OPTIMIZING THE JAVA VIRTUAL MACHINE INSTRUCTION SET BY ...

199
Chapter 9
An Efficient Multicode
Identification Algorithm
Chapter 7 described the multicode identification process. This included a description
of the algorithm used initially as well as later work which reduced the time and space
cost associated with gathering and evaluating the profile data. This chapter presents
an efficient algorithm for identifying multicodes from a collection of profile data by
identifying and solving an equivalent string problem.
9.1 The Most Contributory Substring Problem
The problem of determining the best multicode can be expressed as a string problem.
Considering the problem in this way led to the identification of a new string problem
that had not been considered previously. Furthermore, an efficient algorithm was
developed for determining its solution which has a considerably lower complexity
than the O(n 3 ) algorithm shown in Figure 7.4 and Figure 7.5. This new algorithm
views the problem of identifying multicodes as a string problem where the goal is to
identify the substring that represents the greatest contribution of characters to a set
of strings. More precisely, the most contributory substring w is a string of characters
such that the length of w, denoted by |w|, times the number of times it occurs within
a set of strings is maximal. Equivalently, the most contributory substring, w, can be
viewed as the string that reduces the number of characters in a set of strings by the
greatest amount when all occurrences of w are removed. To the best of the author’s
knowledge, this problem has not been formally defined or solved previously.