Efficiently solving the problem of computing, in a distributed fashion, the shortest paths of a graph whose topology dynamically changes over time is a core functionality of many today’s digital infrastructures, probably the most prominent example being communication networks. Many solutions have been proposed over the years for this problem that can be broadly classified into two categories, namely Distance-Vector and Link-State algorithms. Distance-Vector algorithms are widely adopted solutions when scalability and reliability are key issues or when nodes have either limited hardware resources, as they result in being very competitive approaches in terms of both the memory and the computational point of view. In this paper, we first survey some of the most established solutions of the Distance-Vector category. Then, we discuss some recent algorithmic developments in this area. Finally, we propose a new experimental study, conducted on a prominent category of network instances, namely generalized linear preference (GLP) power-law networks, to rank the performance of such solutions.

The aviation industry has proposed multiple solutions to reduce fuel consumption, air pollution and noise at airports, one of which involves deploying electric trucks for aircraft towing between the stand and the runway. However, the introduction of tow trucks results in increased surface traffic, posing challenges from the perspective of Air Traffic Controller's (ATCO). Various solutions involving automated planning and execution have been proposed, but many are constrained by their inability to manage multiple active runways simultaneously, and their failure to account for tow truck battery state-of-charge during assignments. This paper presents a novel system for taxi operations that employs autonomous tow trucks to enhance ground operations and address deficiencies in existing approaches. The system focuses on identifying conflict-free solutions that minimize taxi-related delays and route length while maximising the efficient use of the tow trucks. The algorithm operates at a strategic level and uses a centralised approach. It has the capacity to cater for multiple active runways and considers factors such as tow truck battery state-of-charge and availability of charging stations. Furthermore, the proposed algorithm is capable of scheduling and routing tow trucks for aircraft taxiing without generating traffic conflicts.

Conceptual distance refers to the degree of proximity between two concepts within a conceptualization. It is closely linked with semantic similarity and relationship, but its computation relies entirely on the context of the given concepts. The DIS-C algorithm, which requires using search algorithms such as Breadth First Search, represents an advance in computing the semantic similarity/relation regardless of the type of knowledge structure and semantic relationships. The shortest path algorithm facilitates the determination of the semantic closeness between two indirectly connected concepts in an ontology by propagating local distances. This process is implemented for each concept pair to establish the most effective and efficient paths to connect these concepts. The algorithm identifies the shortest path between the concepts, allowing for the inference of the most relevant relationships between them. This approach contributes to developing a comprehensive understanding of the ontology and enhances the accuracy and precision of the semantic representation of the concepts. However, one of the critical issues is associated with the computational complexity due to the nature of the algorithm, which is errorn3. This paper studies alternatives to accelerate the DIS-C based on approximation and optimized algorithms, focusing on Dijkstra, pruned Dijkstra, and Sketched-based algorithms to compute conceptual distance. Based on the experiments, we discovered that the bottleneck can be avoided using the proposed 2-hop coverages, bringing DIS-C almost linearity.

A graph based path planning method consisting of off-line part and on-line part for multi-UAV system in windy condition is proposed. In the off-line part, the task area is divided into grids. When two nodes is close enough, they are connected and weighted by the cost, obtained by solving an optimization problem based on difference method, between them. In order to ensure the accuracy of the difference method, the adjacent radius is set to be small enough. In order to ensure the generated paths close to analytical solution, the grid size is set to be much smaller than the adjacent radius. The shortest path algorithm is used to update the adjacent matrix and path matrix. In the on-line part, the target position assignment and optimal velocity can be obtained by accessing the adjacent matrix and path matrix. At the end of this paper, some numerical examples are taken to illustrate the validity of our method and the influence of the parameters.

This paper introduces a novel algorithm for solving the point-to-point shortest path problem in a static regular 8-neighbor connectivity (G8) grid. This algorithm can be seen as a generalization of Hadlock algorithm to G8 grids, and is shown to be theoretically equivalent to the relaxed A* (RA*) algorithm in terms of the provided solution's path length, but with substantial time and memory savings, due to a completely different computation strategy, based on defining a set of lookup matrices. Through an experimental study on grid maps of various types and sizes (1290 runs on 43 maps), it is proven to be 2.25 times faster than RA* and 17 times faster than the original A*, in average. Moreover, it is more memory-efficient, since it does not need to store a G score matrix.

Routing a person through a traffic network presents a tension between selecting a fixed route that is easy to navigate and selecting an aggressively adaptive route that minimizes the expected travel time. We propose to create non-aggressive adaptive routes in the middle-ground seeking the best of both these extremes. Specifically, these routes still adapt to changing traffic conditions, however we limit the number of adjustments made in the route. This improves the user experience, by providing a continuum of options between saving travel time and minimizing navigation. We design strategies to model single and multiple route adjustments, and investigate enumerative techniques to solve these models. To alleviate the intractability with handling real-life traffic data, we develop efficient algorithms with easily computable lower and upper bounds. We finally present computational experiments highlighting the benefits of limited adaptability in terms of reducing the expected travel time.

Transportation is a crucial component of supply chain management, responsible for delivering goods and services to customers. This paper explores the application of game theory concepts, precisely the Shapley value, to cost allocation in transportation operations involving drones and trucks. Our focus is on shortest-path games in which agents own nodes in a network and seek to transport items between nodes at the lowest possible cost. We provide a comprehensive literature review of the Shapley value and its use in shortest-path games, with particular emphasis on transportation networks. Our proposed model includes sets of customers, drones, and trucks and uses binary decision variables to indicate whether a drone or truck serves a given customer. The objective is to minimize the total cost of serving all customers while adhering to capacity and synchronization constraints. We use the Shapley value to determine the contribution and cost-sharing of each drone and truck in serving the customers. Through a combination of denitions, theorems, and examples, we explore the formal meaning of the Shapley value and its relationship to shortest-path games in transportation networks. We highlight exceptional cases and considerations that must be taken into account when applying the Shapley value in such scenarios.

A number of decision support tools facilitating the use of Electric Vehicles (EVs) have been recently developed. Due to the EVs’ limited autonomy, routing and path planning are the main challenges treated in such tools. Specifically, determining at which Charging Stations (CSs) to stop, and how much the EV should charge at them is complex. This complexity is further compounded by the fact that charging times depend on the CS technology, the EV characteristics, and follow a nonlinear function. Considering these factors, we propose a path planning methodology for EVs with user preferences, where charging is performed at public CSs. To achieve this, we introduce the Electric Vehicle Shortest Path Problem with time windows and user preferences (EVSPPWP) and propose an efficient solution algorithm for it. Given an origin and a destination, the algorithm prioritizes CSs close to Points of Interest (POIs) that match user inputted preferences, and user-defined time windows are considered for activities such as lunch and spending the night at hotels. The algorithm produces flexible solutions by considering clusters of charging points (CPs) as separate CSs. Furthermore, the algorithm yields resilient paths by ensuring that recommended paths have a minimum number of CSs in their vicinity. The main contributions of our methodology are: modeling user-defined time windows, including user-defined weights for different POI categories, creating CSs based on clusters of CPs with sufficient proximity, using resilient paths, and proposing an efficient algorithm for solving the EVSPPWP. To facilitate the use of our methodology, the algorithm was integrated into a web interface. We illustrate the use of the web interface, giving usage examples and comparing different settings.

In this paper, a system of searching for optimal paths is developed and concreted on a FPGA. It is based on a memristive emulator, used as a delay element, by configuring the test graph as a memristor network. A parallel algorithm is applied to reduce computing time and increase efficiency. The operation of the algorithm in Matlab is checked beforehand and then exported to two different Intel FPGAs: a DE0-Nano board and an Arria 10 GX 220 FPGA. In both cases reliable results are obtained quickly and conveniently, even for the case of a 300x300 nodes maze.

The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.

Currently, maritime traffic is increasing with economic growth in several regions worldwide. However, this growth in maritime traffic has led to increased risk of marine accidents. These accidents have a higher probability of occurring in regions where geographical features, such as islands, are present. Further, the positioning of rescue ships in a particular ocean region with a high level of maritime activity is critical for rescue operations. This paper proposes a method for determining an optimal set of locations for stationing rescue ships in an ocean region with numerous accident sites in the Wando islands of South Korea. The computational challenge in this problem is identified as the positioning of numerous islands of varying sizes located in the region. Thus, the proposed method combines a clustering-based optimization method and an image processing approach that incorporates flood filling to calculate the shortest distance between two points in the ocean that detours around the islands. Experimental results indicate that the proposed method reduces the distance from rescue ships and each accident site by 5.0 km compared to the original rescue ship locations. Thus, rescue time is reduced.

Bandung and Lembang are the cities that are chosen by many tourists (local and foreign) as their destinations. Geographically, these cities are placed side-by-side and each city has its own characteristics. As in Bandung, there are many hotels and culinary spots, meanwhile, in Lembang, there are many scenery tourism spots. Tourists usually have limited time to visit all the destinations on holiday, which makes them choose several tourist destinations to visit. In this paper, the tourism itinerary recommendation system is proposed by calculating the most optimal route between destinations and approaching the Vehicle Routing Problem with Time Windows. The optimal route is defined by using Dijkstra the shortest path algorithm by using the collaboration between the road information (road length, traffic condition, travel time, and weather condition) and criteria weight that is determined using the Analytics Hierarchy Process as the graph weights. According to the simulation results, the criteria weights are 6.9%, 62.7%, 18.6%, and 11.9% for Route Length, Traffic Condition, Travel Time, and Weather Condition respectively. Moreover, the optimal number of tourism itinerary plans for the tourist in this research is 4 destinations. As the usage of computational resources, it takes 31.8% of CPU and 61.9% of Memory usage. For the time processing, it increases exponentially as the increment of number of requested stops. The output of this research is expected to be a solution to the tourist itinerary plan, especially in Bandung and Lembang.

The connectivity reliability of public transport depends on a number of factors, including public transport routes, the connections between them, their frequency, their availability, and the availability of public transport and infrastructure. A shortest path algorithm is used to find up to "k" paths connecting each Origin-Destination pair in space-time, taking into account the schedules and a constraint on the maximum tolerable waiting time. For each path, four reliability indicators are proposed, as well as an approachability indicator, related to the level of transport supply. Thanks to two sets of equations, these indicators are also computed on the origin-destination and network levels. This enables fleet managers to evaluate and compare strategies for improving the connectivity reliability and the transport supply, such as increasing the number of public transport routes, reducing route length or increasing frequency. From an application on the bus network of a city in Brittany in France, we show how to understand and use these indicators.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string.

In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

Secure Secret Sharing Single-Source Shortest Distance (SSSD) protocols, built on the Secure Multi-Party Computation (SMC) foundation, have emerged as a promising solution to address the secure distribution and management of sensitive secrets among multiple parties. This paper focuses on the crucial aspect of security proof within SSSD protocols based on SMC, aiming to provide a scientifically rigorous understanding of the formal verification process and the robust guarantees they offer. Through a comprehensive examination of the fundamental principles underpinning SMC and the specific design considerations unique to SSSD protocols, this paper meticulously explores the key components and intricate steps involved in constructing a rigorous security proof. Furthermore, it discusses the adversarial model, precise security definitions, cryptographic assumptions utilized within the proof, and sophisticated techniques and reductions to establish its validity. By means of a meticulous analysis of the security proof for SSSD protocols, this paper critically evaluates both the strengths and limitations of the proposed approach, offering valuable insights to inform future research and development within this significant domain of study.

The recent provision of energy-harvesting capabilities to wireless sensor networks has entailed the redefinition of design objectives. Specifically, the traditional goal of maximizing network lifetime has been replaced by optimizing network performance, namely delay and throughput. The present paper contributes to this reformulation by considering the routing problem for the class of time-driven energy-harvesting WSN (EH-WSN) under regular or quasi-periodic energy sources. In particular, this paper shows that the minimum hop count (MHC) criterion maximizes the average duty cycle that can be sustained by nodes in this type of scenarios. This is a primary objective in EH-WSN, since large duty cycles lead to enhanced performance. Based on a previous result, a general expression is first obtained which gives mathematical form to the relationship between duty cycle and traffic load for any node in a time-driven EH-WSN fed by a regular energy source. This expression reveals that the duty cycle achievable by a node decreases as its traffic load increases. Then, it is shown that MHC minimizes the average traffic load over the network, and thus it maximizes the average duty cycle of nodes. This result is numerically validated via simulation by comparison with other well-known routing strategies. Accordingly, this paper suggests assigning top priority to the MHC criterion in the development of routing protocols for time-driven EH-WSN under regular energy sources.