Shortest Path Length Research Articles

Associations of glymphatic function with structural network and cognition in self-limited epilepsy with centrotemporal spikes

PurposeTo investigate glymphatic function by Virchow-Robin space (VRS) counts and volume in patients with newly diagnosed self-limited epilepsy with centrotemporal spikes (SeLECTS) and evaluate its relationship with structural connectivity and cognitive impairment. MethodsThirty-two children with SeLECTS and thirty-two age- and sex-matched typically developing (TD) children were enrolled in this study. VRS counts and volume were quantified. Structural networks were constructed and the topological metrics were analyzed. Wechsler Intelligence Scale (WISC) was used to assess cognitive function in all participants. Correlation analysis assessed the association between VRS counts and volume, network connectivity, and cognitive impairment. Mediation effects of topological metrics of the structural networks on the relationship between glymphatic function and cognitive impairment were explored. ResultsPatients with SeLECTS showed a higher VRS counts, VRS volume, and global shortest path length (Lp); they also showed a lower global efficiency (Eg). VRS counts and volume were significantly correlated with full-scale intelligence quotient (FIQ) (r_VRS counts = -0.520, r_VRS volume = -0.639), performance intelligence quotient (PIQ) (r_VRS counts = -0.693, r_VRS volume = -0.597), verbal intelligence quotient (VIQ) (r_VRS counts = -0.713, r_VRS volume = -0.699), Eg (r_VRS counts = -0.499, r_VRS volume = -0.490), and Lp (r_VRS volume = 0.671) in patients with SeLECTS. Eg mediated 24.59% of the effects for the relationship between VRS volume and FIQ. ConclusionGlymphatic function may be impaired in SeLECTS reflected by VRS counts and volume. Glymphatic dysfunction may result in cognitive impairment by disrupting structural connectivity in SeLECTS.

Power law of path multiplicity in complex networks.

Complex networks describe a wide range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a vital role in network science. Rather than focusing on the path length or path centrality, here we draw attention to the path multiplicity related to decision-making efficiency, which is defined as the number of shortest paths between node pairs and thus characterizes the routing choice diversity. Notably, through extensive empirical investigations from this new perspective, we surprisingly observe a "hesitant-world" feature along with the "small-world" feature and find a universal power-law of the path multiplicity, meaning that a small number of node pairs possess high path multiplicity. We demonstrate that the power-law of path multiplicity is much stronger than the power-law of node degree, which is known as the scale-free property. Then, we show that these phenomena cannot be captured by existing classical network models. Furthermore, we explore the relationship between the path multiplicity and existing typical network metrics, such as average shortest path length, clustering coefficient, assortativity coefficient, and node centralities. We demonstrate that the path multiplicity is a distinctive network metric. These results expand our knowledge of network structure and provide a novel viewpoint for network design and optimization with significant potential applications in biological, social, and man-made networks.

A Full-Coverage Path Planning Method for an Orchard Mower Based on the Dung Beetle Optimization Algorithm

In order to optimize the operating path of orchard mowers and improve their efficiency, we propose an MI-DBO (multi-strategy improved dung beetle optimization algorithm) to solve the problem of full-coverage path planning for mowers in standardized quadrilateral orchard environments. First, we analyzed the operation scenario of lawn mowers in standardized orchards, transformed the full-coverage path planning problem into a TSP (traveling salesman problem), and mathematically modeled the U-turn and T-turn strategies based on the characteristics of lawn mowers in orchards. Furthermore, in order to overcome the issue of uneven distribution of individual positions in the DBO (dung beetle optimization) algorithm and the tendency to fall into local optimal solutions, we incorporated Bernoulli mapping and the convex lens reverse-learning strategy in the initialization stage of DBO to ensure a uniform distribution of the initial population. During the algorithm iteration stage, we incorporated the Levy flight strategy into the position update formulas of breeding beetles, foraging beetles, and stealing beetles in the DBO algorithm, allowing them to escape from local optimal solutions. Simulation experiments show that for 18 types of orchards with different parameters, MI-DBO can find the mowing machine’s operation paths. Compared with other common swarm intelligence algorithms, MI-DBO has the shortest average path length of 456.36 m and can ensure faster optimization efficiency. Field experiments indicate that the algorithm-optimized paths do not effectively reduce the mowing machine’s missed mowing rate, but the overall missed mowing rate is controlled below 0.8%, allowing for the completion of mowing operations effectively. Compared with other algorithms, MI-DBO has the least time and fuel consumption for operations. Compared to the row-by-row operation method, using paths generated by MI-DBO reduces the operation time by an average of 1193.67 s and the fuel consumption rate by an average of 9.99%. Compared to paths generated by DBO, the operation time is reduced by an average of 314.33 s and the fuel consumption rate by an average of 2.79%.

Influence of network structure on spreading dynamics via tie range

Abstract There are various phenomena of malicious information spreading in the real society, which cause many negative impacts on the society. In order to better control the spreading, it is crucial to reveal the influence of network structure on network spreading. Motifs, as fundamental structures within a network, play a significant role in spreading. Therefore, it is of interest to investigate the influence of the structural characteristics of basic network motifs on spreading dynamics. Considering the edges of the basic network motifs in an undirected network correspond to different tie ranges, two edge removal strategies are proposed, short ties priority removal strategy and long ties priority removal strategy. The tie range represents the second shortest path length between two connected nodes. The study focuses on analyzing how the proposed strategies impact network spreading and network structure, as well as examining the influence of network structure on network spreading. Our findings indicate that the long ties priority removal strategy is most effective in controlling network spreading, especially in terms of spread range and spread velocity. In terms of network structure, the clustering coefficient and the diameter of network also have an effect on the network spreading, and the triangular structure as an important motif structure effectively inhibits the spreading.

Complex network of trophic interactions in Burdwood Bank, a sub-Antarctic oceanic marine protected area

The world’s oceans designated under marine protection have increased recently. Most marine protected areas (MPAs) target vulnerable, keystone, charismatic, and/or endemic species. In the sub-Antarctic, ocean protection is associated with oceanic islands, except for the MPAs Namuncurá-Burdwood Bank I and II (MPA N-BB; ~53-55°S, ~56-62°W), which are associated with a submarine plateau and a southern deep slope, respectively. We present the first analysis of the predator-prey network for the MPA N-BB, applying a topological network approach to characterise the complexity and structure of the food web and to identify the species’ role. The MPA N-BB food web consists of 1788 interactions and 379 species, with a connectance of 0.01. Almost half of the consumers feed at more than one trophic level (0.48), and the network displays a small-world pattern (short path length, high clustering of compartments). This network pattern suggests that the ecosystem might be vulnerable to perturbations targeting highly connected species, although some properties might provide resilience and resistance, resulting in a rearranged structure that preserves its original functions. Several species arise as being important in trophic structure and functioning and response to perturbations. Generalist species, mainly fishes, play a crucial role in the bentho-pelagic coupling and should be considered as relevant energy transfer agents for the ecosystem. We argue that the diversity of species, including both the benthic and pelagic habitats, is responsible for securing the connectivity within the food web to withstand perturbations, thereby contributing to the structure and stability of the ecosystem.

In vitro and in vivo evaluation of a tetrazine-conjugated poly-L-lysine effector molecule labeled with astatine-211

BackgroundA significant challenge in cancer therapy lies in eradicating hidden disseminated tumor cells. Within Nuclear Medicine, Targeted Alpha Therapy is a promising approach for cancer treatment tackling disseminated cancer. As tumor size decreases, alpha-particles gain prominence due to their high Linear Energy Transfer (LET) and short path length. Among alpha-particle emitters, 211At stands out with its 7.2 hour half-life and 100% alpha emission decay. However, optimizing the pharmacokinetics of radiopharmaceuticals with short lived radionuclides such as 211At is pivotal, and in this regard, pretargeting is a valuable tool. This method involves priming the tumor with a modified monoclonal antibody capable of binding both the tumor antigen and the radiolabeled carrier, termed the “effector molecule. This smaller, faster-clearing molecule improves efficacy. Utilizing the Diels Alder click reaction between Tetrazine (Tz) and Trans-cyclooctene (TCO), the Tz-substituted effector molecule combines seamlessly with the TCO-modified antibody. This study aims to evaluate the in vivo biodistribution of two Poly-L-Lysine-based effector molecule sizes (10 and 21 kDa), labelled with 211At, and the in vitro binding of the most favorable polymer size, in order to optimize the pretargeted radioimmunotherapy with 211At.ResultsIn vivo results favor the smaller polymer’s biodistribution pattern over the larger one, which accumulates in organs like the liver and spleen. This is especially evident when comparing the biodistribution of the smaller polymer to a directly labelled monoclonal antibody. The smaller variant also shows rapid and efficient binding to SKOV-3 cells preloaded with TCO-modified Trastuzumab in vitro, emphasizing its potential. Both polymer sizes showed equal or better in vivo stability of the astatine-carbon bond compared to a monoclonal antibody labelled with the same prosthetic group.ConclusionsOverall, the small Poly-L-Lysine-based effector molecule (10 kDa) holds the most promise for future research, exhibiting significantly lower uptake in the kidneys and spleen compared to the larger effector (21 kDa) while maintaining an in vivo stability of the astatine-carbon bond comparable to or better than intact antibodies. A proof of concept in vitro cell study demonstrates rapid reaction between the small astatinated effector and a TCO-labelled antibody, indicating the potential of this novel Poly-L-Lysine-based pretargeting system for further investigation in an in vivo tumor model.

Highly sensitive absorbance measurement using droplet microfluidics integrated with an oil extraction and long pathlength detection flow cell.

In droplet microfluidics, UV-Vis absorption spectroscopy along with colorimetric assays have been widely used for chemical and biochemical analysis. However, the sensitivity of the measurement can be limited by the short optical pathlength. Here we report a novel design to enhance the sensitivity by removing oil and converting the droplets into a single-phase aqueous flow, which can be measured within a U-shape channel with long optical pathlength. The flow cells were fabricated via 3D printing. The calibration results have demonstrated complete oil removal and effective optical pathlengths similar to the designed channel lengths (from 5 to 20mm). The flow cell was further employed in a droplet microfluidic-based phosphate sensing system. The measured phosphate levels displayed excellent consistency with data obtained from traditional UV spectroscopy analysis. This flow cell design overcomes the limitations of short optical pathlengths in droplet microfluidics and has the potential to be used for in situ and continuous monitoring.

Coprime networks of the composite numbers: Pseudo-randomness and synchronizability

In this paper, we propose a network whose nodes are labeled by the composite numbers and two nodes are connected by an undirected link if they are relatively prime to each other. As the size of the network increases, the network will be connected whenever the largest possible node index n≥49. To investigate how the nodes are connected, we analytically describe that the link density saturates to 6/π2, whereas the average degree increases linearly with slope 6/π2 with the size of the network. To investigate how the neighbors of the nodes are connected to each other, we find the shortest path length will be at most 3 for 49≤n≤288 and it is at most 2 for n≥289. We also derive an analytic expression for the local clustering coefficients of the nodes, which quantifies how close the neighbors of a node to form a triangle. We also provide an expression for the number of r-length labeled cycles, which indicates the existence of a cycle of length at most O(logn). Finally, we show that this graph sequence is actually a sequence of weakly pseudo-random graphs. We numerically verify our observed analytical results. As a possible application, we have observed less synchronizability (the ratio of the largest and smallest positive eigenvalue of the Laplacian matrix is high) as compared to Erdős–Rényi random network and Barabási–Albert network. This unusual observation is consistent with the prolonged transient behaviors of ecological and predator–prey networks which can easily avoid the global synchronization.

A Dynamic Evolutionary Analysis of the Vulnerability of Global Food Trade Networks

The global food trade network (FTN) is a critical infrastructure for achieving the Sustainable Development Goals (SDGs). The FTN’s vulnerability to geopolitical conflicts, public health crises, and climate change events directly impacts food security and the ability to meet the SDGs. This study aims to analyze the dynamic evolution of the vulnerability of FTN, focusing on the period from 2000 to 2022, to aim for strategies for enhancing the resilience and sustainability of the global food system. Based on complex network analysis, we examine the structural characteristics and evolution of FTN for four major crops: soybeans, wheat, rice, and maize. We identify a trend towards increased network density and regionalization, with a decline in average shortest path length (ASPL) and an increase in the average clustering coefficient (ACC). These changes indicate a shift towards a more interconnected and resilient FTN in response to various shocks, including the COVID-19 pandemic and the Russia–Ukraine conflict. The findings suggest that the global FTN has adapted to increase resilience, which is essential for achieving the SDGs related to food security and sustainable development. The study’s insights can guide policy interventions to further strengthen the network against future shocks and promote global food security.

Stable solvatochromic light-emitting diodes and their potential for color temperature adjustment of white LEDs

A viable technology for liquid phosphor-based light-emitting diodes (LEDs) with emission color tuneability is described. These devices are based on Tris(bipyridine)ruthenium(II) chloride but can be constructed from other similar metal coordination charge transfer complexes. The Frank-Condon excited state generated upon the absorption of blue (450 nm) pump photons has a large electric dipole moment due to intramolecular metal-to-ligand charge transfer from the ruthenium atom to one specific bipyridyl ligand. Polar solvents respond to the dipole field creating a solvatochromic shift that is solvent dependent. The devices were fully sealed in either a long path length or a short path length configuration. The latter encapsulating the luminescing medium in hollow silica spheres that can be easily applied like a slurry on top of InGaN/GaN LED dies. The devices were optically, thermally and environmentally stable. Also discussed is the possibility of using solvatochromic emitters for achieving color temperature tuneability in white LEDs.

Altered individual gray matter structural covariance networks in early abstinence patients with alcohol dependence.

While alterations in cortical thickness have been widely observed in individuals with alcohol dependence, knowledge about cortical thickness-based structural covariance networks is limited. This study aimed to explore the topological disorganization of structural covariance networks based on cortical thickness at the single-subject level among patients with alcohol dependence. Structural imaging data were obtained from 61 patients with alcohol dependence during early abstinence and 59 healthy controls. The single-subject structural covariance networks were constructed based on cortical thickness data from 68 brain regions and were analyzed using graph theory. The relationships between network architecture and clinical characteristics were further investigated using partial correlation analysis. In the structural covariance networks, both patients with alcohol dependence and healthy controls displayed small-world topology. However, compared to controls, alcohol-dependent individuals exhibited significantly altered global network properties characterized by greater normalized shortest path length, greater shortest path length, and lower global efficiency. Patients exhibited lower degree centrality and nodal efficiency, primarily in the right precuneus. Additionally, scores on the Alcohol Use Disorder Identification Test were negatively correlated with the degree centrality and nodal efficiency of the left middle temporal gyrus. The results of this correlation analysis did not survive after multiple comparisons in the exploratory analysis. Our findings may reveal alterations in the topological organization of gray matter networks in alcoholism patients, which may contribute to understanding the mechanisms of alcohol addiction from a network perspective.

Electroacupuncture modulates abnormal brain connectivity after ischemia reperfusion injury in rats: A graph theory-based approach.

Electroacupuncture (EA) has been shown to facilitate brain plasticity-related functional recovery following ischemic stroke. The functional magnetic resonance imaging technique can be used to determine the range and mode of brain activation. After stroke, EA has been shown to alter brain connectivity, whereas EA's effect on brain network topology properties remains unclear. An evaluation of EA's effects on global and nodal topological properties in rats with ischemia reperfusion was conducted in this study. There were three groups of adult male Sprague-Dawley rats: sham-operated group (sham group), middle cerebral artery occlusion/reperfusion (MCAO/R) group, and MCAO/R plus EA (MCAO/R+EA) group. The differences in global and nodal topological properties, including shortest path length, global efficiency, local efficiency, small-worldness index, betweenness centrality (BC), and degree centrality (DC) were estimated. Graphical network analyses revealed that, as compared with the sham group, the MCAO/R group demonstrated a decrease in BC value in the right ventral hippocampus and increased BC in the right substantia nigra, accompanied by increased DC in the left nucleus accumbens shell (AcbSh). The BC was increased in the right hippocampus ventral and decreased in the right substantia nigra after EA intervention, and MCAO/R+EA resulted in a decreased DC in left AcbSh compared to MCAO/R. The results of this study provide a potential basis for EA to promote cognitive and motor function recovery after ischemic stroke.

A New Approach to Computationally- Successful Linear and Polynomial Regression Analytics of Large Data in Medicine

Features like assortative mixing; high clustering, short average path lengths, broad degree distributions, and community structure have been the subject of numerous recent social network studies. All of these features are met by the model that is introduced in this study. Additionally, our model enables interactions between various communities, fostering a rich network environment. The asymptotically scale-free degree distribution is maintained by our model, which achieves a high clustering coefficient. In our model, the community structure is generated by a mix of mechanisms involving implicit preferential attachment and random attachment. We expand our consideration to include neighbor of neighbor of Initial Contact (NNIC) as well, in contrast to earlier approaches that solely focused on neighbor of Initial Contact (NIC) as an implicit preferential contact. If a newly added vertex chooses more than one initial contact, this extension makes it possible for contacts between those initial contacts to occur. Consequently, our model facilitates the development of complex social networks beyond those used as basic references. Finally, we conduct centrality calculations on both the existing model and our developed model, providing a comparative analysis of the results.

A Novel Approach for Analyzing Temporal Influence Dynamics in Social Networks

Features like assortative mixing; high clustering, short average path lengths, broad degree distributions, and community structure have been the subject of numerous recent social network studies. All of these features are met by the model that is introduced in this study. Additionally, our model enables interactions between various communities, fostering a rich network environment. The asymptotically scale-free degree distribution is maintained by our model, which achieves a high clustering coefficient. In our model, the community structure is generated by a mix of mechanisms involving implicit preferential attachment and random attachment. We expand our consideration to include neighbor of neighbor of Initial Contact (NNIC) as well, in contrast to earlier approaches that solely focused on neighbor of Initial Contact (NIC) as an implicit preferential contact. If a newly added vertex chooses more than one initial contact, this extension makes it possible for contacts between those initial contacts to occur. Consequently, our model facilitates the development of complex social networks beyond those used as basic references. Finally, we conduct centrality calculations on both the existing model and our developed model, providing a comparative analysis of the results.

On the transient and equilibrium features of growing fractal complex networks

Complex networks have certain properties that distinguish them from their respective uniform or regular counterparts. One of these properties is the variation of topological properties along different hierarchical levels. In this work, we study how networks that are constructed by repeatedly incorporating a given motif exhibit this property. A motif is henceforth understood as a small subgraph with a reference node where the incorporation respectively occurs. We generate fractal networks using different motifs and observe how their structures change along the growth stages. Two regimes are respectively identified: transient and equilibrium. The former is characterized by significant topological changes that depend on the motif topology, while the equilibrium regime shows more stable, parallel trajectories. A more systematic analysis revealed that the betweenness centrality and the average shortest path lengths were the main topological properties accounting for the changes along the network growth.

Topological Perturbations in the Functional Connectome Support the Deficit/Non-deficit Distinction in Antipsychotic Medication-Naïve First Episode Psychosis Patients.

Heterogeneity in the etiology, pathophysiology, and clinical features of schizophrenia challenges clinicians and researchers. A helpful approach could be stratifying patients according to the presence or absence of clinical features of the deficit syndrome (DS). DS is characterized by enduring and primary negative symptoms, a clinically less heterogeneous subtype of the illness, and patients with features of DS are thought to present abnormal brain network characteristics, however, this idea has received limited attention. We investigated functional brain network topology in patients displaying deficit features and those who do not. We applied graph theory analytics to resting-state functional magnetic resonance imaging data of 61 antipsychotic medication-naïve first episode psychosis patients, 18 DS and 43 non-deficit schizophrenia (NDS), and 72 healthy controls (HC). We quantified small-worldness, global and nodal efficiency measures, shortest path length, nodal local efficiency, and synchronization and contrasted them among the 3 groups. DS presented decreased network integration and segregation compared to HC and NDS. DS showed lower global efficiency, longer global path lengths, and lower global local efficiency. Nodal efficiency was lower and the shortest path length was longer in DS in default mode, ventral attention, dorsal attention, frontoparietal, limbic, somatomotor, and visual networks compared to HC. Compared to NDS, DS showed lower efficiency and longer shortest path length in default mode, limbic, somatomotor, and visual networks. Our data supports increasing evidence, based on topological perturbations of the functional connectome, that deficit syndrome may be a distinct form of the illness.

Aberrant brain topological organization and granger causality connectivity in Parkinson's disease with impulse control disorders.

Impulse control disorders (ICDs) refer to the common neuropsychiatric complication of Parkinson's disease (PD). The white matter (WM) topological organization and its impact on brain networks remain to be established. A total of 17 PD patients with ICD (PD-ICD), 17 without ICD (PD-NICD), and 18 healthy controls (HCs) were recruited. Graph theoretic analyses and Granger causality analyses were combined to investigate WM topological organization and the directional connection patterns of key regions. Compared to PD-NICD, ICD patients showed abnormal global properties, including decreased shortest path length (Lp) and increased global efficiency (Eg). Locally, the ICD group manifested abnormal nodal topological parameters predominantly in the left middle cingulate gyrus (MCG) and left superior cerebellum. Decreased directional connectivity from the left MCG to the right medial superior frontal gyrus was observed in the PD-ICD group. ICD severity was significantly correlated with Lp and Eg. Our findings reflected that ICD patients had excessively optimized WM topological organization, abnormally strengthened nodal structure connections within the reward network, and aberrant causal connectivity in specific cortical- limbic circuits. We hypothesized that the aberrant reward and motor inhibition circuit could play a crucial role in the emergence of ICDs.

Analysis of the Network Efficiency of Chinese Ports in Global Shipping under the Impacts of Typhoons

With the increasing volume of international trade and maritime demand, the requirements for the stability and reliability of the global shipping system are also increasing. The research on the network efficiency of Chinese ports for global shipping can not only examine the importance of Chinese ports in the shipping network but also find out the aspects that need to be improved in the construction of the port’s climate adaptability in the resilience assessment to strengthen port construction and further improve the efficiency of the network. The current study builds a shipping network based on RCEP and systematically examines the key ports in China within the networks. The research paper aims to improve the resilience of the ports and the whole shipping network in response to typhoon disasters. As such, this paper focuses on shipping research based on complex networks and network multi-centricity analysis, followed by a ranking of ports. Firstly, this paper uses UCINET 6 software to build a global shipping network. Such a network evaluates the centrality of ports, calculates the degree of centrality, proximity to centrality, and centrality, and scores them according to the ranking. Then, it selects the top 20 ports in China according to the ranking and researches network efficiency for the listed ports considering the typhoon risks. The analysis of network robustness, average shortest path length, and network efficiency are carried out for the shipping network and China’s essential port nodes in the network. According to the experimental results, no matter the robustness, average shortest path length, or network efficiency, when the important ports of China in the shipping network are affected, they will cause different degrees of impact, and the performance loss caused by multiple ports is higher than that of a single port. They emphasise the significant impact of typhoons on multiple ports and remind people to minimise losses as much as possible based on experimental results, ensuring the stable operation of ports and improving resilience in typhoon prevention under the changing climate. Additionally, they provide a solid foundation to further sustain global shipping network resilience.

Newman-Watts-Strogatz topology in deep echo state networks for speech emotion recognition

Cortical neural connectivity exhibits a small-world (SW) network topology. However, its role in neural information processing remains unclear. In this study, we investigate the learning performance of a Deep Echo State Network (DeepESN) that incorporates the Newman-Watts-Strogatz (NWS) graph topology as a reservoir. The short path length of the SW topology allows input information to reach output nodes faster, and the clustered arrangement of this topology can expand the range of the echo state property. Additionally, in this paper, we seek to identify the best set of these key factors, such as the spectral radius of the reservoir’s weight matrix and the hyperparameters neighbors' and probabilities. We evaluate the NWS-DeepESNs on four Speech Emotion Recognition (SER) tasks, which are RAVDESS, Emo-db, SAVEE, and TESS databases. By examining the NWS-DeepESN’s performance on SER tasks, we aim to determine the role of the NWS graph topology in enhancing neural information processing. The obtained results exhibited significant improvements in recognition accuracies (weighted and unweighted) with (76.45%, 75.79%), (87.89%, 87.14%), (99%, 98.62%), and (63%, 62.24%), respectively, for RAVDESS, Emo-db, SAVEE, and TESS databases. The proposed approach improves emotion recognition capabilities and yields more accurate results compared to existing state-of-the-art approaches.

ERRRT-A*: A fast path planning algorithm suitable for large-scale scenes

In large-scale scenes, how to quickly obtain paths while ensuring the shortest possible path length is a key issue. Rapidly-exploring Random Tree (RRT) have the characteristic of quickly exploring the state space, but it is often difficult to obtain a short path. To overcome this problem, this paper proposes an improved RRT algorithm based on equidistance retention strategy and A* local search(ERRRT-A*). First, RRT is used for large-step global fast exploration to obtain approximate paths. Then, an equidistance retention strategy is used to discard most of the points and retain a small number of key points. Finally, A* is used to search between each segment to obtain a new path. The ERRRT-A* algorithm is compared with other commonly used algorithms on maps of different size in terms of path length and planning time. Simulation results indicate that compared with other algorithms, this algorithm achieves fast planning in large-scale scenes while obtaining short path length, which can effectively balance the path length and planning time.