K-shortest Path Research Articles

Research on Passenger Path Search Method Based on the Service Network of Urban Rail Transit

This study focuses on the major factors influencing the passenger flow assignment in the service network of Urban Rail Transit (URT). A passenger path search method was modeled. It also took full consideration of travelers’ route choice behavior in the service network of URT. Then the figure of service network was built, and assignment indicators of arc segments were set up and quantized. Finally, the traditional K-shortest paths algorithm had been improved based on the case study of calculating and analyzing line A. The results confirm passengers’ traveling behavior can be reflected better by service network.

Resource allocation with multi-factor node ranking in data center networks

In data center networks, resource allocation refers to mapping a large number of workloads to substrate networks. Existing heuristic mapping algorithms evaluate the resources of the nodes according to one resource factor or a product of resource factors, which will probably lead to an imbalance of the resource allocation. Furthermore, neglecting the hops of the substrate paths in the resource allocation may result in low resource utilization. In this paper, we adopt a top-k dominating model to rank the nodes, aiming at balancing these factors to improve resource allocation. Moreover, we propose a novel mapping algorithm TK-Match, which consists of a node mapping stage and link mapping stage. In the node mapping stage, TK-Match maps the virtual nodes to the substrate nodes in terms of the node ranking and the hops of the substrate paths. In the link mapping stage, TK-Match adopts the k-shortest path algorithm to map the virtual links. Extensive simulation experiments show that TK-Match can greatly increase the long-term average revenue and the acceptance ratio.

Research on Urban Rail Transit Resource Allocation Based on K-Shortest Paths Algorithm

This paper considers the major factors of passenger flow distribution and the running cost of train, explains and demonstrates how to sove the problem of urban rail transit resource allocation. The paper at first constructs urban rail network assignment model in the multiple operating lines based on the k-shortest paths algorithm, then proposes the k shortest paths search algorithm, finally the effectiveness of the model and algorithm are verified with the data from the Beijing urban rail transit network.

Taxi Driver's Route Choice Behavior Analysis Based on Floating Car Data

Taxi drivers are viewed having more driving experience, being more familiar with road traffic condition, and in turn having more rational route choice behaviors than ordinary drivers. Using floating car data (FCD) of Beijing taxi in 2010, this study discusses the influence of road network conditions and traffic status to taxi drivers route choice behaviors. First, trip information is extracted from FCD using trip-identification method; Second, map matching and K-shortest paths are used to construct the trajectories and the sets of alternate routes, and route similarity evaluation is conducted to build the sample data of route choice behavior analysis; Finally, route choice model for taxi drivers based on Multinomial Logit (MNL) Model is estimated. The result shows that taxi drivers tend to choose the route which has faster driving speed, less frequency of left turns, more proportion of express way and less proportion of minor road, and increasing a left-turn or decreasing travel speed by 2.12km/h has the same effect on route choice utility. This study is expected to be helpful to establish map-matching algorithm of FCD, route guidance scheme and traffic assignment model.

Bicriterion shortest path problem with a general nonadditive cost

A bicriterion shortest path problem with a general nonadditive cost seeks to optimize a combination of two path costs, one of which is evaluated by a nonlinear function. This paper first identifies a number of emerging transportation applications for which such a shortest path problem might be considered a core subproblem. We propose to first approximate the general nonlinear cost function with a piecewise linear counterpart, and then solve each linear subproblem sequentially. A specialized algorithm is developed to solve the subproblems, which makes use of the efficient path set (or the convex hull) to update upper and lower bounds of the original problem. Conditions under which the solution to a subproblem must belong to the efficient path set are specified. Accordingly, we show that the optimal path must be efficient if the nonlinear cost function is concave. If the optimal path to a subproblem is not efficient, partial path enumeration, implemented using a simple K-shortest path ranking procedure, is conducted to close the gap. The proposed algorithm includes strategies aiming to expedite path enumeration by using upper bounds derived from the efficient path set. Numerical experiments are conducted to demonstrate correctness and effectiveness of the proposed algorithm.

Bicriterion Shortest Path Problem with a General Nonadditive Cost

A bicriterion shortest path problem with a general nonadditive cost seeks to optimize a combination of two path costs, one of which is evaluated by a nonlinear function. This paper first identifies a number of emerging transportation applications for which such a shortest path problem might be considered a core subproblem. We propose to first approximate the general nonlinear cost function with a piecewise linear counterpart, and then solve each linear subproblem sequentially. A specialized algorithm is developed to solve the subproblems, which makes use of the efficient path set (or the convex hull) to update upper and lower bounds of the original problem. Conditions under which the solution to a subproblem must belong to the efficient path set are specified. Accordingly, we show that the optimal path must be efficient if the nonlinear cost function is concave. If the optimal path to a subproblem is not efficient, partial path enumeration, implemented using a simple K-shortest path ranking procedure, is conducted to close the gap. The proposed algorithm includes strategies aiming to expedite path enumeration by using upper bounds derived from the efficient path set. Numerical experiments are conducted to demonstrate correctness and effectiveness of the proposed algorithm.

Assessing the effectiveness of k-shortest path sets in problems of network interdiction

This paper focuses on the network interdiction problem and integration of a solution methodology based on k-shortest path sets. We design and conduct an experiment using the road network of Northridge, California to assess performance of the k-shortest path approach under varying assumptions which include homogeneous and heterogeneous arc metrics, the use or non-use of pseudo nodes and alternate origin-destination scenarios. We compare the obtained solutions from the k-shortest path set approach to optimal solutions obtained by implementing Benders Decomposition and observe the differences in computation time and the objective gap for all cases of the experimental design. We also introduce a similarity measure based on spatial analysis techniques to compare coverage as a secondary measure of performance. The observed findings support the use of a k-shortest path set approach in situations where computation time prohibits the need to derive an optimal solution. Additionally, we show that the k-shortest path set approach performs better on heterogeneous networks and that only a small number need be used for k to achieve strong interdiction solutions.

Top-Down Network Analysis to Drive Bottom-Up Modeling of Physiological Processes

Top-down analyses in systems biology can automatically find correlations among genes and proteins in large-scale datasets. However, it is often difficult to design experiments from these results. In contrast, bottom-up approaches painstakingly craft detailed models that can be simulated computationally to suggest wet lab experiments. However, developing the models is a manual process that can take many years. These approaches have largely been developed independently. We present LINKER, an efficient and automated data-driven method that can analyze molecular interactomes to propose extensions to models that can be simulated. LINKER combines teleporting random walks and k-shortest path computations to discover connections from a source protein to a set of proteins collectively involved in a particular cellular process. We evaluate the efficacy of LINKER by applying it to a well-known dynamic model of the cell division cycle in Saccharomyces cerevisiae. Compared to other state-of-the-art methods, subnetworks computed by LINKER are heavily enriched in Gene Ontology (GO) terms relevant to the cell cycle. Finally, we highlight how networks computed by LINKER elucidate the role of a protein kinase (Cdc5) in the mitotic exit network of a dynamic model of the cell cycle.

Polynomial-time adaptive routing algorithm based on spectrum scan in dynamic flexible optical networks

Optical Orthogonal Frequency Division Multiplexing (OOFDM) has been proposed as a highly spectrum-efficient modulation technique, which can provide flexible spectrum assignment with fine granularity. In OOFDM-based flexible optical networks, Routing and Spectrum Assignment (RSA) has become a key problem. However, widely used dynamic RSA schemes, such as Fixed Routing (FR) and K-shortest Paths (KSP) routing schemes, are not able to realize route computation based on the link state information, thus leading to poor blocking performance and inefficient resource utilization. To solve this problem, Adaptive Routing (AR) schemes, e.g., the Entire Path Searching (EPS) scheme, have been proposed recently. These schemes have low blocking probability; however, since their computational complexities are factorial, they are not suitable for use in real networks. In this paper, we propose a novel Spectrum-Scan Routing (SSR) scheme in dynamic flexible optical networks. To the best of our knowledge, SSR is the first polynomial-time AR scheme that can realize adaptive shortest-route computation. Simulation results show that our proposed SSR scheme has lower blocking probability and higher resource utilization compared with FR and EPS. Moreover, the worst-case computational complexity of SSR increases linearly with the network scale of the torus topologies, making it applicable to real networks.

Efficient heuristics for energy-aware routing in networks with bundled links

Current networks are typically over-provisioned to ensure low delays, redundancy and reliability. These Quality of Service (QoS) guarantees are typically achieved using high end, high power network equipments. Their use, however, has led to concerns regarding green house gas emissions, which garnered a lot of attention recently and have resulted in a number of global initiatives aim at reducing the carbon footprint of Internet Service Providers (ISPs). These initiatives have motivated ISPs and researchers to design novel network algorithms and hardware that scale the usage or active time of a network according to traffic load. To this end, this paper considers the problem of shutting down a subset of bundled links during off-peak periods in order to minimize energy expenditure. Unfortunately, identifying the cables that minimize this objective is an NP-complete problem. Henceforth, we propose several practical heuristics based on Dijkstra’s algorithm and Yen’s k-shortest paths algorithm. We evaluated our heuristics on the Abilene network – with both real and synthetic traffic matrices and several larger random topologies with various loads. Our results show that the proposed heuristics to be effective and efficient. Moreover, our approaches could potentially reduce the energy usage of cables used in the Abilene network by up to 56.7%, assuming the traffic demands recorded on September 5, 2004.

Robust Optimization Model of Bus Transit Network Design with Stochastic Travel Time

The design of urban bus transit systems aims to determine a network configuration with a set of bus lines and associated frequencies that achieve the targeted objective. This paper presents a methodology framework to formulate and solve the bus transit network design problem (TNDP). It first proposes a TNDP taking into account the travel time stochasticity. A robust optimization model is formulated for the proposed problem, which aims to minimize the sum of the expected value of the operator cost and its variability multiplied by a weighting value. A heuristic solution approach, based on k-shortest path algorithm, simulated annealing algorithm, Monte Carlo simulation, and probit-type discrete choice model, is subsequently developed to solve the robust optimization model. Finally, the proposed methodology is applied to a numerical example. (C) 2013 American Society of Civil Engineers.

CMPF: Class-switching minimized pathfinding in metabolic networks

BackgroundThe metabolic network is an aggregation of enzyme catalyzed reactions that converts one compound to another. Paths in a metabolic network are a sequence of enzymes that describe how a chemical compound of interest can be produced in a biological system. As the number of such paths is quite large, many methods have been developed to score paths so that the k-shortest paths represent the set of paths that are biologically meaningful or efficient. However, these approaches do not consider whether the sequence of enzymes can be manufactured in the same pathway/species/localization. As a result, a predicted sequence might consist of groups of enzymes that operate in distinct pathway/species/localization and may not truly reflect the events occurring within cell.ResultsWe propose a path weighting method CMPF (Class-switching Minimized Pathfinder) to search for routes in a metabolic network which minimizes pathway switching. In biological terms, a pathway is a series of chemical reactions which define a specific function (e.g. glycolysis). We conjecture that routes that cross many pathways are inefficient since different pathways define different metabolic functions. In addition, native routes are also well characterized within pathways, suggesting that reasonable paths should not involve too many pathway switches. Our method can be generalized when reactions participate in a class set (e.g., pathways, species or cellular localization) so that the paths predicted have minimal class crossings.ConclusionsWe show that our method generates k-paths that involve the least number of class switching. In addition, we also show that native paths are recoverable and alternative paths deviates less from native paths compared to other methods. This suggests that paths ranked by our method could be a way to predict paths that are likely to occur in biological systems.

Feeder Bus Network Design Problem: a New Metaheuristic Procedure and Real Size Applications

The present paper deals with the transit network design problem related to the feeder routes defined as transit services for the connection of local areas, where the demand has to be gathered, with the stops of the main transit network, usually railway or underground station. The objective of the research is the development of a procedure that simultaneously generates routes and frequencies of the feeder bus network in a real size large urban area. The solving procedure is articulated in 2 phases: in the first one, a heuristic algorithm generates two different and complementary sets of feasible routes, in order to provide a good balance between maximization of the service coverage area and minimization of the overall travel time. First set is composed by circular routes, generated solving a travelling salesman problem (TSP) connecting the highest demand node pairs in the area with the stop of main transit network. The second feasible set aims at developing feeder routes more direct than the others using the k-shortest path algorithm. The set of all feasible routes, generated taking into account only the main skeleton of the road network, is then the input data for the second phase where a GA is utilized for finding a sub-optimal set of routes with the associated frequencies. The proposed procedure has been implemented on two real-life size networks, Winnipeg and Rome, in order to compare its effectiveness with the performances of the existing transit networks. The results of the applications of the design procedure show that the feeder routes imply a more integrated transit network with a reduction of the total travel time, despite an increase of the number of transfers, in a more efficient way as demonstrated by the reduction of the operating costs and the increase of the average load factor.

Study on Optimization of Integrated Transportation Organization Mode Based on Various Types of Goods

According to the coupling relationship of goods’ transport attributes and transport service’s attributes, the transport goods are divided into four categories. Based on the classification of transport goods, the generalized transport cost functions of time-sensitive goods, hazardous goods, general goods and bulk goods are established considering transportation cost, opportunity cost, risk cost and time losing cost. In the application of traffic assignment theory and transport path optimization method, the multi-transportation mode optionassignment model based on the generalized transportation cost of different types of goods is established, and Genetic Algorithm based on rational K-shortest path to solve the optimization mode is proposed. Finally, it takes the transportation organization mode optimization in the Three Gorges Region for empirical study ,the related suggestions and reasonable transport organization mode for main cargoes in Three Gorges areas are proposed, which provides valuable references for transport companies and cargo owners to take reasonable integrated transport organization mode.

A single source k-shortest paths algorithm to infer regulatory pathways in a gene network

Motivation: Inferring the underlying regulatory pathways within a gene interaction network is a fundamental problem in Systems Biology to help understand the complex interactions and the regulation and flow of information within a system-of-interest. Given a weighted gene network and a gene in this network, the goal of an inference algorithm is to identify the potential regulatory pathways passing through this gene.Results: In a departure from previous approaches that largely rely on the random walk model, we propose a novel single-source k-shortest paths based algorithm to address this inference problem. An important element of our approach is to explicitly account for and enhance the diversity of paths discovered by our algorithm. The intuition here is that diversity in paths can help enrich different functions and thereby better position one to understand the underlying system-of-interest. Results on the yeast gene network demonstrate the utility of the proposed approach over extant state-of-the-art inference algorithms. Beyond utility, our algorithm achieves a significant speedup over these baselines.Availability: All data and codes are freely available upon request.Contact: srini@cse.ohio-state.eduSupplementary information: Supplementary data are available at Bioinformatics online.

An Efficient K-Shortest Paths Based Routing Algorithm

We present an efficient K-shortest paths routing algorithm for computer networks. This Algorithm is based on enhancements to currently used link-state routing algorithms such as OSPF and IS-IS, which are only focusing on finding the shortest path route by adopting Dijkstra algorithm. Its desire effect to achieve is through the use of K-shortest paths algorighm, which has been implemented successfully in some fileds like traffic engineering. The correctness of this Algorithm is discussed at the same time as long as the comparison with OSPF.

Topology awareness algorithm for virtual network mapping

Network virtualization is recognized as an effective way to overcome the ossification of the Internet. However, the virtual network mapping problem (VNMP) is a critical challenge, focusing on how to map the virtual networks to the substrate network with efficient utilization of infrastructure resources. The problem can be divided into two phases: node mapping phase and link mapping phase. In the node mapping phase, the existing algorithms usually map those virtual nodes with a complete greedy strategy, without considering the topology among these virtual nodes, resulting in too long substrate paths (with multiple hops). Addressing this problem, we propose a topology awareness mapping algorithm, which considers the topology among these virtual nodes. In the link mapping phase, the new algorithm adopts the k-shortest path algorithm. Simulation results show that the new algorithm greatly increases the long-term average revenue, the acceptance ratio, and the long-term revenue-to-cost ratio (R/C).

Comprehensive Study on Computational Methods for K-Shortest Paths Problem

application domains like network connection routing, highway and power line engineering, robot motion planning and other optimization problems require the computation of shortest path. Computations of K-shortest paths provide more (K-1) numbers of backup shortest paths for consideration, which enable the applicability of additional constraints on the particular domains. For instance, a biologist can determine the best of an alignment from the available instances of biological sequence alignments generated from more than one shortest paths computation. The purpose of this paper is to provide a comprehensive review of existing algorithms available for K- shortest paths computation. It will be useful for researcher to implement the effective K-shortest paths computation based on their matching computational requirements over the domain of their interest.

Incorporating transfer reliability into equilibrium analysis of railway passenger flow

Passenger’s transfer route choice behavior is one of the prominent research topics in the field of railway transportation. Existing traffic assignment approaches do not properly account for passenger’s expectation for transfer reliability. In this study, the transfer reliability is explicitly defined and a multi-class user equilibrium model is established, given which passengers choose the minimal-cost path based on their expected reliability thresholds. In particular, a path-based traffic assignment algorithm which combines a k-shortest path algorithm and the method of successive averages is proposed. The validity of the proposed approach is verified by an illustrative example. Using the proposed modeling approach, it is possible to determine the passenger’s collective route choice behavior based on the user equilibrium pattern. Moreover, the railway timetables can be evaluated and optimized based on the cost-based level of service estimation.

Dynamically Generating Operationally Acceptable Route Alternatives Using Simulated Annealing

This paper presents a simulated annealing (SA) methodology for defining operationally acceptable route alternatives for flights impacted by weather. By dynamically generating route alternatives that inherently possess traits amenable to traffic managers and users, more efficient use of the airspace can be realized. This paper explores the use of SA to provide quality solutions quickly and to capture additional route alternative options, such as ground delay. For comparison, a k-shortest path approach and an ad hoc heuristic search approach have also been employed to generate reroutes and the results show that SA indeed provides competitive alternatives to the k-shortest path approach and improved alternatives over the heuristic search procedure. Furthermore, SA can potentially generate these alternatives with less computation effort than the k-shortest path approach and, therefore, represents a desirable method for generating alternate flight paths.