Parallel Label-Correcting Algorithms for Large-Scale Static and Dynamic Transportation Networks on Laptop Personal Computers

A parallel implementation of the Label Correcting Algorithm (LCA) for finding shortest paths on static networks is first presented. The parallel static LCA is then extended to include time-dependent link costs. For both the static and time-dependent cases, an efficient sparse matrix storage scheme that has been frequently employed by “sparse equations solver researchers” is adopted. It can be shown that the proposed sparse storage scheme is equivalent (in terms of computer memory requirement) to the forward or reverse star representation that is often used by transportation researchers. The proposed parallel (time-dependent) LCA simply assigns each processor to handle a number of source (or destination) nodes within a network. Both real (and randomly generated), static and time-dependent transportation networks (including a network with 100,000 nodes and 349,850 links) are extensively used to evaluate the numerical efficiency (in terms of accuracy, and wall-time) of the proposed parallel LCA, using inexpensive desktop/laptop Personal Computers (PCs), and under the C#, C++, and MATLAB programming languages. Numerical results demonstrate that the proposed parallel LCA is simple and very efficient. While implementing the proposed parallel LCA in the MATLAB / C++ environments offer the reasonable / very good efficiency of around 65% / 87%, its efficiency increased to be in the remarkable range of 95.11 % (which is very close to the 100% ideal/ perfectly linear efficiency) through 167.12% (which is considered as “super-linear” performance) when implementing in the C # environment.