The STEM Methodology and Graph Theory: Some Practical Examples

In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at STEM undergraduate students to be solved by using shortest path algorithms from Graph Theory after previous modeling.

Parallel Privacy-Preserving Shortest Path Algorithms

In this paper, we propose and present secure multiparty computation (SMC) protocols for single-source shortest distance (SSSD) and all-pairs shortest distance (APSD) in sparse and dense graphs. Our protocols follow the structure of classical algorithms—Bellman–Ford and Dijkstra for SSSD; Johnson, Floyd–Warshall, and transitive closure for APSD. As the computational platforms offered by SMC protocol sets have performance profiles that differ from typical processors, we had to perform extensive changes to the structure (including their control flow and memory accesses) and the details of these algorithms in order to obtain good performance. We implemented our protocols on top of the secret sharing based protocol set offered by the Sharemind SMC platform, using single-instruction-multiple-data (SIMD) operations as much as possible to reduce the round complexity. We benchmarked our protocols under several different parameters for network performance and compared our performance figures against each other and with ones reported previously.

Time-dependent Dijkstra’s algorithm under bipolar neutrosophic fuzzy environment

Determining the shortest path and calculating the shortest travel time of a complex networks are important for transportation problems. Numerous approaches has been developed to search shortest path on graphs, and one of the well-known is the Dijkstra’s label correcting algorithm. Dijkstra’s approach is capable of determining shortest path of directed or undirected graph with non-negative weighted arcs. To handle with uncertainty in real-life, the Dijkstra’s algorithm should be adapted to fuzzy environment. The weight of arc -which is the vague travel time between two nodes- can be expressed in bipolar neutrosophic fuzzy sets containing positive and negative statements. In addition, the weights of arcs in bipolar neutrosophic fuzzy graphs can be affected by time. This study proposes the extended Dijkstra’s algorithm to search the shortest path and calculate the shortest travel time on a single source time-dependent network of bipolar neutrosophic fuzzy weighted arcs. The proposed approach is illustrated, and the results demonstrate the validity of the extended algorithm. This article is intended to guide future shortest path algorithms on time-dependent fuzzy graphs.

Novel insights into the design of stretchable electrical systems

Soft electronics have recently gathered considerable interest because of their biomechanical compatibility. An important feature of deformable conductors is their electrical response to strain. While development of stretchable materials with high gauge factors has attracted considerable attention, there is a growing need for stretchable conductors whose response to deformation can be accurately engineered to provide arbitrary resistance-strain relationships. Rare studies addressing this issue have focused on deterministic geometries of single rigid materials, limiting the scope of these strategies. We introduce the novel concept of periodic stretchable patterns combining multiple conductive materials to produce tailored responses. Using shortest path algorithms, we establish a computationally efficient selection method to obtain the required resistance-strain relationship. Using this algorithm, we identify and experimentally demonstrate constant resistance-strain responses up to 50% elongation using a single microtextured material. Last, we demonstrate counterintuitive sinusoidal responses by integrating three materials, with interesting applications in sensing and soft robotics.

Path computation enhancement in SDN networks

Path computation is always the core topic in networking. The target of the path computation is to choose an appropriate path for the traffic flow. With the emergence of Software-defined networking (SDN), path computation moves from the distributed network nodes to a centralized controller. In this thesis, we will present a load balancing algorithm in SDN framework for popular data center networks and a fault management approach for hybrid SDN networks. The proposed load balancing algorithm computes and selects appropriate paths based on characteristics of data center networks and congestion status. In addition, a solution that supports proper operations of a hybrid SDN network will also be proposed. The evaluation shows the proposed load balancing algorithm performs better than classic shortest path algorithms. We also demonstrated that the proposed solution for hybrid SDN networks can support proper operations in complicated hybrid SDN networks.

Path computation enhancement in SDN networks

Path computation is always the core topic in networking. The target of the path computation is to choose an appropriate path for the traffic flow. With the emergence of Software-defined networking (SDN), path computation moves from the distributed network nodes to a centralized controller. In this thesis, we will present a load balancing algorithm in SDN framework for popular data center networks and a fault management approach for hybrid SDN networks. The proposed load balancing algorithm computes and selects appropriate paths based on characteristics of data center networks and congestion status. In addition, a solution that supports proper operations of a hybrid SDN network will also be proposed. The evaluation shows the proposed load balancing algorithm performs better than classic shortest path algorithms. We also demonstrated that the proposed solution for hybrid SDN networks can support proper operations in complicated hybrid SDN networks.

Research on Real-Time Optimal Path Planning Model and Algorithm for Ship Block Transportation in Shipyard

Special vehicles called transporters are used to deliver heavy blocks in the shipyard. With the development and application of information and communication technology in shipyards, the real-time positioning and ship blocks online scheduling system for transporters are being developed. The real-time path planning of transporters is important for maintaining the overall production schedule of ship blocks. Because of the large volume and heavy weight of ship blocks, there may be some problems, such as high energy consumption, block deformation and other security issues, when transporters loading a block make a turn. So, fewer turns of the transporters are also important to make a block transportation schedule. The minimum driving distance and fewer turns are considered simultaneously for transporter real-time path planning in this paper. A hybrid model considering the number of turns and the optimal path of the transporter is constructed. Moreover, the optimal scheduling model, considering path missing, is also discussed. Several shortest path algorithms are analyzed, which show that the Dijkstra algorithm is the best way to solve this model. From the attained simulation results, we demonstrate that the proposed model and algorithm have the ability to effectively solve real-time path planning for the ship block transportation in shipyards.