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Dynamic shortest path algorithms are the ones which are used to accommodate the online sequence of update operations to the underlying graph topology and also facilitate the subsequent query operations. Many solutions exist for the different versions of the problem, all of which identify the set of vertices whose shortest paths may be affected by the changes and then update their shortest paths according to the update sequence. In this paper, we are dynamizing the Dijkstra algorithm which helps to efficiently solve the dynamic single source shortest path problem. Dynamization is achieved by using the retroactive priority queue data structure. Retroactive data structure identify the set of affected vertices step by step and thus help to accommodate the changes in least number of computations. So, with a suitable dynamic graph representation and the use of retroactive priority queue, we have proposed algorithm to dynamize Dijkstra algorithm giving solution of dynamic single source shortest path problem with complexity O(nlg m) for the update time. We have performed experimental analysis by comparing the performance of the proposed algorithm with other algorithms. Our experimental results indicate that the proposed algorithm has better performance in terms of time and memory usage.

Shortest path length methods are routinely used to validate whether genes of interest are functionally related to each other based on biological network information. However, the methods are computationally intensive, impeding extensive utilization of network information. In addition, non-weighted shortest path length approach, which is more frequently used, often treat all network connections equally without taking into account of confidence levels of the associations. On the other hand, graph-based information diffusion method, which employs both the presence and confidence weights of network edges, can efficiently explore large networks and has previously detected meaningful biological patterns. Therefore, in this study, we hypothesized that the graph-based information diffusion method could prioritize genes with relevant functions more efficiently and accurately than the shortest path length approaches. We demonstrated that the graph-based information diffusion method substantially differentiated not only genes participating in same biological pathways (p << 0.0001) but also genes associated with specific human drug-induced clinical symptoms (p << 0.0001) from random. Furthermore, the diffusion method prioritized these functionally related genes faster and more accurately than the shortest path length approaches (pathways: p = 2.7e-28, clinical symptoms: p = 0.032). These data show the graph-based information diffusion method can be routinely used for robust prioritization of functionally related genes, facilitating efficient network validation and hypothesis generation, especially for human phenotype-specific genes.

Algorithms for finding the shortest path between two nodes in a graph have been heavily studied for decades. Half a century ago solutions were found for the specific class of problems that involves finding the path of least length, when edges are weighted with a single metric. For example, although the Bellman-Ford and Dijkstra algorithms use different methodologies, both techniques depend on a single metric where the lengths of paths are found by adding path weights in the conventional way. The situation becomes more complicated when multiple metrics or single metrics other than simple Euclidean distance are involved. In these cases, the definition of ``shortest,'' or ``best'' is not straightforward. In addition, it is not always a simple matter to verify that packets in a distributed network are forwarded on best paths that are guaranteed loop-free. We call the set of edge weights, plus the rules that determine how paths are concatenated and compared, the path algebra. We find that the structure of a path algebra is the key to understanding how packets will be forwarded in a distributed network; specifically whether they will be forwarded on best, loop-free paths. This is independent of any path-finding algorithm. We show that ``best'' paths and loop-free paths are separate (albeit subtly related) properties, that are dependent on whether or not a path algebra is monotonic and strictly bounded. We examine examples of path algebras that possess various combinations of those two properties in order to illustrate how they affect the construction of forwarding paths. Finally, we prove that if a path algebra is monotonic and strictly bounded, it is guaranteed to produce forwarding paths that are best and loop-free. Previous works have introduced these ideas in separate contexts. We provide a consistent framework and prove general concepts that have only been introduced or discussed in special cases.

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails., Author summary We investigated the trail networks of arboreal turtle ants in the canopy of the tropical forest, to ask what characterizes the colony’s choice of foraging paths within the vegetation. We monitored day to day changes in the junctions and edges of trail networks of colonies in the dry forest of western Mexico. We compared the paths used by the ants to simulated random paths in the surrounding vegetation. We found that the paths of turtle ants prioritize coherence, keeping ants together on the trail, over minimizing the average edge length. The choice of paths reduces the number of junctions in the trail where ants could get lost, and favors junctions with a physical configuration that makes it likely that successive ants will reinforce the same path. Our work suggests that design principles that emphasize keeping information flow constrained to streamlined, coherent trails may be useful in human-designed distributed routing and transport networks or robot swarms.

Nearest neighbor (NN) and range (RN) queries are basic query types in spatial databases. In this study, we refer to collections of NN and RN queries as spatial proximity (SP) queries. At peak times, location-based services (LBS) need to quickly process SP queries that arrive simultaneously. Timely processing can be achieved by increasing the number of LBS servers, however, this also increases service costs. Existing solutions evaluate SP queries sequentially, thus, such solutions involve unnecessary distance calculations. This study proposes a unified batch algorithm (UBA) that can effectively process SP queries in dynamic spatial networks. With the proposed UBA, the distance between two points is indicated by the travel time on the shortest path connecting them. The shortest travel time changes frequently depending on traffic conditions. The goal of the proposed UBA is to avoid unnecessary distance calculations for nearby SP queries. Thus, the UBA clusters nearby SP queries and exploits shared distance calculations for query clusters. Extensive evaluations using real-world roadmaps demonstrated the superiority and scalability of UBA compared with state-of-the-art sequential solutions.

The five Platonic solids—tetrahedron, cube, octahedron, dodecahedron, and icosahedron—have found many applications in mathematics, science, and art. Path planning for the Platonic solids had been suggested, but not validated, except for solving the rolling-cube puzzles for a cubic dice. We developed a path-planning algorithm based on the breadth-first-search algorithm that generates a shortest path for each Platonic solid to reach a desired pose, including position and orientation, from an initial one on prescribed grids by edge-rolling. While it is straightforward to generate triangular and square grids, various methods exist for regular-pentagon tiling. We chose the Penrose tiling because it has five-fold symmetry. We discovered that a tetrahedron could achieve only one orientation for a particular position.

Many popular algorithms for searching the space of leaf-labelled (phylogenetic) trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is $${\mathbf {N}}{\mathbf {P}}$$ N P -hard in each of these graphs, making tree inference and comparison algorithms challenging to design in practice. Although ranked phylogenetic trees are one of the central objects of interest in applications such as cancer research, immunology, and epidemiology, the computational complexity of the shortest path problem for these trees remained unsolved for decades. In this paper, we settle this problem for the ranked nearest neighbour interchange operation by establishing that the complexity depends on the weight difference between the two types of tree rearrangements (rank moves and edge moves), and varies from quadratic, which is the lowest possible complexity for this problem, to $${\mathbf {N}}{\mathbf {P}}$$ N P -hard, which is the highest. In particular, our result provides the first example of a phylogenetic tree rearrangement operation for which shortest paths, and hence the distance, can be computed efficiently. Specifically, our algorithm scales to trees with tens of thousands of leaves (and likely hundreds of thousands if implemented efficiently).

This paper presents an integrated model for energy consumption and range estimation, capable of energy-efficient routing. This integrated model predicts the energy consumption on all road segments in the road network and applies shortest path algorithms to calculate energy-efficient routes. A temperature-dependent model of the battery internal resistance based on real-world data translates the energy consumption prediction into driving range. The graph representation of the road network is transformed from a node-based graph to an edge-based graph to allow cost allocation of one edge based on the characteristics of the preceding edge. The integrated model is used to perform an analysis of energy-efficient routes for a real-life scenario. The analysis showed that the energy-optimal route is different from the time- and distance-optimal route with energy-efficiency gains up to 37% for the chosen scenario. The energy-efficient route tends to lean toward a distance-optimal route in the case of low auxiliary consumption and to lean toward a time-optimal route in the case of high auxiliary consumption. The energy-efficient route generation is tested in real life for one case of the chosen scenario. The measured results showed a good match with the predicted values for the energy consumption with a 9% mean relative error and preserved the ranking of all routes in terms of the travel distance, travel time, and energy consumption. The proposed integrated model is a functional model for energy consumption in real-life that differentiates many energy consumption influencing factors and produces energy-efficient routes with good accuracy.

The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this paper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.

This paper proposes a stochastic shortest path approach to find an optimal sequence of tests to confirm or discard a disease, for any prescribed optimality criterion. The idea is to select the best sequence in which to apply a series of available tests, with a view at reaching a diagnosis with minimum expenditure of resources. The proposed approach derives an optimal policy whereby the decision maker is provided with a test strategy for each a priori probability of disease, aiming to reach posterior probabilities that warrant either immediate treatment or a not-ill diagnosis.

Collision risk assessment and collision avoidance of vessels have always been an important topic in ocean engineering. Decision support systems are increasingly becoming the focus of many studies in the maritime industry today as vessel accidents are often caused by human error. This study proposes an anticollision decision support system that can determine surrounding obstacles by using the information received from radar systems, obtain the position and speed of obstacles within a certain time period, and suggest possible routes to prevent collisions. In this study we use a neural network to predict the subsequent positions of surrounding vessels, a fuzzy logic system to obtain the risk of collision, and a particle swarm optimization algorithm to find the safe and shortest path for collision avoidance.

We investigated the influence of processing steps in the estimation of multivariate directed functional connectivity during seizures recorded with intracranial EEG (iEEG) on seizure-onset zone (SOZ) localization. We studied the effect of (i) the number of nodes, (ii) time-series normalization, (iii) the choice of multivariate time-varying connectivity measure: Adaptive Directed Transfer Function (ADTF) or Adaptive Partial Directed Coherence (APDC) and (iv) graph theory measure: outdegree or shortest path length. First, simulations were performed to quantify the influence of the various processing steps on the accuracy to localize the SOZ. Afterwards, the SOZ was estimated from a 113-electrodes iEEG seizure recording and compared with the resection that rendered the patient seizure-free. The simulations revealed that ADTF is preferred over APDC to localize the SOZ from ictal iEEG recordings. Normalizing the time series before analysis resulted in an increase of 25–35% of correctly localized SOZ, while adding more nodes to the connectivity analysis led to a moderate decrease of 10%, when comparing 128 with 32 input nodes. The real-seizure connectivity estimates localized the SOZ inside the resection area using the ADTF coupled to outdegree or shortest path length. Our study showed that normalizing the time-series is an important pre-processing step, while adding nodes to the analysis did only marginally affect the SOZ localization. The study shows that directed multivariate Granger-based connectivity analysis is feasible with many input nodes (> 100) and that normalization of the time-series before connectivity analysis is preferred. Electronic supplementary material The online version of this article (10.1007/s10548-018-0646-7) contains supplementary material, which is available to authorized users.

Modern computer networks support interesting new routing models in which traffic flows from a source sto a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network functions (VNFs), to create innovative network services like service chains or segment routing. While the benefits and technological challenges of providing such routing models have been articulated and studied intensively over the last years, less is known about the underlying algorithmic traffic routing problems. The goal of this paper is to provide the network community with an overview of algorithmic techniques for waypoint routing and also inform about limitations due to computational hardness. In particular, we put the waypoint routing problem into perspective with respect to classic graph theoretical problems. For example, we find that while computing a shortest path from a source s to a destination t is simple (e.g., using Dijkstra's algorithm), the problem of finding a shortest route from s to t via a single waypoint already features a deep combinatorial structure.

For urban rail transit network, the space-time flow distribution can play an important role in evaluating and optimizing the space-time resource allocation. For obtaining the space-time flow distribution without the restriction of schedules, a dynamic assignment problem is proposed based on the concept of continuous transmission. To solve the dynamic assignment problem, the cell transmission model is built for urban rail transit networks. The priority principle, queuing process, capacity constraints and congestion effects are considered in the cell transmission mechanism. Then an efficient method is designed to solve the shortest path for an urban rail network, which decreases the computing cost for solving the cell transmission model. The instantaneous dynamic user optimal state can be reached with the method of successive average. Many evaluation indexes of passenger flow can be generated, to provide effective support for the optimization of train schedules and the capacity evaluation for urban rail transit network. Finally, the model and its potential application are demonstrated via two numerical experiments using a small-scale network and the Beijing Metro network.

Bioinformatics, 27 (15), ISSN:1367-4803, ISSN:1460-2059

Service routes optimization (SRO) of pallet service center should meet customers’ demand firstly and then, through the reasonable method of lines organization, realize the shortest path of vehicle driving. The routes optimization of pallet service center is similar to the distribution problems of vehicle routing problem (VRP) and Chinese postman problem (CPP), but it has its own characteristics. Based on the relevant research results, the conditions of determining the number of vehicles, the one way of the route, the constraints of loading, and time windows are fully considered, and a chance constrained programming model with stochastic constraints is constructed taking the shortest path of all vehicles for a delivering (recycling) operation as an objective. For the characteristics of the model, a hybrid intelligent algorithm including stochastic simulation, neural network, and immune clonal algorithm is designed to solve the model. Finally, the validity and rationality of the optimization model and algorithm are verified by the case.

This work presents a localization scheme for use in wireless sensor networks (WSNs) that is based on a proposed connectivity-based RF localization strategy called the distributed Fermat-point location estimation algorithm (DFPLE). DFPLE applies triangle area of location estimation formed by intersections of three neighboring beacon nodes. The Fermat point is determined as the shortest path from three vertices of the triangle. The area of estimated location then refined using Fermat point to achieve minimum error in estimating sensor nodes location. DFPLE solves problems of large errors and poor performance encountered by localization schemes that are based on a bounding box algorithm. Performance analysis of a 200-node development environment reveals that, when the number of sensor nodes is below 150, the mean error decreases rapidly as the node density increases, and when the number of sensor nodes exceeds 170, the mean error remains below 1% as the node density increases. Second, when the number of beacon nodes is less than 60, normal nodes lack sufficient beacon nodes to enable their locations to be estimated. However, the mean error changes slightly as the number of beacon nodes increases above 60. Simulation results revealed that the proposed algorithm for estimating sensor positions is more accurate than existing algorithms, and improves upon conventional bounding box strategies.

Motivation: For many biotechnological purposes, it is desirable to redesign proteins to be more structurally and functionally stable at higher temperatures. For example, chemical reactions are intrinsically faster at higher temperatures, so using enzymes that are stable at higher temperatures would lead to more efficient industrial processes. We describe an innovative and computationally efficient method called Improved Configurational Entropy (ICE), which can be used to redesign a protein to be more thermally stable (i.e. stable at high temperatures). This can be accomplished by systematically modifying the amino acid sequence via local structural entropy (LSE) minimization. The minimization problem is modeled as a shortest path problem in an acyclic graph with nonnegative weights and is solved efficiently using Dijkstra's method. Contact: mitchell@biochem.wisc.edu

Recently, the number of studies involving complex network applications in transportation has increased steadily as scholars from various fields analyze traffic networks. Nonetheless, research on rail network growth is relatively rare. This research examines the evolution of the Public Urban Rail Transit Networks of Kuala Lumpur (PURTNoKL) based on complex network theory and covers both the topological structure of the rail system and future trends in network growth. In addition, network performance when facing different attack strategies is also assessed. Three topological network characteristics are considered: connections, clustering and centrality. In PURTNoKL, we found that the total number of nodes and edges exhibit a linear relationship and that the average degree stays within the interval [2.0488, 2.6774] with heavy-tailed distributions. The evolutionary process shows that the cumulative probability distribution (CPD) of degree and the average shortest path length show good fit with exponential distribution and normal distribution, respectively. Moreover, PURTNoKL exhibits clear cluster characteristics; most of the nodes have a 2-core value, and the CPDs of the centrality's closeness and betweenness follow a normal distribution function and an exponential distribution, respectively. Finally, we discuss four different types of network growth styles and the line extension process, which reveal that the rail network's growth is likely based on the nodes with the biggest lengths of the shortest path and that network protection should emphasize those nodes with the largest degrees and the highest betweenness values. This research may enhance the networkability of the rail system and better shape the future growth of public rail networks.

Pancreatic cancer (PC) is a highly malignant tumor derived from pancreas tissue and is one of the leading causes of death from cancer. Its molecular mechanism has been partially revealed by validating its oncogenes and tumor suppressor genes; however, the available data remain insufficient for medical workers to design effective treatments. Large-scale identification of PC-related genes can promote studies on PC. In this study, we propose a computational method for mining new candidate PC-related genes. A large network was constructed using protein-protein interaction information, and a shortest path approach was applied to mine new candidate genes based on validated PC-related genes. In addition, a permutation test was adopted to further select key candidate genes. Finally, for all discovered candidate genes, the likelihood that the genes are novel PC-related genes is discussed based on their currently known functions.

Mesh network topologies are becoming increasingly popular in battery-powered wireless sensor networks, primarily because of the extension of network range. However, multihop mesh networks suffer from higher energy costs, and the routing strategy employed directly affects the lifetime of nodes with limited energy resources. Hence when planning routes there are trade-offs to be considered between individual and system-wide battery lifetimes. We present a multiobjective routing optimisation approach using hybrid evolutionary algorithms to approximate the optimal trade-off between the minimum lifetime and the average lifetime of nodes in the network. In order to accomplish this combinatorial optimisation rapidly, our approach prunes the search space using k-shortest path pruning and a graph reduction method that finds candidate routes promoting long minimum lifetimes. When arbitrarily many routes from a node to the base station are permitted, optimal routes may be found as the solution to a well-known linear program. We present an evolutionary algorithm that finds good routes when each node is allowed only a small number of paths to the base station. On a real network deployed in the Victoria & Albert Museum, London, these solutions, using only three paths per node, are able to achieve minimum lifetimes of over 99% of the optimum linear program solution’s time to first sensor battery failure.

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.

We present a novel direction based shortest path search algorithm to guide evacuees during an emergency. It uses opportunistic communications (oppcomms) with low-cost wearable mobile nodes that can exchange packets at close range of a few to some tens of meters without help of an infrastructure. The algorithm seeks the shortest path to exits which are safest with regard to a hazard, and is integrated into an autonomous Emergency Support System (ESS) to guide evacuees in a built environment. The algorithm proposed that ESSs are evaluated with the DBES (Distributed Building Evacuation Simulator) by simulating a shopping centre where fire is spreading. The results show that the directional path finding algorithm can offer significant improvements for the evacuees.

To solve the persistently multiple object tracking in cluttered environments, this paper presents a novel tracking association approach based on the shortest path faster algorithm. First, the multiple object tracking is formulated as an integer programming problem of the flow network. Then we relax the integer programming to a standard linear programming problem. Therefore, the global optimum can be quickly obtained using the shortest path faster algorithm. The proposed method avoids the difficulties of integer programming, and it has a lower worst-case complexity than competing methods but better robustness and tracking accuracy in complex environments. Simulation results show that the proposed algorithm takes less time than other state-of-the-art methods and can operate in real time.

Shortest path is among classical problems of computer science. The problems are solved by hundreds of algorithms, silicon computing architectures and novel substrate, unconventional, computing devices. Acellular slime mouldP. polycephalumis originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients. Several algorithms were designed based on properties of the slime mould. Many of thePhysarum-inspired algorithms suffer from a low converge speed. To accelerate the search of a solution and reduce a number of iterations we combined an original model of Physarum-inspired path solver with a new a parameter, called energy. We undertook a series of computational experiments on approximating shortest paths in networks with different topologies, and number of nodes varying from 15 to 2000. We found that the improvedPhysarumalgorithm matches well with existing Physarum-inspired approaches yet outperforms them in number of iterations executed and a total running time. We also compare our algorithm with other existing algorithms, including the ant colony optimization algorithm and Dijkstra algorithm.

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.