Dynamic event detection by using participatory sensing paradigms has received growing interests recently, where detection tasks are assigned to smart-device users who can potentially collect needed sensory data from device-equipped sensors. Typical applications include, but are not limited to, noise and air pollution detections, people gathering, even disaster prediction. Given this problem, although many existing centralized solutions are effective and widely used, they usually cause heavy communication overhead. Thus, it is strongly desired to design distributed solutions to reduce energy consumption, while achieving a high level of detection accuracy with limited sensing task budget. In this paper, we first present two novel centralized detection algorithms as the performance benchmark, which make use of the Minimum Cut theory and support vector machine (SVM)-based pattern recognition techniques. Then, we introduce a novel distributed and energy-efficient event detection framework under task budget constraint, where we formulate an optimization problem and derive an optimal utility function. Finally, based on a real trace-driven data set in an urban area of Beijing, extensive simulation results demonstrate the effectiveness of our proposed algorithms.