We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to static algorithms on random, real-world and hard instances. Our experimental data suggest that some of the dynamic algorithms and their algorithmic techniques can be really of practical value in many situations. 1

Abstract. Internet protocol (IP) traffic follows rules established by routing protocols. Shortest path based protocols, such as Open Shortest Path First (OSPF), direct traffic based on arc weights assigned by the network operator. Each router computes shortest paths and creates destination tables used for routing flow on the shortest paths. If a router has multiple outgoing links on shortest paths to a given destination, it splits traffic evenly over these links. It is also the role of the routing protocol to specify how the network should react to changes in the network topology, such as arc or router failures. In such situations, IP traffic is re-routed through the shortest paths not traversing the affected part of the network. This paper addresses the issue of assigning OSPF weights and multiplicities to each arc, aiming to design efficient OSPF-routed networks with minimum total weighted multiplicity (multiplicity multiplied by the arc length) needed to route the required demand and handle any single arc or router failure. The multiplicities are limited to a discrete set of values and we assume that the topology is given. We propose an evolutionary algorithm for this problem, and present results applying it to several real-world problem instances. 1.

Abstract. This article relates some combinatorial optimization problems encountered by an optimizer in an industrial research laboratory at AT&T, a large telecommunications company. The article will appear in the Fall 2007 issue of SIAM SIAG/Optimization Views-and-News which will try to cover some aspects of the industrial applications of optimization and of the life of optimizers at AT&T, IBM, and Exxon. 1.

Let G =(V,E,w) be a simple digraph, in which all edge weights are non-negative real numbers. Let G ′ be obtained from G by the application of a set of edge weight updates to G. Lets∈V, and let Ts and T ′ s be a Shortest Path Tree (SPT) rooted at s in G and G ′ , respectively. The Dynamic Shortest Path (DSP) problem is to compute T ′ s from Ts. For the DSP problem, we correct and extend a few existing SPT algorithms to handle multiple edge weight updates. We prove that these extended algorithms are correct. The complexity of these algorithms is also analyzed. To evaluate the proposed algorithms, we compare them with the well-known static Dijkstra algorithm. Extensive experiments are conducted with both real-life and artificial data sets. The real-life data are road system graphs obtained from the Connecticut road system and are relatively sparse. The artificial data are randomly generated graphs and are relatively dense. The experimental results suggest the most appropriate algorithms to be used under different circumstances.

A dynamic shortest-path algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fully-dynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an extensive experimental study of the existing algorithms for the single-edge and the batch case, including a broad set of test instances. We further present tuned variants of the already existing SWSF-FP-algorithm being up to 15 times faster than SWSF-FP. A surprising outcome of the paper is the astonishing level of data dependency of the algorithms.

Among the variants of the well known shortest path problem, those that refer to a dynamically changing graphs are theoretically interesting, as well as computationally challenging. Applicationwise, there is an industrial need for computing point-to-point shortest paths on large-scale road networks whose arcs are weighted with a travelling time which depends on traffic conditions. We survey recent techniques for dynamic graph weights as well as dynamic graph topology. 1

Abstract. We propose heuristic improvements in the procedure to obtain a (1+ω)-approximation of the multicommodity flow which satisfies all demands when the cost bound is given as an input parameter. Through a series of improvements we are able to significantly reduce the number of shortest path computations. We also present a new version of the algorithm given in [1] which is amenable to our optimizations. Finally we compare our results against those given in [2] and demonstrate significant improvement in the results. We also propose methods to reduce the running time of the algorithm. 1

The computation of point-to-point shortest paths on time-dependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in time-dependent graphs, which is the difficulty of using bidirectional search: since the exact arrival time at the destination is unknown, we start a backward search from the destination node using lower bounds on arc costs in order to restrict the set of nodes that have to be explored by the forward search. Our algorithm is based on A ∗ with landmarks (ALT); extensive computational results show that it is very effective in practice if we are willing to accept a small approximation factor, resulting in a speed-up of more than one order of magnitude with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. The main idea presented here can also be generalized to other types of search algorithms.

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