Efficient Shortest Path Algorithm Research Articles

Design of an efficient routing algorithm on the WK-recursive network

The WK-recursive network proposed by Vecchia and Sanges[1] is widely used in the design and implementation of local area networks and parallel processing architectures. It provides a high degree of regularity and scalability, which conform well to a design and realization of distributed systems involving a large number of computing elements. In this paper, the routing of a message is investigated on the WK-recursive network, which is key to the performance of this network. We present an efficient shortest path algorithm on the WK-recursive network, which is simpler than Chen and Duh[2] in terms of design complexity.

Shortest Path Algorithms for Pedestrian Navigation Systems

Efficient shortest path algorithms are of key importance for routing and navigation systems. However, these applications are designed focusing on the requirements of motor vehicles, and therefore, finding paths in pedestrian sections of urban areas is not sufficiently supported. In addition, finding the shortest path is often not adequate for urban sidewalk routes, as users of these applications may also be interested in alternative routes that, although slightly longer, possess other desirable features and properties. According to the literature, the search for alternative routes is carried out mainly using the k-shortest paths (KSP) algorithm which represents an ordered list of all available alternatives. Even though various KSP algorithms have been proposed, to the best of our knowledge, there is no research addressing all issues inherent in a pedestrian navigation system. The purpose of this paper is to present a heuristic algorithm for graph datasets that implements a penalty-based method which, by increasing certain edge weights, effectively searches for the most accessible alternative paths in multi-route cases. To demonstrate how the algorithm works, we present experimental results on finding the most accessible paths in pedestrian sections of the historical center of Thessaloniki city.

An efficient shortest path algorithm for content-based routing on 2-D mesh accelerator networks

Reconfigurable units such as Field Programmable Gate Arrays (FPGAs) have been used widely as high-performance hardware accelerators for a variety of applications and offer a promising solution to the power bottleneck of current multi-core processors. One emerging trend in hardware acceleration is to build a specialized network for accelerators to support inter-accelerator communications with the goal of increasing acceleration throughput by sharing functions and avoiding frequent reconfiguration. On accelerator networks, data packets are routed in a content-based instead of an address-based manner in that the destinations are determined by the acceleration task—any nodes that support the current acceleration step could be a receiver. Designing an effective and efficient routing algorithm that supports content-based routing becomes an important problem. Adopting shortest path routing for each acceleration task is a standard approach. While Breadth-First Search (BFS) algorithm can be applied, a naive implementation is computationally unaffordable. We propose a new routing algorithm called the Shortest Cycle Routing Algorithm and address the computation inefficiency of standard BFS. We design a branch-and-bound method to effectively prune the search tree without compromising path optimality. The time and space complexities for searching the shortest cycles of an acceleration task of k steps improve from Onk to O(1) where n is the number of accelerators in the network. We analyze locality and path diversity properties of shortest cycle routing and show how they can be used to develop adaptive routing strategy, restrict global flooding to local neighborhood and reduce the number of path cycles.

Improving centralized path calculation based on graph compression

Shortest-path calculation on weighted graphs are an essential operation in computer networks. The performance of such algorithms has become a critical challenge in emerging software-defined networks (SDN), since SDN controllers need to centralizedly perform a shortest-path query for every flow, usually on large-scale network. Unfortunately, one of the challenges is that current algorithms will become incalculable as the network size increases. Therefore, inspired by the compression graph in the field of compute visualization, we propose an efficient shortest path algorithm by compressing the original big network graph into a small one, but the important graph properties used to calculate path is reserved. We implement a centralized version of our approach in SDN-enabled network, and the evaluations validate the improvement compared with the well-known algorithms.

Highway Dimension and Provably Efficient Shortest Path Algorithms

Computing driving directions has motivated many shortest path algorithms based on preprocessing. Given a graph, the preprocessing stage computes a modest amount of auxiliary data, which is then used to speed up online queries. In practice, the best algorithms have storage overhead comparable to the graph size and answer queries very fast, while examining a small fraction of the graph. In this article, we complement the experimental evidence with the first rigorous proofs of efficiency for some of the speedup techniques developed over the past decade or variations thereof. We define highway dimension, which strengthens the notion of doubling dimension. Under the assumption that the highway dimension is low (at most polylogarithmic in the graph size), we show that, for some algorithms or their variants, preprocessing can be implemented in polynomial time, the resulting auxiliary data increases the storage requirements by a polylogarithmic factor, and queries run in polylogarithmic time. This gives a unified explanation for the performance of several seemingly different approaches. Our best bounds are based on a result that may be of independent interest: we show that unique shortest paths induce set systems of low VC-dimension, which makes them combinatorially simple.

Pruning Algorithms to Determine Reliable Paths on Networks with Random and Correlated Link Travel Times

This study addresses various formulations of the optimal reliability path problem on stochastic networks. Robust-Cost is adopted as the measure of reliability, which is defined as a weighted combination of the mean and standard deviation of travel time. The principal problem solved is the Minimum Robust-Cost Path (MRCP) problem in the presence of Correlated link travel times. It is shown that the subpath optimality and subpath non-dominance principles, which are conventionally adopted in the literature, cannot be used to solve this problem. In this light, this study proposes an algorithm based on the subpath pruning approach, which eliminates nonoptimal subpaths by using a pruning criterion. We construct the novel pruning criterion, which depends on only two independent objectives, by transforming the network and using efficient shortest path algorithms. The correctness of the algorithm is established, and its good practical performance is demonstrated on real-world networks. Furthermore, the pruning procedure is generalized with suitable modifications to solve three related problems: (i) the MRCP problem with independent link travel times, (ii) the K-best Robust-Cost Paths problem, and (iii) the MRCP problem with stochastic nondominance constraints. These extensions demonstrate the potential wider applications of the proposed solution approach.

A Lagrangian Relaxation Method for Crew and Vehicle Rescheduling of Railway Passenger Transportation and its Application

We propose a method for solving the crew rescheduling problem (CRP) and the vehicle rescheduling problem (VRP) based on the Lagrangian relaxation method. The CRP/VRP is formulated as an integer programming problem on the basis of a network flow modeling approach from which a Lagrangian relaxation problem is constructed by relaxing the constraint that links multiple resources. Using two procedures that generate the upper and lower bounds of the primal problem, both of which utilize an efficient shortest path algorithm for the directed acyclic graph (DAG), the proposed method gradually improves the gap between the upper and lower bounds while updating Lagrangian multipliers. Experimental results of real-world vehicle rescheduling data from Japanese railway lines indicated that the proposed method generated feasible solutions that were confirmed to be fairly close to the optimal solutions according to the gap between the upper and lower bounds, and also clarified the quality of the other method's solution by using the gap, which could lead to streamlining and sophisticating real-world rescheduling related activities.

Improvement A* Algorithm Based on Dynamic Consistency Assumption

Efficient dynamic shortest path algorithm in static networks plays an important role in ITS. To solve this problem, this paper brings forward the dynamic form of Consistency Assumption and Dynamic A* algorithm (A* algorithm based on dynamic lower bound, DA* algorithm) based on dynamic lower bound. DA* algorithm and the dynamic form of Consistency Assumption are described in detail. It is proved that DA* algorithm can solve one origin node to one destination node shortest paths problem in dynamic networks, if DA* algorithm’s dynamic lower bound satisfies the dynamic form of Consistency Assumption.

Optimal routing in double loop networks

In this paper, we study the problem of finding the shortest path in circulant graphs with an arbitrary number of jumps. We provide algorithms specifically tailored for weighted undirected and directed circulant graphs with two jumps which compute the shortest path. Our method only requires O ( log N ) arithmetic operations and the total bit complexity is O ( log 2 N log log N log log log N ) , where N is the number of the graph’s vertices. This elementary and efficient shortest path algorithm has been derived from the Closest Vector Problem (CVP) of lattices in dimension two and with an ℓ 1 norm.

Scheduling with timed automata

In this work, we present timed automata as a natural tool for posing and solving scheduling problems. We show how efficient shortest path algorithms for timed automata can find optimal schedules for the classical job-shop problem. We then extend these results to synthesize adaptive scheduling strategies for problems with uncertainty in task durations.

A new parallel and distributed shortest path algorithm for hierarchically clustered data networks

This paper presents new efficient shortest path algorithms to solve single origin shortest path problems (SOSP problems) and multiple origins shortest path problems (MOSP problems) for hierarchically clustered data networks. To solve an SOSP problem for a network with n nodes, the distributed version of our algorithm reaches the time complexity of O(log(n)), which is less than the time complexity of O(log/sup 2/ (n)) achieved by the best existing algorithm. To solve an MOSP problem, our algorithm minimizes the needed computation resources, including computation processors and communication links for the computation of each shortest path so that we can achieve massive parallelization. The time complexity of our algorithm for an MOSP problem is O(m log(n)), which is much less than the time complexity of O(M log/sup 2/ (0)) of the best previous algorithm. Here, M is the number of the shortest paths to be computed and m is a positive number related to the network topology and the distribution of the nodes incurring communications, m is usually much smaller than M. Our experiment shows that m is almost a constant when the network size increases. Accordingly, our algorithm is significantly faster than the best previous algorithms to solve MOSP problems for large data networks.

A computational study of efficient shortest path algorithms

Five efficient shortest path algorithms are implemented and compared in this report. The selected algorithms are the most efficient, measured either in terms of worst case bounds or from previous computational studies. The algorithms include two using threshold functions, two using heaps, and one using buckets for sorting node labels. The last three algorithms have not been studied in detail before. The computational experiment employs a rigorous design to ensure that the results have statistical validity. Three different cost functions are generated to measure the sensitivity of each algorithm to cost distributions. Curve fittings are performed to summarize the results and they show high degrees of goodness-of-fit. The results reveal some heretofore unknown properties of some of the algorithms.

Multifacility in-series production-planning model with capacity constraints

A single-product M facilities in-series production-planning model is analysed in which known demands on the last facility must be satisfied. The model considers concave production costs and piecewise concave inventory costs in the introduction of production capacity constraints. Backlogging of unsatisfied demand is permitted. The structure of optimal production schedules is exploited and then used to develop an efficient shortest-path algorithm for the systems with parallel production (inventory) cost functions. A numerical example is presented

A new variant of the partitioning shortest path algorithm

This paper proposes a new variant of a label correcting polynomially bounded and computationally efficient shortest path algorithm, called the partitioning shortest path (PSP) algorithm. This variant, called the Extended PSP algorithm, provides a new rule for selecting scan eligible nodes to scan which has promising computational properties, particularly when shortest path algorithms are employed in relaxation strategies. In addition, results are established for this variant which provide a percent of optimality solution procedure.

A distance geometry program for determining the structures of small proteins and other macromolecules from nuclear magnetic resonance measurements of intramolecular 1H- 1H proximities in solution

DISGEO is a new implementation of a distance geometry algorithm which has been specialized for the calculation of macromolecular conformation from distance measurements obtained by two-dimensional nuclear Overhauser enhancement spectroscopy. The improvements include (1) a decomposition of the complete embedding process into two successive, more tractable calculations by the use of “substructures”, (2) a compact data structure for storing incomplete distance information on a structure, (3) a more efficient shortest-path algorithm for computing the triangle inequality limits on all distances from this information, (4) a new algorithm for selecting random metric spaces from within these limits, (5) the use of chirality constraints to obtain good covalent geometry without the use of ad hoc weights or excessive optimization. The utility of the resultant program with nuclear magnetic resonance data is demonstrated by embedding complete spatial structures for the protein basic pancreatic trypsin inhibitor vs all 508 intramolecular, interresidue proton-proton contacts shorter than 4.0 A that were present in its crystal structure. The crystal structure could be reproduced from this data set to within 1.3 A minimum root mean square coordinate difference between the backbone atoms. We conclude that the information potentially available from nuclear magnetic resonance experiments in solution is sufficient to define the spatial structure of small proteins.