Knowing the shape of the valleys in complex energy landscapes bears on a number of fields, ranging from the design of stochastic
optimization algorithms, such as simulated annealing, to the study of thermal relaxation of glassy systems and to the prediction
of metastable compounds for chemical synthesis. The ‘lid’ algorithm is designed to exhaustively explore the neighborhoods
of local energy minima of model systems, extracting the features which are relevant for the dynamics.
In this paper the algorithm is presented and some implementation issues, including those of parallel performance and scalability,
are discussed. In addition, we present selected results pertaining to different models. These results are chosen to illustrate
the versatility of the method and to highlight the important traits, e.g. the exponential nature of the dependence of the
local density of states on the energy and of the local state space volume on the energy barrier, which are shared by a wide
range of applications. The implications for the relaxation behavior and the thermal metastability of the systems considered
are briefly discussed.