Computing Shortest Paths Research Articles

Bipartite Matching

The Kuhn-Munkres (KM) algorithm is a classical combinatorial optimization algorithm that is widely used for minimum cost bipartite matching in many real-world applications, such as transportation. For example, a ride-hailing service may use it to find the optimal assignment of drivers to passengers to minimize the overall wait time. Typically, given two bipartite sets, this process involves computing the edge costs between all bipartite pairs and finding an optimal matching. However, existing works overlook the impact of edge cost computation on the overall running time. In reality, edge computation often significantly outweighs the computation of the optimal assignment itself, as in the case of assigning drivers to passengers which involves computation of expensive graph shortest paths. Following on from this, we also observe common real-world settings exhibit a useful property that allows us to incrementally compute edge costs only as required using an inexpensive lower-bound heuristic. This technique significantly reduces the overall cost of assignment compared to the original KM algorithm, as we demonstrate experimentally on multiple real-world data sets and workloads. Moreover, our algorithm is not limited to this domain and is potentially applicable in other settings where lower-bounding heuristics are available.

Inferring Spatial Distance Rankings with Partial Knowledge on Routing Networks

The most common problem on routing networks is to compute the shortest paths from a source vertex to a set of target vertices. A variation of it, with applications for recommender systems, asks to merely rank the target vertices with respect to the shortest distances from the source. A classic solution is Dijkstra’s algorithm; however, it is too slow for large but meaningful applications. A setting where the target vertices are fixed but the source vertex is only known at query time allows for preprocessing. Following the line of research on preprocessing the routing network to speed up the computation of shortest paths, we study in this article a novel approach tackling the problem of ranking the static set of target vertices on the routing network with regard to the distance from a given source vertex to these target vertices by leveraging preprocessing. Our approach allows us to generate a partial solution by pre-computing the distances between all targets so that a shortest-path algorithm does not have to determine the shortest path from the source to every target in general. Our proposal can be adopted for both static and time-dependent networks, and it can be used in conjunction with a general shortest-path algorithm. We can experimentally observe significant speed-ups when using our proposed techniques.

Map-Matching on Low Sampling Rate Trajectories through Frequent Pattern Mining

Map-matching, an important preprocessing task in many location-based services (LBS), projects each point of the global positioning system (GPS) within a trajectory dataset onto a digital map. The state-of-the-art map-matching algorithms typically employ Hidden Markov model (HMM) via shortest path computation. But the computation of the shortest path might not work well on low-sampling-rate trajectory data (e.g., one GPS point every 1–5 min), leading to low matching precision and high running time. To solve the problem, this paper firstly identifies frequent patterns (FPs) in historical trajectories to capture meaningful mobility behaviors, and then extracts mobile behavior criterion (MBC) of mobile users. Such a criterion generally represents the route choice of mobile users on road networks. Moreover, the temporal information within trajectory data was employed to estimate the speed of mobile users on road segments. The identified FPs, coupled with MBC and moving speed, help to improve the map-matching precision of low-sampling-rate trajectories. In addition, an FP-forest structure was proposed to index the identified FPs. The structure could greatly speed up the lookup of frequent paths for shorter running time. Furthermore, the FP-forest structure was pruned to reduce redundancy with smaller space cost. Finally, experiments were carried out on real-world datasets. The results confirm that our FP-matching method outperforms state-of-the-art in terms of effectiveness and efficiency.

Prioritized Shortest Path Computation Mechanism (PSPCM) for wireless sensor networks.

Routing Protocol for Low-power and Lossy Networks (RPL), the de facto standard routing protocol for the Internet of Things (IoT) administers the smooth transportation of data packets across the Wireless Sensor Network (WSN). However, the mechanism fails to address the heterogeneous nature of data packets traversing the network, as these packets may carry different classes of data with different priority statuses, some real-time (time-sensitive) while others non-real-time (delay-tolerant). The standard Objective Functions (OFs), used by RPL to create routing paths, treat all classes of data as the same, this practice is not only inefficient but results in poor network performance. In this article, the Prioritized Shortest Path Computation Mechanism (PSPCM) is proposed to resolve the data prioritization of heterogeneous data and inefficient power management issues. The mechanism prioritizes heterogeneous data streaming through the network into various priority classes, based on the priority conveyed by the data. The PSPCM mechanism routes the data through the shortest and power-efficient path from the source to the destination node. PSPCM generates routing paths that exactly meet the need of the prioritized data. It outperformed related mechanisms with an average of 91.49% PDR, and average power consumption of 1.37mW which translates to better battery saving and prolonged operational lifetime while accommodating data with varying priorities.

Physarum-inspired multi-commodity flow dynamics

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them the computation of shortest paths and the design of efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we generalize the dynamics to the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterizations of the optimum solution.

Personalised statistical modelling of soft tissue structures in the ankle

Background and objectiveRevealing the complexity behind subject-specific ankle joint mechanics requires simultaneous analysis of three-dimensional bony and soft-tissue structures. 3D musculoskeletal models have become pivotal in orthopedic treatment planning and biomechanical research. Since manual segmentation of these models is time-consuming and subject to manual errors, (semi-) automatic methods could improve the accuracy and enlarge the sample size of personalised ‘in silico’ biomechanical experiments and computer-assisted treatment planning. Therefore, our aim was to automatically predict ligament paths, cartilage topography and thickness in the ankle joint based on statistical shape modelling. MethodsA personalised cartilage and ligamentous prediction algorithm was established using geometric morphometrics, based on an ‘in-house’ generated lower limb skeletal model (N = 542), tibiotalar cartilage (N = 60) and ankle ligament segmentations (N = 10). For cartilage, a population-averaged thickness map was determined by use of partial least-squares regression. Ligaments were wrapped around bony contours based on iterative shortest path calculation. Accuracy of ligament path and cartilage thickness prediction was quantified using leave-one-out experiments. The novel personalised thickness prediction was compared with a constant cartilage thickness of 1.50 mm by use of a paired sample T-test. ResultsMean distance error of cartilage and ligament prediction was 0.12 mm (SD 0.04 mm) and 0.54 mm (SD 0.05 mm), respectively. No significant differences were found between the personalised thickness cartilage and segmented cartilage of the tibia (p = 0.73, CI [-1.60 .10−17, 1.13 .10−17]) and talus (p = 0.95, CI[ -1.35 .10−17, 1.28 .10−17]). For the constant thickness cartilage, a statistically significant difference was found in 89% and 92% of the tibial (p < 0.001, CI [0.51, 0.58]) and talar (p < 0.001, CI [0.33, 0.40]) cartilage area. ConclusionsIn this study, we described a personalised prediction algorithm of cartilage and ligaments in the ankle joint. We were able to predict cartilage and main ankle ligaments with submillimeter accuracy. The proposed method has a high potential for generating large (virtual) sample sizes in biomechanical research and mitigates technological advances in computer-assisted orthopaedic surgery.

HESML: a real-time semantic measures library for the biomedical domain with a reproducible survey

BackgroundOntology-based semantic similarity measures based on SNOMED-CT, MeSH, and Gene Ontology are being extensively used in many applications in biomedical text mining and genomics respectively, which has encouraged the development of semantic measures libraries based on the aforementioned ontologies. However, current state-of-the-art semantic measures libraries have some performance and scalability drawbacks derived from their ontology representations based on relational databases, or naive in-memory graph representations. Likewise, a recent reproducible survey on word similarity shows that one hybrid IC-based measure which integrates a shortest-path computation sets the state of the art in the family of ontology-based semantic measures. However, the lack of an efficient shortest-path algorithm for their real-time computation prevents both their practical use in any application and the use of any other path-based semantic similarity measure.ResultsTo bridge the two aforementioned gaps, this work introduces for the first time an updated version of the HESML Java software library especially designed for the biomedical domain, which implements the most efficient and scalable ontology representation reported in the literature, together with a new method for the approximation of the Dijkstra’s algorithm for taxonomies, called Ancestors-based Shortest-Path Length (AncSPL), which allows the real-time computation of any path-based semantic similarity measure.ConclusionsWe introduce a set of reproducible benchmarks showing that HESML outperforms by several orders of magnitude the current state-of-the-art libraries in the three aforementioned biomedical ontologies, as well as the real-time performance and approximation quality of the new AncSPL shortest-path algorithm. Likewise, we show that AncSPL linearly scales regarding the dimension of the common ancestor subgraph regardless of the ontology size. Path-based measures based on the new AncSPL algorithm are up to six orders of magnitude faster than their exact implementation in large ontologies like SNOMED-CT and GO. Finally, we provide a detailed reproducibility protocol and dataset as supplementary material to allow the exact replication of all our experiments and results.

Transcriptomic profiling in mild cognitive impairment using peripheral blood gene co‐expression networks

AbstractBackgroundIn an effort towards AD prodromal risk assessment, precision medicine and biomarker development, we evaluated the efficacy of characterizing and clustering peripheral blood transcriptomic data by constructing gene‐coexpression networks from differentially expressed genes between normal controls and MCI subjects.MethodData from the ImaGene study (Imaging and Genetics Biomarkers study of Alzheimer’s Disease, ImaGene) was used. This included 160 subjects clinically diagnosed with amnestic MCI (n=70), non‐amnestic MCI (n=38) and normal controls (n=52) (Table 1). Quantile‐normalized and log‐transformed mRNA levels were obtained from peripheral blood. In a preliminary analysis we selected 2062 genes (out of HOW MANY) which were significantly differentially expressed between normal controls and MCI (two sample t‐test, pfdr&lt;0.05). Gene‐coexpression networks were built by creating correlation matrices of the differentially expressed mRNA values. Network backbones were then built using the shortest path computation to remove redundancy and identify important edges. Hierarchical clustering was performed on the co‐expression matrix to identify important communities or clusters within the network. We identified the strongest cluster associated with amnestic MCI phenotype (pfdr&lt;0.0001) by using the first principal component of the cluster as the eigen gene. The genes within the cluster and edges within the backbone were investigated.ResultUpon backbone computation, the number of edges compared to original correlation matrix were significantly reduced (Figure 1). Hierarchical clustering yielded 42 clusters of genes. One cluster (eigen gene) had the strongest association with amnestic MCI phenotype (r=0.45, pfdr&lt;0.0001). This cluster consisting of 46 genes warrants further investigation for specific function and interactions with other nodes in the cluster backbone. Two of the driver genes ADRA1A and ARHGAP4 were involved in noradrenergic receptor signaling pathway and PDGF signaling pathway, both of which are dysregulated in AD pathogenesis.ConclusionA large noisy transcriptomic data was reduced to a critical number of mRNA measures from peripheral blood. The backbone method pruned the gene coexpression network significantly. The cluster analysis identified a set of genes which had highly significant association with amnestic MCI. This approach can also help build models for risk assessment, gene therapy and help identify novel therapeutic targets/ dysregulated pathways.

Shortest path-based centrality metrics in attributed graphs with node-individual context constraints

Centrality measurements are a well-known method to assess the importance of actors in networks. They are easy to obtain and provide a versatile interpretability adaptable to the meaning of nodes and edges. The current centrality measurements use structural information alone. In real-world situations, however, actors and the connections between them are subject to contextual settings and can be significantly influenced by these settings. In fact, such real-world observations are often modeled using attributed networks in which contextual information can be associated as attributes to nodes and edges. However, this information is disregarded when evaluating the importance of actors in terms of network centrality measurements. Hence, this paper proposes a method for obtaining shortest path-based centrality measurements for attributed networks that exploit attribute information on nodes for shortest path calculations. We add abstracts of scientific publications to a co-publishing network and use topic models to create node-individual context constraints for shortest path calculations. This creates additional analytic opportunities and can aid in gaining a detailed understanding of complex social networks.

The Hierarchy in Grid Graphs (Extended Abstract)

Many speed-up techniques developed for accelerating the computation of shortest paths in road networks, like reach or contraction hierarchies, are based on the property that some streets are ’more important’ than others, e.g. on long routes the usage of an interstate is almost inevitable. In grids there is no obvious hierarchy among the edges, especially if the costs are uniform. Nevertheless we will show that contraction hierarchies can be applied to grid graphs as well. We will point out interesting connections to speed-up techniques shaped for routing on grids, like swamp hierarchies and jump points, and provide experimental results for game maps, mazes, random grids and rooms.

Sublinear search spaces for shortest path planning in grid and road networks

Shortest path planning is a fundamental building block in many applications. Hence developing efficient methods for computing shortest paths in, e.g., road or grid networks is an important challenge. The most successful techniques for fast query answering rely on preprocessing. However, for many of these techniques it is not fully understood why they perform so remarkably well, and theoretical justification for the empirical results is missing. An attempt to explain the excellent practical performance of preprocessing based techniques on road networks (as transit nodes, hub labels, or contraction hierarchies) in a sound theoretical way are parametrized analyses, e.g., considering the highway dimension or skeleton dimension of a graph. Still, these parameters may be large in case the network contains grid-like substructures—which inarguably is the case for real-world road networks around the globe. In this paper, we use the very intuitive notion of bounded growth graphs to describe road networks and also grid graphs. We show that this model suffices to prove sublinear search spaces for the three above mentioned state-of-the-art shortest path planning techniques. Furthermore, our preprocessing methods are close to the ones used in practice and only require expected polynomial time.

On scenario construction for stochastic shortest path problems in real road networks

Stochastic shortest path (SSP) computations are often performed under very strict time constraints, so computational efficiency is critical. A major determinant for the CPU time is the number of scenarios used. We demonstrate that by carefully picking the right scenario generation method for finding scenarios, the quality of the computations can be improved substantially over random sampling for a given number of scenarios. We study extensive SSP instances from a freeway network and an urban road network, which involve 10,512 and 37,500 spatially and temporally correlated speed variables, respectively. On the basis of experimental results from a total of 42 origin–destination pairs and 6 typical objective functions for SSP problems, we find that (1) the scenario generation method generates unbiased scenarios and strongly outperforms random sampling in terms of stability (i.e., relative difference and variance) whichever origin–destination pair and objective function is used; (2) to achieve a certain accuracy, the number of scenarios required for scenario generation is much lower than that for random sampling, typically about 6–10 times lower for a stability level of 1% in the freeway network; and (3) different origin–destination pairs and different objective functions could require different numbers of scenarios to achieve a specified stability.

An experimental evaluation and guideline for path finding in weighted dynamic network

Shortest path computation is a building block of various network applications. Since real-life networks evolve as time passes, the Dynamic Shortest Path (DSP) problem has drawn lots of attention in recent years. However, as DSP has many factors related to network topology, update patterns, and query characteristics, existing works only test their algorithms on limited situations without sufficient comparisons with other approaches. Thus, it is still hard to choose the most suitable method in practice. To this end, we first identify the determinant dimensions and constraint dimensions of the DSP problem and create a complete problem space to cover all possible situations. Then we evaluate the state-of-the-art DSP methods under the same implementation standard and test them systematically under a set of synthetic dynamic networks. Furthermore, we propose the concept of dynamic degree to classify the dynamic environments and use throughput to evaluate their performance. These results can serve as a guideline to find the best solution for each situation during system implementation and also identify research opportunities. Finally, we validate our findings on real-life dynamic networks.

Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance

In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. All these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.

Horizon Line Detection in Historical Terrestrial Images in Mountainous Terrain Based on the Region Covariance

Horizon line detection is an important prerequisite for numerous tasks including the automatic estimation of the unknown camera parameters for images taken in mountainous terrain. In contrast to modern images, historical photographs contain no color information and have reduced image quality. In particular, missing color information in combination with high alpine terrain, partly covered with snow or glaciers, poses a challenge for automatic horizon detection. Therefore, a robust and accurate approach for horizon line detection in historical monochrome images in mountainous terrain was developed. For the detection of potential horizon pixels, an edge detector is learned based on the region covariance as texture descriptor. In combination with shortest path search the horizon in monochrome images is accurately detected. We evaluated our approach on 250 selected historical monochrome images in average dating back to 1950. In 85% of the images the horizon was detected with an error less than 10 pixels. In order to further evaluate the performance, an additional dataset consisting of modern color images was used. Our method, using only grayscale information, achieves comparable results with methods based on color information. In comparison with other methods using only grayscale information, accuracy of the detected horizons is significantly improved. Furthermore, the influence of color, choice of neighborhood for the shortest path calculation, and patch size for the calculation of the region covariance were investigated. The results show that both the availability of color information and increasing the patch size for the calculation of the region covariance improve the accuracy of the detected horizons.

Path planning of a mobile robot among curved obstacles through tangent drawing and trapezoidal decomposition

Most of the previous studies on mobile robot path planning consider the obstacles as polygons. However, the complex shaped obstacles should be considered as curves rather than polygons, since the latter may result in non-optimal paths. Three new algorithms are proposed for finding the shortest path of a mobile robot among curved obstacles: TAD which uses a tangent drawing method, TRAD which uses trapezoidal decomposition, and TAD-TRAD which uses a combination of the TAD and the TRAD algorithms. The time complexities of the TAD algorithm, the TRAD algorithm, and the TAD-TRAD algorithm are O(n3logn), O(nlogn), and O(n(logn)2) respectively, where n is the total number of arcs in all the obstacles. The TAD and the TAD-TRAD algorithms compute an optimal shortest path, whereas the TRAD algorithm computes an approximate shortest path, among curved obstacles. The TAD algorithm has a lower time complexity than existing algorithms which are implemented for the computation of the optimal shortest path. The TRAD algorithm has a lower time complexity than existing algorithms which compute an approximate shortest path and the TAD-TRAD algorithm has a lower time complexity than existing algorithms which compute an optimal shortest path. The experimental comparison of the TAD, TRAD, and TAD-TRAD algorithms on 200 randomly generated problems shows that the TAD-TRAD algorithm has the least running time. Moreover, the TAD-TRAD algorithm computes an optimal path using a lesser number of tangents and with lesser time complexity when experimental comparisons are performed with existing algorithms in the literature.

On Energy-constrained Quickest Path Problem in Green Communication Using Intuitionistic Trapezoidal Fuzzy Numbers

Objective: A new variant of energy-constrained Quickest Path Problem (QPP) is being addressed in Intuitionistic Trapezoidal Fuzzy environment. The consideration of energy with QPP enables to compute the path for continuity aware critical applications. This new variant problem called as Energy-constrained Intuitionistic Trapezoidal Fuzzy Quickest Path Problem (EITFQPP) has been considered and the computations for quickest path have been carried out. Methods: As one of the important feature of the proposed model, the weight parameters associated with a given link, e.g., delay, capacity, energy and data which are completely unknown and therefore, based on the real life situations, they may be assumed as intuitionistic trapezoidal fuzzy numbers. An algorithm to solve the EITFQPP for transmitting the fuzzy data in the network, where the nodes are associated with a sufficient amount of energy (imprecise) for continuous data flow, has been proposed. Results: In order to illustrate the implementation of the proposed algorithm, a numerical example of a benchmark network has been provided. The proposed algorithm successfully provides a quickest path using shortest paths computations under the energy constrained approach. Conclusion: The illustration through a numerical example shows the effectiveness of consideration of energy in the selections of set of paths. Finally, some of the possible directions for the future research are also discussed.

The faster the better: On the shortest paths role for near real-time decision making of water utilities

Near real-time monitoring and control of critical infrastructure is essential for the operation and management of cities in a world that is, today, more complex and interconnected than ever. Such an infrastructure can be represented as complex networks an some of their related indices and statistics, many of them based on the shortest paths, play a pivotal role in the decision making for public services such as internet, energy or water. Particularly, the literature has shown that shortest paths are key for resilience and criticality assessment in a water distribution systems (WDS). This paper proposes a procedure to speed-up the computation of shortest paths in a WDS, as it can straightforwardly benefit any critical infrastructure. The proposal is based on a reduced dimension of a complex network representing any critical infrastructure. Despite the consequent decrease in the number of all possible paths in the network, the main advantage and novelty of this proposal is to continue finding the exact solution for the shortest paths. Experimental results show that the procedure brings a computational-time reduction consistently over 50% and up to 90% in some cases. In addition, the paper reveals how the use of shortest paths benefits WDS operation and management, as well as playing a key role in near real-time contamination detection and leakage control.

Optimizing bipartite matching in real-world applications by incremental cost computation

The Kuhn-Munkres (KM) algorithm is a classical combinatorial optimization algorithm that is widely used for minimum cost bipartite matching in many real-world applications, such as transportation. For example, a ride-hailing service may use it to find the optimal assignment of drivers to passengers to minimize the overall wait time. Typically, given two bipartite sets, this process involves computing the edge costs between all bipartite pairs and finding an optimal matching. However, existing works overlook the impact of edge cost computation on the overall running time. In reality, edge computation often significantly outweighs the computation of the optimal assignment itself, as in the case of assigning drivers to passengers which involves computation of expensive graph shortest paths. Following on from this observation, we observe common real-world settings exhibit a useful property that allows us to incrementally compute edge costs only as required using an inexpensive lower-bound heuristic. This technique significantly reduces the overall cost of assignment compared to the original KM algorithm, as we demonstrate experimentally on multiple real-world data sets, workloads, and problems. Moreover, our algorithm is not limited to this domain and is potentially applicable in other settings where lower-bounding heuristics are available.

A Coupling Path Analysis Method for High Power Microwave Interaction With Electronic Systems

In order to analyze the electromagnetic coupling path of real complex electronic system in high power microwave more conveniently and effectively, based on the electromagnetic topology theory, a signal flow graph drawing and simplification method based on coupling port is proposed, and the assignment principle of coupling path are given. The new method can satisfy the construction of signal flow graph in high power microwave environment with multiple interference sources and different bandwidths. Furthermore, aiming at the bidirectional coupling problem of signal flow graph and the shortest path calculation problem under different limit encountered in practical engineering application, this letter proposes an improved Floyd algorithm combined with double-sweep algorithm, which can solve the deficiency of traditional Dijkstra algorithm and Ford algorithm in solving the above engineering problems. Finally, the coupling path analysis method under the action of multiple interference sources is briefly discussed. The method proposed in this letter is more suitable for practical engineering, and it’s the base of the further electromagnetic protection work.