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 present a simple shortest path algorithm. If the input lengths are positive and uniformly distributed, the algorithm runs in linear time. The worst-case running time of the algorithm is O(m + n log C), where n and m are the number of vertices and arcs of the input graph, respectively, and C is the ratio of the largest and the smallest nonzero arc length.

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We review shortest path algorithms based on the multi-level bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an e#cient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.

: Yen's algorithm is a classical algorithm for ranking the K shortest loopless paths between a pair of nodes in a network. In this paper an implementation of Yen's algorithm is presented. Although with no consequences in what concerns the computational complexity order when considering a worst-case analysis, O(Kn(m+ n log n)), in practice this new implementation outperforms a straightforward one, as the reported comparative computational experiments allow us to conclude. Keywords: network, path, loopless path, paths ranking. 1 Introduction The problem of determining the K shortest paths, or the ranking of the K shortest paths between a pair of nodes in a network was due to Hoffman and Pavley, [6], who proposed an algorithm for solving it. In this problem, for a given integer K 1, is intended to determine successively the shortest path, the second shortest path, . . . , until the K-th shortest path between the given pair of nodes. Since 1951 numerous articles on this subject have be...

: In this paper, the optimal path problem will be studied from a global point of view and having no restrictions imposed on the network. The concepts of boundness and finiteness will be presented for the general problem and will be studied in two particular cases. Special emphasis will be given to the optimality principle since it allows one to design a class of algorithms -- the labelling algorithms -- which determine an optimal path when the weak optimality principle is satisfied. Its importance will be stressed by two problems which, in its turn, are similar in their description and completly different in what concerns their resolution. Keywords: network, path, optimality principle, labelling algorithms. 1 Introduction In the optimal path problem, a real function is considered which assigns a value to each path that can be defined between a given pair of nodes in a given network; a path with the best value in a subset of paths between that pair of nodes is what has to be determin...

: Ranking shortest paths is a classical network problem consisting of the determination of the K shortest paths connecting a given initial--destination pair of nodes such as the distance of the k th path that is determined is no greater than the distance of any j th one, for some j ? k . In this paper an algorithm for ranking paths is reviewed being its complexity improved in terms of the required memory space. This improvement allows the ranking of really larger problems in reasonably small execution times, which is comproved by the presented computational experiments. In fact, for randomly generated networks with 10000 nodes, the algorithm ranks more than half of a million of paths in a few cents of seconds of CPU execution time. This performance can be very important because of the potential practical applications of the problem, nameley as a subproblem of the constrained shortest path problem and of the multiobjective shortest path problem. Keywords: network, tree, path, pat...

The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K ? 1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction is considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition -- for example, to be loopless. In this paper new algorithms are proposed for the unconstrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths. Keywords: Network, tree, path, path d...

Developing a polynomial time algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n 2 m log nC, n 2 m 2 log n)) time, where n is the number of nodes in the network, m is the number of arcs, and C denotes the maximum absolute arc costs if arc costs are integer and 0 otherwise. We first introduce a pseudopolynomial variant of the network simplex algorithm called the "premultiplier algorithm. " A vector X of node potentials is called a vector of premultipliers with respect to a rooted tree if each arc directed towards the root has a non-positive reduced cost and each arc directed away from the root has a non-negative reduced cost. We then develop a cost-scaling version of the premultiplier algorithm that solves the minimum cost flow problem in O(min(nm log nC, nm 2 log n)) pivots, With certain simple data structures, the average time per pivot can be shown to be O(n). We also show that the diameter of the network polytope is O(nm log n).