding is based on the multi-dimensional range lookup approach, in which rules are divided into several multi-dimensional collision-free rule sets. These sets are then used to form the new coding vector to replace the bit vector of the bitmap intersection algorithm. The average memory storage of this encoding is θ (LNlog N) for each dimension, where L denotes the number of collision-free rule sets, and N represents the number of rules. The multi-dimensional encoding practically requires much less memory than bitmap intersection algorithm. Additionally, the computation needed for this encoding is as simple as bitmap intersection algorithm. The low memory requirement of the proposed scheme means that it not only decreases the cost of packet classification engine, but also increases the classification performance, since memory represents the performance bottleneck in the packet classification engine implementation using a network processor.

In this letter, we propose a novel approach using wireless sensor networks (WSNs) to enhance the safety and efficiency of four-way stop-sign-controlled (FWSC) intersections. The proposed algorithm provides right of way (RoW) and crash avoidance information by means of an intelligent WSN system. The system is composed of magnetic sensors, embedded in the center of a lane, with relay nodes and a base station placed on the side of the road. The experimental results show that the vehicle detection accuracy is over 99% and the sensor node battery life expectancy is over 3 years for traffic of 5,800 vehicles per day. For the traffic application we consider, a strong effect is observed as the projected conflict rate was reduced by 72% compared to an FWSC intersection operated with only driver perception.