  Using a non-thermal local search, called Extremal Optimization (EO), in
conjunction with a recently developed scheme for classifying the valley
structure of complex systems, we analyze a short-range spin glass. In
comparison with earlier studies using a thermal algorithm with detailed
balance, we determine which features of the landscape are algorithm dependent
and which are inherently geometrical. Apparently a characteristic for any local
search in complex energy landscapes, the time series of successive energy
records found by EO also is characterized approximately by a log-Poisson
statistics. Differences in the results provide additional insights into the
performance of EO. In contrast with a thermal search, the extremal search
visits dramatically higher energies while returning to more widely separated
low-energy configurations. Two important properties of the energy landscape are
independent of either algorithm: first, to find lower energy records,
progressively higher energy barriers need to be overcome. Second, the Hamming
distance between two consecutive low-energy records is linearly related to the
height of the intervening barrier.
