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The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversalbased approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in O(n 3 ) steps and has a tight approximation factor of 3−2/b(G), where b(G) is the size of an optimal solution. The main attribute of BFF is that it has a better approximation factor than the state-of-the-art approximation algorithms for general graphs, which report an approximation factor of 3. Despite being simple, BFF proved practical when tested over some benchmark datasets.

Bad air quality due to free pollutants such as particulate matter (PM), carbon dioxide (CO 2 ), nitrogen oxides (NO x ) and volatile organic components (VOC) increases the risk of long- term health diseases. The impact of traffic-calming measures on air quality has been studied using specialized equipment at control sites or mounted on cars to monitor pollutants levels. However, this approach suffers from a large number of variables on the experiments such as vehicles types, number of monitored vehicles, driver’s behavior, traffic density, time of the day, elapsed monitoring time, road conditions and weather. In this work, we use a cellular automata and an instantaneous traffic emissions model to capture the effect of speed humps on traffic flow and on the generation of CO 2 , NO x , VOC and PM pollutants. This approach allows us to study and characterize the effect of many speed humps on a single lane. We found that speed humps significantly promote the generation of pollutants when the number of vehicles on a lane is low. Our results may provide insight into urban planning strategies to reduce the generation of traffic emissions and lower the risk of long-term health diseases.

Unsignalized mid-block raised crosswalks have been adopted as inclusive transport strategies, providing humps to reduce vehicles’ speed to promote drivers to yield to pedestrians. The interaction between vehicles and pedestrians can induce local jams that can merge to become a gridlock. The purpose of this paper is to investigate the interaction between vehicles and the mid-block raised crosswalk, analyzing its effects on traffic flow, instantaneous CO2 emissions, and energy dissipation. A pedestrian–vehicle cellular automata model was developed, where a single-lane road with a mid-block raised crosswalk is considered. The lane boundaries were controlled with the injections rate (α) and extraction rate (β), while the pedestrians’ entrance was controlled with the rate (αp). The system’s phase diagram was constructed, identifying four phases: maximum current, jamming, congestion, and gridlock. All observed phase transitions are of the second order. The transition from maximum current (or jamming) phase to gridlock phase is not noticed. Moreover, since the crosswalk is a bottleneck, the gridlock phase takes place when the pedestrians’ influx exceeds a critical value (αp > 0.8). The study also revealed that the crosswalk is the main precursor of energy dissipation and CO2 emissions, whose major effects are observed during the jamming phase.

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