Shortest Path Tree Research Articles

Resilience enhancement for interdependent power systems by AI-assisted disaster response

The failure of urban Electrical Distribution Systems (EDSs) can lead to direct or indirect consequences for their interdependent critical infrastructures, for example, the hospitals, the fire department, etc., negatively affecting the well-being of citizens in the city. To improve the resilience of the coupled power network, the Operational Interdependence Simulator (OIS) is proposed to help prioritize the queue of failure recovery and Minimum Spanning Tree and Shortest Path Tree topology reconfiguration to minimize critical load downtime. Additionally, AI agents are introduced to assist decision-making processes. By utilizing machine learning and training in thousands of offline scenarios, the system can be used for real-time calculation of the optimal recovery paths when given the number and location of electrical faults. The IEEE 70-node distribution system case validated the high prediction accuracy and post-disaster topology reconfiguration while considering the interdependencies.

On the aggregation of FIBs at ICN routers using routing strategy

Utilizing in-network caching is essential for the current communication network. In the last decade, ICN (Information-Centric Networking) has been under the spotlight as a network that mainly focuses on transmitted and received data rather than on hosts that transmit and receive data. In ICNs, to appropriately forward request packets, a router maintains a routing table called FIB (Forwarding Information Base). However, it is unsuitable for us to assume that FIB can store entries of all contents within a network. This is mainly because the FIB memory is not large enough to store the prefix of all contents. Thus, for realizing global-scale ICNs, it is crucial to develop an effective technique to reduce the size of FIB. In this paper, to tackle the reduction in the FIB size with the aggregation, we propose a routing strategy called constrained shortest-path tree (CSPT) routing. The fundamental idea of our CSPT routing is to combine shortest-paths on the network and that on a shortest-path tree of the network, which is intended to enhance the effect of FIB aggregation. Furthermore, we extensively investigate the relationship, i.e., trade-off, between the FIB aggregation and the communication performance of ICN using CSPT routing. Consequently, we reveal that our CSPT routing can dramatically reduce the number of FIB entries while suppressing the increase in the number of hops required to deliver request packets.

Comparison of data-driven thresholding methods using directed functional brain networks.

Over the past two centuries, intensive empirical research has been conducted on the human brain. As an electroencephalogram (EEG) records millisecond-to-millisecond changes in the electrical potentials of the brain, it has enormous potential for identifying useful information about neuronal transactions. The EEG data can be modelled as graphs by considering the electrode sites as nodes andthe linear and nonlinear statistical dependencies among them as edges (with weights). The graph theoretical modelling of EEG data results in functional brain networks (FBNs), which are fully connected (complete) weighted undirected/directed networks. Since various brain regions are interconnected via sparse anatomical connections, the weak links can be filtered out from the fullyconnected networks using a process called thresholding. Multiple researchers in the past decades proposed many thresholding methods to gather more insights about the influential neuronal connections of FBNs. This paper reviews various thresholding methods used in the literature for FBN analysis. The analysis showed that data-driven methods are unbiased since no arbitrary user-specified threshold is required. The efficacy of four data-driven thresholding methods, namely minimum spanning tree (MST), minimum connected component (MCC), union of shortest path trees (USPT), and orthogonal minimum spanning tree (OMST), in characterizing cognitive behavior of the normal human brain is analysed using directed FBNs constructed from EEG data of different cognitive load states. The experimental results indicate that both MCC and OMST thresholding methods can detect cognitive load-induced changes in the directed functional brain networks.

Minimizing the Number of Distrustful Nodes on the Path of IP Packet Transmission

One of the important directions for improving modern Wide Area Networks is efficient and secure packet routing. Efficient routing is often based on using the shortest paths, while ensuring security involves preventing the possibility of packet interception. The work is devoted to improving the security of data transmission in IP networks. A new approach is proposed to minimize the number of distrustful nodes on the path of IP packet transmission. By a distrustful node, we mean a node that works correctly in terms of hardware and software and fully implements its data transport functions, but from the point of view of its organizational subordination, we are not sure that the node will not violate security rules to prevent unauthorized access and interception of data. A distrustful node can be either a transit or an end node. To implement this approach, we modified Dijkstra’s shortest path tree construction algorithm. The modified algorithm ensures that we obtain a path that will pass only through trustful nodes, if such a path exists. If there is no such path, the path will have the minimum possible number of distrustful intermediate nodes. The number of intermediate nodes in the path was used as a metric to obtain the shortest path trees. Routing tables of routers, built on the basis of trees obtained using a modified algorithm, provide increased security of data transmission, minimizing the use of distrustful nodes.

Voronoi-based splinegon decomposition and shortest-path tree computation

In motion planning, two-dimensional (2D) splinegons are typically used to represent the contours of 2D objects. In general, a 2D splinegon must be pre-decomposed to support rapid queries of the shortest paths or visibility. Herein, we propose a new region decomposition strategy, known as the Voronoi-based decomposition (VBD), based on the Voronoi diagram of curved boundary-segment generators (either convex or concave). The number of regions in the VBD is O(n+c1). Compared with the well-established horizontal visibility decomposition (HVD), whose complexity is O(n+c2), the VBD decomposition generally contains less regions because c1≤c2, where n is the number of the vertices of the input splinegon, and c1 and c2 are the number of inserted vertices at the boundary. We systematically discuss the usage of VBD. Based on the VBD, the shortest path tree (SPT) can be computed in linear time. Statistics show that the VBD performs faster than HVD in SPT computations. Additionally, based on the SPT, we design algorithms that can rapidly compute the visibility between two points, the visible area of a point/line-segment, and the shortest path between two points.

Towards geodesic ridge curve for region-wise linear representation of geodesic distance field

This paper addresses the challenge of representing geodesic distance fields on triangular meshes in a piecewise linear manner. Unlike general scalar fields, which often assume piecewise linear changes within each triangle, geodesic distance fields pose a unique difficulty due to their non-differentiability at ridge points, where multiple shortest paths may exist. An interesting observation is that the geodesic distance field exhibits an approximately linear change if each triangle is further decomposed into sub-regions by the ridge curve. However, computing the geodesic ridge curve is notoriously difficult. Even when using exact algorithms to infer the ridge curve, desirable results may not be achieved, akin to the well-known medial-axis problem. In this paper, we propose a two-stage algorithm. In the first stage, we employ Dijkstra's algorithm to cut the surface open along the dual structure of the shortest path tree. This operation allows us to extend the surface outward (resembling a double cover but with distinctions), enabling the discovery of longer geodesic paths in the extended surface. In the second stage, any mature geodesic solver, whether exact or approximate, can be employed to predict the real ridge curve. Assuming the fast marching method is used as the solver, despite its limitation of having a single marching direction in a triangle, our extended surface contains multiple copies of each triangle, allowing various geodesic paths to enter the triangle and facilitating ridge curve computation. We further introduce a simple yet effective filtering mechanism to rigorously ensure the connectivity of the output ridge curve. Due to its merits, including robustness and compatibility with any geodesic solver, our algorithm holds great potential for a wide range of applications. We demonstrate its utility in accurate geodesic distance querying and high-fidelity visualization of geodesic iso-lines.

An Analysis of Hierarchical Routing Strategy with Advanced Additional Sensors in WSNs

Two kinds of sensors will be discussed in some sort of wireless sensor networks (WSNs). One is named a normal sensor (called A_nodes) with fixed initial energy, which can get perception data from the surrounding environment and have functions of storage and forwarding. The other is named relay sensor (called B_node) with sufficient energy, which only can store data and forward data. Cluster heads (called A_heads) are chosen among A_nodes by probability mode to create clusters first. Local adjustments would be done inter-cluster. Then the sink is selected as the root and a backbone shortest path tree with hops limited is built dynamically from A_heads, B_Nodes and sink. Inside the backbone shortest path aggregation tree, two steps are done. The first step, select some B_node as cluster head (denoted as B_node) and make local adjustment intra-clusters if it is possible. The second step, adjust the shortest path aggregation tree. By using both particle swarm optimization (PSO) and ant colony optimization (ACO), a traveling salesman problem (TSP) cycle with shorter path length is obtained (this method is noted as TSP_PSO_ACO). This TSP cycle consists of all nodes in the aggregation backbone tree. Along this cycle, energy is offered to nodes except sink. The above strategy would be discussed for its feasibility and time complexity. The experimental results imply that the energy consumption is reduced by using local adjustment. The relative failure rate of nodes can be reduced in the later stage of WSN survival. Offering energy to a small number of nodes several times has no obvious impact on the overall energy consumption and survival time of WSN. The case with some small-sized obstacles in WSN area is also discussed. There are little affections on TSP cycles both from results on theoretical analysis and simulation if there are some obstacles with small size in WSN area.

Dynamic coordinated strategy for parking guidance in a mixed driving parking lot involving human-driven and autonomous vehicles

<abstract> <p>The advent of autonomous vehicles (AVs) poses challenges to parking guidance in mixed driving scenarios involving human-driven vehicles (HVs) and AVs. This study introduced a dynamic and coordinated strategy (DCS) to optimize parking space allocation and path guidance within a mixed driving parking lot, aiming to enhance parking-cruising efficiency. DCS considers the distinctive characteristics of HVs and AVs and dynamically formulates parking guiding schemes based on real-time conditions. The strategy encompasses four main steps: Triggering scheme formulation, identifying preoccupied parking spaces, updating the parking lot traffic network and optimizing the vehicle-path-space matching scheme. A programming model was established to minimize the total remaining cruising time, and iterative optimization was conducted with vehicle loading test based on timing. To elevate computational efficiency, the concept of parking-cruising path tree (PCPT) and its updating method were introduced based on the dynamic shortest path tree algorithm. Comparative analysis of cases and simulations demonstrated the efficacy of DCS in mitigating parking-cruising duration of different types of vehicles and minimizing forced delays arising from lane blocking. Notably, the optimization effect is particularly significant for vehicles with extended cruising durations or in parking lots with low AV penetration rates and high saturation, with an achievable optimization rate reaching up to 18%. This study addressed challenges related to drivers' noncompliance with guidance and lane blocking, thereby improving overall operational efficiency in mixed driving parking lots.</p> </abstract>

Finding the k Shortest Simple Paths: Time and Space Trade-offs

The k shortest simple path problem ( k SSP) asks to compute a set of top- k shortest simple paths from a source to a sink in a digraph. Yen (1971) proposed an algorithm with the best-known polynomial time complexity for this problem. Since then, the problem has been widely studied from an algorithm engineering perspective. The most noticeable proposals are the node-classification (NC) algorithm (Feng, 2014) and the sidetracks-based (SB) algorithm (Kurz, Mutzel, 2016). The latest offers the best running time at the price of a significant memory consumption. We first show how to speed up the SB algorithm using dynamic updates of shortest path trees resulting in a faster algorithm (SB*) with the same memory consumption. We then propose the parsimonious SB (PSB) algorithm that significantly reduces the memory consumption of SB at the cost of a small increase of the running time. Furthermore, we propose the postponed node-classification (PNC) algorithm that combines the best of the NC and the SB algorithms. It offers a significant speed up compared to the SB algorithm while using the same amount of memory as the NC algorithm. Our experimental results on complex networks show that all the considered algorithms have low memory consumption, and that the PSB algorithm is the fastest. On road networks, the relative performances of the algorithms depend on the number k of requested paths. Indeed, when the number k of requested paths is small (i.e., k ≤ 20 in our experiments), the SB* algorithm is the fastest among the considered algorithms, but it suffers from a large memory consumption and it offers very bad performances on some queries. When the number of requested paths is large (i.e., larger than 20 according to our experiments), the PNC algorithm is the fastest among the considered algorithms on road networks and it has a low memory footprint. The PNC algorithm is therefore a better choice on road networks.

On de novo Bridging Paired-end RNA-seq Data.

The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced two ends in the absence of the reference genome-a problem here we refer to as de novo bridging. Solving this problem provides longer, more informative RNA-seq reads, and benefits downstream RNA-seq analysis such as transcript assembly, expression quantification, and splicing differential analysis. However, de novo bridging is a challenging and complicated task owing to alternative splicing, transcript noises, and sequencing errors. It remains unclear if the data provides sufficient information for accurate bridging, let alone efficient algorithms that determine the true bridges. Methods have been proposed to bridge paired-end reads in the presence of reference genome (called reference-based bridging), but the algorithms are far away from scaling for de novo bridging as the underlying compacted de Bruijn graph (cdBG) used in the latter task often contains millions of vertices and edges. We designed a new truncated Dijkstra's algorithm for this problem, and proposed a novel algorithm that reuses the shortest path tree to avoid running the truncated Dijkstra's algorithm from scratch for all vertices for further speeding up. These innovative techniques result in scalable algorithms that can bridge all paired-end reads in a cdBG with millions of vertices. Our experiments showed that paired-end RNA-seq reads can be accurately bridged to a large extent. The resulting tool is freely available at https://github.com/Shao-Group/rnabridge-denovo.

Dynamic resource allocation for multicast in SDM-EON: time-decoupled dynamic path cross talk and joint weight

With the development of the Internet and the rise of multicast, enabling multicast in a space division multiplexing elastic optical network (SDM-EON) is considered highly necessary. This paper focuses on the dynamic resource allocation for multicast in SDM-EON. First, to ensure service survivability and reduce the complexity of inter-core cross talk computation, we design a path-based strict cross talk avoidance routing, modulation, core, and spectrum allocation (PSCA-RMCSA) algorithm. Then, based on PSCA-RMCSA, a joint weight and PSCA-RMCSA (JW-PSCA-RMCSA) algorithm is proposed to further reduce the blocking probability (BBP) of services. Simulation results show that PSCA-RMCSA reduces the BBP by up to 7.55% and the resource allocation time by up to 88.63%, while JW-PSCA-RMCSA reduces the BBP by up to 10.43% and the resource allocation time by up to 82.11%, when compared to the shortest path tree RMSCA.

A Range Space with Constant VC Dimension for All-pairs Shortest Paths in Graphs

Let $G$ be an undirected graph with non-negative edge weights and let $S$ be a subset of its shortest paths such that, for every pair $(u,v)$ of distinct vertices, $S$ contains exactly one shortest path between $u$ and $v$. In this paper we define a range space associated with $S$ and prove that its VC dimension is 2. As a consequence, we show a bound for the number of shortest paths trees required to be sampled in order to solve a relaxed version of the All-pairs Shortest Paths problem (APSP) in $G$. In this version of the problem we are interested in computing all shortest paths with a certain "importance" at least $\varepsilon$. Given any $0 < \varepsilon$, $ \delta < 1$, we propose a $\mathcal{O}(m + n \log n + (\textrm{diam}_{V(G)})^2)$ sampling algorithm that outputs with probability $1 - \delta$ the (exact) distance and the shortest path between every pair of vertices $(u, v)$ that appears as subpath of at least a proportion $\varepsilon$ of all shortest paths in the set $S$, where $\textrm{diam}_{V(G)}$ is the vertex-diameter of $G$. The bound that we obtain for the sample size depends only on $\varepsilon$ and $\delta$, and do not depend on the size of the graph.

Mechanical equipment fault diagnosis based on wireless sensor network data fusion technology

Abstract To save network energy consumption and prolong network life cycle in complex mechanical fault diagnosis, a research method of data fusion routing protocol algorithm based on wireless sensor network (WSN) is proposed. The specific content of the method is as follows: First, the low-energy adaptive clustering hierarchy algorithm is analyzed and discussed. On this basis, the prim route fusion algorithm is proposed to realize the effective utilization of energy and prolong the life of the network. Then, the WSN is abstracted as an undirected graph. From the perspective of saving the energy of the whole network, several current algorithms for building fusion trees are compared. The experimental results show that the prim algorithm consumes energy only after 700 rounds of clustering, while the leach clustering algorithm consumes energy only after 500 rounds. This shows that applying the prim algorithm can reduce the energy consumption of the whole network and prolong the life cycle of the network. However, the algorithm is carried out on the premise of uniform distribution of nodes, and there is a certain gap with the specific application of WSN in mechanical fault diagnosis. In the comparison of node energy consumption, it is found that compared with using the shortest path tree, using the central point of graph algorithm can greatly save the energy consumption of the node and has better performance. Practice has proved that this method can effectively remove redundant data information and solve the problem of unreliable data collected by a single sensor node. It is more suitable for the specific application of WSN in mechanical fault diagnosis.

A Reverse Shortest Path Tree-Based Multicast Joining Node Selection Method

Network layer multicast is a powerful method for transmitting data from sources to multiple group members. When joining a multicast group, a group member first sends a request to a designated router (DR). Then, the DR selects a node in the existing multicast tree (known as a multicast joining node, or MJN) to establish a multicast distribution path from the MJN to itself. The MJN selection method runs on the DR and has a significant impact on the distribution of the multicast tree, that directly affects the load distribution in the network. However, the current MJN selection method cannot effectively detect the load status of the downlink multicast path in the case of asymmetric routing, leading to network congestion and limiting the number of multicast groups that the network can accommodate (multicast capacity). To solve this problem, we propose an MJN selection method based on the reverse shortest path tree (RSPT). RSPT can effectively detect the load status of downlink multicast paths in case of routing asymmetry. Based on the detection results of RSPT, DR can select the MJN with the lowest path load to join the multicast tree. Our experimental results indicate that compared to existing multicast methods, our method has a lower cost and delay, and can effectively balance the network load in the case of asymmetric routing, increasing multicast capacity by more than two times.

C3P-RPL: A collaborative and proactive approach for optimal peer to peer path selection and sustenance

Internet of Things is evolving from information gathering platforms into collaborative systems wherein, smart devices actively interact with each other in a seamless manner. For instance, Internet of Robotic Things is envisioned to provide augmented solutions through collaboration of varied smart devices and robots. These visions revolve around the ability of smart devices to directly communicate and cooperate with each other in real time. In this context, this paper is an attempt to study RPL’s (Routing Protocol for Low-power Lossy Networks) point to point routing that creates multi-hop paths between peer nodes. This standard routing protocol is known for robust and failsafe upward paths but its peer to peer (P2P) routes are reported to be suboptimal. This work assesses P2P performance of RPL’s storing mode in a network of new generation devices having higher memory. Further, a Collaborative and Proactive Peer to Peer (C3P) path selection and sustenance approach is proposed where, root node collates incremental topology from collaborative nodes and disseminates optimal single source shortest path trees SPT(n). A progressive node betweenness centrality score ensures spread out paths. Minor topology changes are accommodated through incremental node and edge updates to targeted SPT(n) locally. Storing SPTs in intermediate nodes reduces storage and packet size. Through simulations and testbed experiments, it is proven that C3P-RPL improves simultaneous peer to peer communication between all the nodes. Specifically, the path length is reduced by 30% and subsequently the network latency drops by 65% in an experimental testbed of 47 nodes, making it suitable for collaborations.

Connectivity Guarantee Within UAV Cluster: A Graph Coalition Formation Game Approach

Unmanned Aerial Vehicle (UAV) clustering is promising for performing large-scale missions because of high mobility and easy deployment. However, the connectivity problems caused by the high mobility of UAVs and the interferences are mostly ignored in existing UAV mission executions. Rapid restoration of UAV network connectivity is essential for preventing communication disruption and improving the overall network performance. Thus, a graph coalition formation game that integrates the UAV time-varying topology graph with the coalition formation game is proposed to rapidly restore the connectivity of the UAV network in need. The method improves the utility of UAV clustering and ensures the network connectivity. Then, a graph coalition formation game algorithm based on the shortest path tree (SPT-GCF) rapidly forms an approximately optimal coalition structure. The simulation results show that the proposed approach increases the average utility of UAV clustering by 6.5% and 14.5% respectively when compared with the existing non-overlapping coalition formation game (NOCFG) and the coalition formation game without considering the cluster connectivity.

Tree-based Multicast Routing and Channel Assignment for Enhanced Throughout in Emerging Cognitive Radio Networks

In future multi-hop wireless networks like 5G and B5G, efficient large-scale video sharing and data dissemination are expected to rely heavily on multicast routing and Cognitive Radio (CR) technology. While multicast routing is efficient when the network always has access to the spectrum, the dynamic nature of Primary User (PU) activities, heterogeneous spectrum across the CR Network (CRN), and PU access priority make it challenging to implement efficient multicast routing protocols in CRNs. This paper proposes a hierarchical multicast routing mechanism for multi-hop CRNs that exploits the Shortest Path Tree (SPT) and Minimum Spanning Tree (MST) concepts. The proposed multicast routing mechanism consists of tree construction and channel assignment algorithms. The tree-construction algorithm models the network topology as a multicast tree rooted at the CR source and spanning all the CR nodes. Based on the constructed tree, the channel assignment algorithm employs the Probability Of Success (POS) metric to assign channels to the various layers defined by the constructed SPT or MST, ensuring that the most reliable channel is used for the multi-hop multicast transmissions. Simulation experiments are conducted to evaluate the mechanism’s effectiveness, revealing significant improvements in throughput and Packet Delivery Rate (PDR) compared to state-of-the-art protocols under different network conditions. The simulations also show that the SPT-based mechanism outperforms the MST-based mechanism in terms of throughput but has a higher tree construction complexity.

Reducing Waiting Times at Charging Stations With Adaptive Electric Vehicle Route Planning

Electric vehicles are becoming more popular all over the world. With increasing battery capacities and a growing fast-charging infrastructure, they are becoming suitable for long distance travel. However, queues at charging stations could lead to long waiting times, making efficient route planning even more important. In general, optimal multi-objective route planning is extremely computationally expensive. We propose an adaptive charging and routing strategy, which considers driving, waiting, and charging time. For this, we developed a multi-criterion shortest-path search algorithm using contraction hierarchies. To further reduce the computational effort, we precompute shortest-path trees between the known locations of the charging stations. We propose a central charging station database (CSDB) that helps estimating waiting times at charging stations ahead of time. This enables our adaptive charging and routing strategy to reduce these waiting times. In an extensive set of simulation experiments, we demonstrate the advantages of our concept, which reduces average waiting times at charging stations by up to 97 %. Even if only a subset of the cars uses the CSDB approach, we can substantially reduce waiting times and thereby the total travel time of electric vehicles.

Comparison on Routing Processing Performance between Shortest Paths Tree (SPT) and Minimum Spanning Tree (MST)

This study’s objective is to assess the performance of routing processing between Shortest Paths Tree (SPT) and Minimum Spanning Tree (MST). In this paper we propose and create software to calculate the efficiency path of routing processing in the network. Extensive simulations are being carried out with two different algorithms specific for Dijkistra’s algorithm and Kruskal’s algorithm. The network loads in the performance plots are characterized by two important parameters (a number of vertices) - 7 nodes and 10 nodes, more vertices could show good performance in the simulation results and showed that the performance of Kruskal’s algorithm is better than Dijkistra’s algorithm when the network loads are increased from 7 nodes to 10 nodes. In this simulation, Because of the total cost of distance matrix for Kruskal is less than Dijkistra when the number of routers or nodes is increased from 7 nodes to 10 nodes. This software namely Network Aids Design (NAD), is useful for calculation about the performance of routing processing in the network.

Enumeration of Far-apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation

Hyperbolicity is a graph parameter that indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of complex networks, the design of routing schemes, and the analysis of graph algorithms. Despite recent progress, computing the hyperbolicity of a graph remains challenging. Indeed, the best known algorithm has time complexity O(n 3.69 ) , which is prohibitive for large graphs, and the most efficient algorithms in practice have space complexity O(n 2 ) . Thus, time as well as space are bottlenecks for computing the hyperbolicity. In this article, we design a tool for enumerating all far-apart pairs of a graph by decreasing distances. A node pair (u, v) of a graph is far-apart if both v is a leaf of all shortest-path trees rooted at u and u is a leaf of all shortest-path trees rooted at v . This notion was previously used to drastically reduce the computation time for hyperbolicity in practice. However, it required the computation of the distance matrix to sort all pairs of nodes by decreasing distance, which requires an infeasible amount of memory already for medium-sized graphs. We present a new data structure that avoids this memory bottleneck in practice and for the first time enables computing the hyperbolicity of several large graphs that were far out of reach using previous algorithms. For some instances, we reduce the memory consumption by at least two orders of magnitude. Furthermore, we show that for many graphs, only a very small fraction of far-apart pairs has to be considered for the hyperbolicity computation, explaining this drastic reduction of memory. As iterating over far-apart pairs in decreasing order without storing them explicitly is a very general tool, we believe that our approach might also be relevant to other problems.