ABSTRACT. Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the CRITICAL NODE PROBLEM has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is N P -complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

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The results of research involving a well-designed before-and-after evaluation of the safety effects of providing left- and right-turn lanes for at-grade intersections are presented. Geometric design, traffic control, traffic volume, and traffic accident data were gathered for a total of 280 improved intersections as well as 300 similar intersections that were not improved during the study period. The types of improvement projects evaluated included installation of added left-turn lanes, added right-turn lanes, and extension of the length of existing left- or right-turn lanes. An observational before-and-after evaluation of these projects was performed by using several alternative evaluation approaches. Three contrasting approaches to before-and-after evaluation were used: the yoked comparison or matched-pair approach, the comparison group approach, and the empirical Bayes approach. The research not only evaluated the safety effectiveness of left- and right-turn lane improvements but also compared the performances of these three alternative approaches in making such evaluations. The research developed quantitative safety effectiveness measures for installation design improvements involving added left-turn lanes and added right-turn lanes. The research concluded that the empirical Bayes method provides the most accurate and reliable results. Further use of this method is recommended.