Parameterized Algorithms and Data Reduction for Safe Convoy Routing

We study a problem that models safely routing a convoy through a transportation network, where any vertex adjacent to the travel path of the convoy requires additional precaution: Given a graph G=(V,E), two vertices s,t in V, and two integers k,l, we search for a simple s-t-path with at most k vertices and at most l neighbors. We study the problem in two types of transportation networks: graphs with small crossing number, as formed by road networks, and tree-like graphs, as formed by waterways. For graphs with constant crossing number, we provide a subexponential 2^O(sqrt n)-time algorithm and prove a matching lower bound. We also show a polynomial-time data reduction algorithm that reduces any problem instance to an equivalent instance (a so-called problem kernel) of size polynomial in the vertex cover number of the input graph. In contrast, we show that the problem in general graphs is hard to preprocess. Regarding tree-like graphs, we obtain a 2^O(tw) * l^2 * n-time algorithm for graphs of treewidth tw, show that there is no problem kernel with size polynomial in tw, yet show a problem kernel with size polynomial in the feedback edge number of the input graph

FRAMEWORK FOR INCORPORATING NETWORK CONNECTIVITY IN TRANSPORTATION SYSTEMS EVALUATION

In transportation investment evaluation, agencies often do not consider the impact of proposed projects in terms of the increased connectivity of the parent network. Thus, agencies may be inadvertently omitting a key and critical goal of transportation investment evaluation and decision making, particularly in regions and countries with sparse networks. This dissertation develops a framework for measuring network connectivity performance for use as an input for the evaluation process and is applicable to existing or proposed networks in any mode of transportation. The steps for the framework include selection of network performance measures (PMs), scaling the PMs, determining the level of topological performance for a given network, establishing the levels of node and link importance, and calculating the overall network connectivity performance. Another framework is used to quantify the overall connectivity level of the sparse networks with due consideration of the contribution of individual nodes in terms of economic, social, or political importance to the entire network. This dissertation also proposes a methodology to investigate the effect of prospective projects on sparse network connectivity to develop PM tradeoff curves (PMTC) that could be used to investigate the tradeoffs between the different measures of network topological performance. Application of the network connectivity framework using a case study network is also presented in this dissertation to demonstrate the usefulness of the framework in developing vital information of interest to transportation decision makers. The developed PM tradeoff curves were found to be useful for scenario analysis and investigating the relationships between PMs. The case study also demonstrated that the overall topological performance impact of a number of projects can be significantly different from the sum of their individual topological performance impacts. In other words, the effect of the sum of the stimuli is superior to the sum of the individual effects of the stimuli, which is consistent with holism, a basic concept in systems engineering. More importantly, this finding suggests that inter-project interdependencies, a phenomenon whose characterization has been largely elusive in the literature, can be demonstrated and measured in terms of network topological performance