Shortest Path Distance Research Articles

Antipodal Turiyam Neutrosophic Graphs

Graph theory, a mathematical field, investigates the relationships between entities through vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model uncertainties in realworld networks. This paper presents the concept of the Antipodal Turiyam Neutrosophic Graph. In an Antipodal Graph, two nodes are connected if their shortest path distance equals the graph's diameter, emphasizing connections between the farthest nodes. Turiyam Neutrosophic Graphs extend traditional graphs by introducing four membership values-truth, indeterminacy, falsity, and liberal state-assigned to each vertex and edge, enabling a more nuanced representation of complex relationships.

Wireless routeing scheme for UAV-assisted access networks based on the link path loss

ABSTRACT In this work, a group of unmanned aerial vehicles (UAVs) is aimed to function as relay nodes that provide a multi-hop wireless link between ground users. The communication route between the sender and receiver is established with awareness of the link path loss between the cooperating UAV relay nodes. Then, Dijkstra’s shortest path algorithm is used to find the optimal route that has the minimum total path loss among all other possible routes. MATLAB simulation results show a high-performance gain when using Dijkstra’s algorithm for establishing the communication route compared with the baseline approach in which the route is formed based on the shortest-distance path through the UAV relay nodes. It is worth mentioning that both shadow fading and nonfading radio environments were taken into account. Moreover, the performance is further improved when the standard deviation of shadow fading increases. The work also investigates the probability of selecting each of the UAV nodes in forming the multi-hop link considering the total simulated realizations. Here, it is shown that more variability is observed in the indexes of the traversed UAV nodes when routeing through a random fading environment compared to a nonfading environment.

A Fast Algorithm for All-Pairs-Shortest-Paths Suitable for Neural Networks.

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: if the edges are given by the adjacency matrix Aij, then with a suitably small value of γ, the shortest path distances are Dij=ceil(logγ[(I-γA)-1]ij).We derive several graph-theoretic bounds on the value of γ and explore its useful range with numerics on different graph types. Even when the distance function is not globally accurate across the entire graph, it still works locally to instruct pursuit of the shortest path. In this mode, it also extends to weighted graphs with positive edge weights. For a wide range of dense graphs, this distance function is computationally faster than the best available alternative. Finally, we show that this method leads naturally to a neural network solution of the all-pairs-shortest-path problem.

Mapping the Memory Structure of High-Knowledge Students: A Longitudinal Semantic Network Analysis.

Standard learning assessments like multiple-choice questions measure what students know but not how their knowledge is organized. Recent advances in cognitive network science provide quantitative tools for modeling the structure of semantic memory, revealing key learning mechanisms. In two studies, we examined the semantic memory networks of undergraduate students enrolled in an introductory psychology course. In Study 1, we administered a cumulative multiple-choice test of psychology knowledge, the Intro Psych Test, at the end of the course. To estimate semantic memory networks, we administered two verbal fluency tasks: domain-specific fluency (naming psychology concepts) and domain-general fluency (naming animals). Based on their performance on the Intro Psych Test, we categorized students into a high-knowledge or low-knowledge group, and compared their semantic memory networks. Study 1 (N = 213) found that the high-knowledge group had semantic memory networks that were more clustered, with shorter distances between concepts-across both the domain-specific (psychology) and domain-general (animal) categories-compared to the low-knowledge group. In Study 2 (N = 145), we replicated and extended these findings in a longitudinal study, collecting data near the start and end of the semester. In addition to replicating Study 1, we found the semantic memory networks of high-knowledge students became more interconnected over time, across both domain-general and domain-specific categories. These findings suggest that successful learners show a distinct semantic memory organization-characterized by high connectivity and short path distances between concepts-highlighting the utility of cognitive network science for studying variation in student learning.

Sensitivity to network perturbations in the randomized shortest paths framework: theory and applications in ecological connectivity

The randomized shortest paths (RSP) framework, developed for network analysis, extends traditional proximity and distance measures between two nodes, such as shortest path distance and commute cost distance (related to resistance distance). Consequently, the RSP framework has gained popularity in studies on landscape connectivity within ecology and conservation, where the behavior of animals is neither random nor optimal. In this work, we study how local perturbations in a network affect proximity and distance measures derived from the RSP framework. For this sensitivity analysis, we develop computable expressions for derivatives with respect to weights on the edges or nodes of the network. Interestingly, the sensitivity of expected cost to edge or node features provides a new signed network centrality measure, the negative covariance between edge/node visits and path cost, that can be used for pinpointing strong and weak parts of a network. It is also shown that this quantity can be interpreted as minus the endured expected detour (in terms of cost) when constraining the walk to pass through the node or the edge. Our demonstration of this framework focuses on a migration corridor for wild reindeer (Rangifer rangifer) in Southern Norway. By examining the sensitivity of the expected cost of movement between winter and calving ranges to perturbations in local areas, we have identified priority areas crucial for the conservation of this migration corridor. This innovative approach not only holds great promise for conservation and restoration of migration corridors, but also more generally for connectivity corridors between important areas for biodiversity (e.g. protected areas) and climate adaptation. Furthermore, the derivations and computational methods introduced in this work present fundamental features of the RSP framework. These contributions are expected to be of interest to practitioners applying the framework across various disciplines, ranging from ecology, transport and communication networks to machine learning.

Structural and positional ensembled encoding for Graph Transformer

In the Transformer architecture, positional encoding is a vital component because it provides the model with information about the structure and position of data. In Graph Transformer, there have been attempts to introduce different positional encodings and inject additional structural information. Therefore, in terms of integrating positional and structural information, we propose a Structural and Positional Ensembled Graph Transformer (SPEGT). We developed SPEGT by noting the different properties of structural and positional encodings of graphs and the similarity of their computational processes. We have set a unified component that integrates the functionalities: (i) Random Walk Positional Encoding, (ii) Shortest Path Distance between each node, and (iii) Hierarchical Cluster Encoding. We find a problem with a well-known positional encoding and experimentally verify that combining it with other encodings can solve their problem. In addition, SPEGT outperforms previous models on a variety of graph datasets. We also show that SPEGT using unified positional encoding, performs well on structurally indistinguishable graph data through error case analysis.

Network Analysis of Past Presidents of the North American Skull Base Society.

Background Little is known about the relative contributions and interactions of the past presidents of the North American Skull Base Society (NASBS) and skull base centers. Objectives (1) Measure academic contributions of past presidents; (2) identify influential nodes of academic collaboration; (3) identify opportunities for future collaboration. Methods Peer-reviewed publications of past presidents of NASBS from 1964 to July 2019 were identified using Scopus author name search. Network structures were constructed and analyzed using the graph-tool python library to produce a weighted co-authorship network base and compute centrality measures. Girvan-Newman clustering was applied to identify community structure. Network maps were then produced using Gephi network visualization software with force-directed layout algorithms. Results The coauthor network of 29 presidents was fully connected, with a maximum shortest-path distance between presidents of 5. The mean number of connections from each node without respect to weighting was 5.31 (standard deviation [SD]: 3.53), and the mean number of connections with weighting was 8.40 (SD: 7.28). The number of unweighted connections ranged from 1 to 14 and weighted connections ranged from 0.25 to 24.7. Girvan-Newman clustering identified three communities with two that covered 93% of the network. The largest communities contained 14 and 13 presidents. The number of connections was correlated with h-index, both unweighted ( r 2 = 0.34) and weighted ( r 2 = 0.26). Conclusion Network mapping of past presidents of the NASBS helps to capture the history of the NASBS and reveals areas of concentration and influence within the specialty.

Neural graph distance embedding for molecular geometry generation.

This article introduces neural graph distance embedding (nGDE), a method for generating 3D molecular geometries. Leveraging a graph neural network trained on the OE62 dataset of molecular geometries, nGDE predicts interatomic distances based on molecular graphs. These distances are then used in multidimensional scaling to produce 3D geometries, subsequently refined with standard bioorganic forcefields. The machine learning-based graph distance introduced herein is found to be an improvement over the conventional shortest path distances used in graph drawing. Comparative analysis with a state-of-the-art distance geometry method demonstrates nGDE's competitive performance, particularly showcasing robustness in handling polycyclic molecules-a challenge for existing methods.

Hierarchical path planner combining probabilistic roadmap and deep deterministic policy gradient for unmanned ground vehicles with non-holonomic constraints

Path planning plays a vital role in autonomous driving as it needs to guide the vehicle to achieve the target position without collision while satisfying the vehicle's non-holonomic constraints. A good path planner should be able to cope with sophisticated environments and try to make the planned path as short as possible. Traditional path planning methods when being applied on four-wheel vehicles may suffer from one of the following disadvantages including conflicting with non-holonomic constraints, far from close-optimal length solution, or easy to get stuck in specific environments. In this paper, a hierarchical path planning method for a four-wheel vehicle combining probabilistic roadmap (PRM) and deep deterministic policy gradient (DDPG) is proposed to address existing problems. In the upper level, PRM is used to generate a guidance path quickly, which doesn't consider the vehicle's non-holonomic constraints but gives the sketch of the path that helps the vehicle to jump out of some dilemmas in specific environments while maintaining a relatively short path distance. In the lower level, reinforcement learning, specifically DDPG, is used to optimize the guidance path generated by PRM considering multiple factors including non-holonomic constraints and obstacle avoidance. The proposed method is validated in four different environments including a simple map, an easy-to-stuck specific map, a maze-like complex map and an office-like complex map. Results show that the proposed method could generate a smooth path satisfying non-holonomic constraints while demonstrating desirable obstacle avoidance performance. The planned path of the proposed method is superior to that of both traditional and state-of-the-art methods in terms of path length and smoothness, which could be 1.3–12.9 % shorter and 2.6–52.1 % smoother in different environments.

Enhancing sustainable urban air transportation: Low-noise UAS flight planning using noise assessment simulator

Low-altitude flights of unmanned aircraft systems (UASs), such as drones, can cause substantial noise pollution in urban areas. This study aims to tackle the crucial issue of noise in UAS flight planning and analyze the feasibility of implementing low-noise urban flights at a micro level. We employ a virtual flight simulator to accurately model the UAS noise impact in realistic flights and optimize the flight path via a heuristic algorithm accordingly. The flight noise assessment incorporates a sound source modeling technique for practical UAS models and an efficient Gaussian beam tracing method for outdoor noise propagation in realistic environments. Case studies for flight simulations are conducted in a representative resident community and metropolitan area to evaluate the noise impact resulting from different flight paths. By comparing our approach with benchmark shortest-distance paths, we validate its effectiveness in significantly reducing en-route noise exposure, encompassing both instantaneous and continuous noise levels. This method holds great potential for contributing to the planning and management of urban air transport systems. It effectively mitigates noise impact, promoting quieter and more environmentally friendly UAS operations and sustainable urban transportation.

SPASTC: a Spatial Partitioning Algorithm for Scalable Travel-time Computation

Travel-time computation with large transportation networks is often computationally intensive for two main reasons: 1) large computer memory is required to handle large networks; and 2) calculating shortest-distance paths over large networks is computing intensive. Therefore, previous research tends to limit their spatial extent to reduce computational intensity or resolve computational intensity with advanced cyberinfrastructure. In this context, this article describes a new Spatial Partitioning Algorithm for Scalable Travel-time Computation (SPASTC) that is designed based on spatial domain decomposition with computer memory limit explicitly considered. SPASTC preserves spatial relationships required for travel-time computation and respects a user-specified memory limit, which allows efficient and large-scale travel-time computation within the given memory limit. We demonstrate SPASTC by computing spatial accessibility to hospital beds across the conterminous United States. Our case study shows that SPASTC achieves significant efficiency and scalability making the travel-time computation tens of times faster.

Bridging the gap between movement data and connectivity analysis using the Time-Explicit Habitat Selection (TEHS) model

BackgroundUnderstanding how to connect habitat remnants to facilitate the movement of species is a critical task in an increasingly fragmented world impacted by human activities. The identification of dispersal routes and corridors through connectivity analysis requires measures of landscape resistance but there has been no consensus on how to calculate resistance from habitat characteristics, potentially leading to very different connectivity outcomes.MethodsWe propose a new model, called the Time-Explicit Habitat Selection (TEHS) model, that can be directly used for connectivity analysis. The TEHS model decomposes the movement process in a principled approach into a time and a selection component, providing complementary information regarding space use by separately assessing the drivers of time to traverse the landscape and the drivers of habitat selection. These models are illustrated using GPS-tracking data from giant anteaters (Myrmecophaga tridactyla) in the Pantanal wetlands of Brazil.ResultsThe time model revealed that the fastest movements tended to occur between 8 p.m. and 5 a.m., suggesting a crepuscular/nocturnal behavior. Giant anteaters moved faster over wetlands while moving much slower over forests and savannas, in comparison to grasslands. We also found that wetlands were consistently avoided whereas forest and savannas tended to be selected. Importantly, this model revealed that selection for forest increased with temperature, suggesting that forests may act as important thermal shelters when temperatures are high. Finally, using the spatial absorbing Markov chain framework, we show that the TEHS model results can be used to simulate movement and connectivity within a fragmented landscape, revealing that giant anteaters will often not use the shortest-distance path to the destination patch due to avoidance of certain habitats.ConclusionsThe proposed approach can be used to characterize how landscape features are perceived by individuals through the decomposition of movement patterns into a time and a habitat selection component. Additionally, this framework can help bridge the gap between movement-based models and connectivity analysis, enabling the generation of time-explicit connectivity results.

SHORTEST PATH DISTANCE AND HAUSDORFF DIMENSION OF SIERPINSKI NETWORKS

In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.

An exact algorithm for maximum electric vehicle flow coverage problem with heterogeneous chargers, nonlinear charging time and route deviations

Typical electric vehicles (EVs) should be recharged multiple times to reach a long distance due to the limited travel ranges. The EV flow covering problem determines the locations of charging stations to maximize the “covered” OD flows, respecting a given budget for the new charging stations. This paper proposes an exact algorithm for solving the problem by considering the heterogeneous EV chargers, nonlinear charging time, and route deviations from the shortest distance paths. We develop an exact Benders decomposition-based algorithm, in which the Benders subproblem utilizes a nested cut-generation via a customized labeling algorithm. Two methods for solving the Benders subproblem are developed, which are combined to accelerate the Benders cut generation. In addition, we present a heuristic algorithm based on the proposed exact algorithm for the larger-sized problems. The computational results show that the proposed algorithm could solve real-life problems. Especially, the heuristic algorithm could solve problems up to 339 nodes and 500 km of the EV’s travel range. The extensive computational study shows that addressing the multiple charger types, the charging time, and the deviation routes can be crucial to provide realistic charging infrastructure for EVs.

Hierarchical Cut Labelling - Scaling Up Distance Queries on Road Networks

Answering the shortest-path distance between two arbitrary locations is a fundamental problem in road networks. Labelling-based solutions are the current state-of-the-arts to render fast response time, which can generally be categorised into hub-based labellings, highway-based labellings, and tree decomposition labellings. Hub-based and highway-based labellings exploit hierarchical structures of road networks with the aim to reduce labelling size for improving query efficiency. However, these solutions still result in large search spaces on distance labels at query time, particularly when road networks are large. Tree decomposition labellings leverage a hierarchy of vertices to reduce search spaces over distance labels at query time, but such a hierarchy is generated using tree decomposition techniques, which may yield very large labelling sizes and slow querying. In this paper, we propose a novel solution hierarchical cut 2-hop labelling (HC2L) to address the drawbacks of the existing works. Our solution combines the benefits of hierarchical structures from both perspectives - reduce the size of a distance labelling at preprocessing time and further reduce the search space on a distance labelling at query time. At its core, we propose a new hierarchy, balanced tree hierarchy, which enables a fast, efficient data structure to reduce the size of distance labelling and to select a very small subset of labels to compute the shortest-path distance at query time. To speed up the construction process of HC2L, we further propose a parallel variant of our method, namely HC2L^p. We have evaluated our solution on 10 large real-world road networks through extensive experiments. The results show that our method is 1.5-4 times faster in terms of query processing while being comparable in terms of labelling construction time and achieving up to 60% smaller labelling size compared to the state-of-the-art approaches.

GEODESIC DISTANCES ON SIERPINSKI-LIKE SPONGES AND THEIR SKELETON NETWORKS

In this paper, we investigate the equivalence of connectedness for the Sierpinski-like sponge and skeleton networks, and find out the relation between the geodesic distance on the sponge and renormalized shortest path distance on the skeleton networks. Furthermore, under some assumption on the IFS, we obtain the comparability of the Manhattan distance and the geodesic distance on the sponge.

An improved gravity centrality for finding important nodes in multi-layer networks based on multi-PageRank

How to identify important nodes in multi-layer networks is still an unresolved issue in network science, which has aroused the interest of many researchers. In addition, the relationships between entities in many real-world systems are diverse and can be modeled as multi-layer networks. In the past few decades, scholars have defined various centrality methods from different perspectives to find influential nodes in multi-layer networks, but they only utilize the local or global topology information. Recently, various gravity centralities that utilize both the local and global topological structure information have been defined for identifying key nodes in single-layer networks. In the gravity model, the interaction between two nodes is related to their mass and distance. In consideration of the advantages of gravity model, in this paper, we define an improved gravity centrality for identifying key nodes in multi-layer networks based on multi-PageRank centrality, referred to as the PRGC. Unlike the existing gravity centralities that treat each node degree as its mass, our proposed centrality views the multi-PageRank centrality value of each node as its mass. Furthermore, PRGC weights the shortest path distance between any two nodes across all network layers to define their distance in multi-layer networks. Finally, to illustrate the effectiveness and superiority of the proposed centrality approach, numerical experiments are conducted on six real-world multi-layer networks show that our proposed centrality method outperforms state-of-the-art centralities.

On metric dimensions of flower graphs

The metric dimension of a connected graph G is the smallest number of nodes (resolving set) required to identify all other nodes based on shortest path distances uniquely. The notion of resolving set is vital in robotic navigation and to create various plan of action for the mastermind game. If certain vertices of a set S ⊂ V(G) resolve each pair of nodes u and v of G, then that set is a resolving set. A metric basis represents the lowest number of nodes in the set S. In this study, we describe the distance matrix and metric dimension of sunflower graphs and flower snarks.

Local intrinsic dimensionality measures for graphs, with applications to graph embeddings

The notion of local intrinsic dimensionality (LID) is an important advancement in data dimensionality analysis, with applications in data mining, machine learning and similarity search problems. Existing distance-based LID estimators were designed for tabular datasets encompassing data points represented as vectors in a Euclidean space. After discussing their limitations for graph-structured data considering graph embeddings and graph distances, we propose NC-LID, a novel LID-related measure for quantifying the discriminatory power of the shortest-path distance with respect to natural communities of nodes as their intrinsic localities. It is shown how this measure can be used to design LID-aware graph embedding algorithms by formulating two LID-elastic variants of node2vec with personalized hyperparameters that are adjusted according to NC-LID values. Our empirical analysis of NC-LID on a large number of real-world graphs shows that this measure is able to point to nodes with high link reconstruction errors in node2vec embeddings better than node centrality metrics. The experimental evaluation also shows that the proposed LID-elastic node2vec extensions improve node2vec by better preserving graph structure in generated embeddings.

On algorithmic complexity of imprecise spanners

Let t>1 be a real number. A geometric t-spanner is a geometric graph for a point set in Rd with straight line segments between vertices such that the ratio of the shortest-path distance between every pair of vertices in the graph (with Euclidean edge lengths) to their actual Euclidean distance is at most t.An imprecise point set is modeled by a set R of regions in Rd. If one chooses a point inside each region of R, then the resulting point set is called a precise instance from R. An imprecise t-spanner for an imprecise point set R is a graph G=(R,E) such that for each precise instance S from R, graph GS=(S,ES), where ES is the set of edges corresponding to E and S, is a t-spanner.In this paper, we show an imprecise point set R of n straight-line segments in the plane such that any imprecise t-spanner for R has Ω(n2) edges. Then, we give an algorithm that computes an imprecise t-spanner for a set of n pairwise disjoint d-dimensional balls with arbitrary sizes. This imprecise t-spanner has O(n/(t−1)d) edges and can be computed in O(nlog⁡n/(t−1)d) time. Finally, we show that given an imprecise spanner, finding a precise instance such that its corresponding precise spanner has minimum dilation between all possible precise instances of the imprecise spanner is NP-hard, no matter if crossing edges are allowed or not.