Figure 6.

Empirical time and memory requirements for structural alignment. Plots of data from Table 1. Filled circles: divide and conquer algorithm; open circles: standard CYK algorithm. Left: Memory use in megabytes on a log-log scale. Lines represent weighted least-squares regression fits to the theoretically expected memory scaling: aN² log N for divide and conquer (solid line) and aN³ for standard CYK (dashed line). Right: CPU times in seconds on a log-log scale. Lines represent least-squares regression fits to a power law (aN^b). According to this fit, divide and conquer time (solid line) empirically scales as N^3.24, and standard CYK without traceback (dashed line) scales as N^3.29. A line representing O(N⁴) scaling (the theoretical upper bound on performance) is shown for comparison.