. We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research. Andrew V. Goldberg was supported in part by ONR Young Investigator Award N00014-91-J-1855, NSF Presidential Young Investigator Grant CCR-8858097 with matching funds from AT&T, DEC, and 3M, and a grant from Powell Foundation. This work was done while Boris V. Cherkassky was visiting Stanford University Compu...

The classic problem of finding the shortest path over a network has been the target of many research efforts over the years. These research efforts have resulted in a number of different algorithms and a considerable amount of empirical findings with respect to performance. Unfortunately, prior research does not provide a clear direction for choosing an algorithm when one faces the problem of computing shortest paths on real road networks. Most of the computational testing on shortest path algorithms has been based on randomly generated networks, which may not have the characteristics of real road networks. In this paper, we provide an objective evaluation of 15 shortest path algorithms using a variety of real road networks. Based on the evaluation, a set of recommended algorithms for computing shortest paths on real road networks is identified. This evaluation should be particularly useful to researchers and practitioners in operations research, management science, transportation, and Geographic Information Systems. The computation of shortest paths is an important task in many network and transportation related analyses. The development, computational testing, and efficient implementation of shortest path algorithms have remained important research topics within related disciplines such as operations

We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of our discoveries is that a cycle detection strategy of Tarjan greatly improves practical performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of our study, we develop problem families for testing negative cycle algorithms. This work was done while the author was visiting NEC Research Institute, Inc. 1 Introduction The negative cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. [15]). The problem is closely related to the shortest path problem (see e.g. [1, 7, 16, 18, 19, 20]) of finding shortest path distances in a netwo...

We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic as well as exact solutions and associated data structures affect the computational performance of the software developed for realistic transportation networks. For this purpose we have used a road network representing with high degree of resolution the Dallas Ft-Worth urban area. We discuss and experimentally analyze various one-to-one shortest path algorithms. These include classical exact algorithms studied in the literature as well as heuristic solutions that are designed to take into account the geometric structure of the input instances. Computational results are provided to empirically compare the efficiency of various algorithms. Our studies indicate that a modified Dijkstra's algorithm is computationally fast and an ex...

Abstract not found

This paper introduces a transformer for improving the communication complexity of several classes of distributed algorithms. The transformer takes a distributed algorithm whose message complexity is O(f \Delta m) and produces a new distributed algorithm to solve the same problem with O(f \Delta n log n+m log n) message complexity, where n and m are the total number of nodes and links in the network, and f is an arbitrary function of n and m. Applying our paradigm to the standard all shortest paths algorithm [Gal76, Gal82, Seg83] yields a new algorithm which solves the problem in O(n 2 log n) messages (The previous best that we know of is O(m \Delta n) messages). When applied to the O(m \Delta log 3 n) breadth-first search algorithm of Awerbuch and Peleg [AP90a] our paradigm yields an O(m+ n \Delta log 4 n) messages algorithm. 1 introduction One way to run a distributed algorithm is to collect all its inputs to one node, run a sequential algorithm on all the inputs at this ...

We propose a new and simple algorithm for finding shortest paths in a directed graph. In the single origin/single destination case, the algorithm maintains a single path starting at the origin, which is extended or contracted by a single node at each iteration. Simultaneously, at most one dual variable is adjusted at each iteration so as to either improve or maintain the value of a dual function. For the case of multiple origins, the algorithm is well suited for parallel computation. It maintains multiple paths that can be extended or contracted in parallel by several processors that share the results of their computations. Based on experiments with randomly generated problems on a serial machine, the algorithm outperforms substantially its closest competitors for problems with few origins and a single destination. It also seems better suited for parallel computation than other shortest path algorithms.

We propose a new method for ordering the candidate nodes in label correcting methods for shortest path problems. The method is equally simple but much faster than the D'Esopo-Pape algorithm. It is similar to the threshold algorithm in that it tries to scan nodes with small labels as early as possible, and performs comparably with that algorithm. Our algorithm can also be combined with the threshold algorithm thereby considerably improving the practical performance of both algorithms.

. We describe a new shortest paths algorithm. Our algorithm achieves the same O(nm) worst-case time bound as Bellman-Ford algorithm but is superior in practice. 1. Introduction The Bellman-Ford algorithm [1, 4, 7] is a classical algorithm for the single-source shortest paths problem. The algorithm runs in O(nm) time on a graph with n nodes and m arcs. This is the best currently known strongly polynomial bound for the problem (see [6] for the best weakly polynomial bound). In practice, however, the Bellman-Ford algorithm is usually outperformed by the deque algorithm of D'Escopo-Pape [9] and by the two-queue algorithm of Pallottino [8]. The workcase time bounds for these algorithms, however, are worse than those for the Bellman-Ford algorithm. The deque algorithm may take exponential time in the worst case [10] and the two-queue algorithm may take \Omega\Gamma n 2 m) time. We propose a new topological-scan algorithm for the shortest paths problem. The algorithm combines, in a natur...

Abstract. In this paper we develop parallel asynchronous implementations of some known and some new label correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved with some of the methods, and it is found that the asynchronous versions of these methods are substantially faster than their synchronous counterparts.