M.Sc Student | Yaron Ben-Shoshan |
---|---|

Subject | Labeling Fork-Join Task Graphs for Data Race Detection |

Department | Department of Electrical Engineering |

Supervisor | Full Professor Moses Yoram |

Labeling schemes
are a central tool in dynamic data race detection. The
space complexity of the labels and the time complexity of comparing two labels
are a crucial factor in the time and space complexity of data race detection
methods that use that scheme. This work establishes two tight lower bounds on
the space complexity of a single label produced by a labeling method in a fork-join
run. Consider the following parameters of a fork-join structured run _{}:

_{} - The maximal nesting
level of fork-join pairs in r.

_{} - The size of a maximal
set containing pairwise parallel blocks.

_{} - The maximal number of
fork-join pairs within the same nesting level.

_{} - The maximal number of
threads forked form a “fork” operation.

One lower bound,
which is given in term of the parameters *N*, *S *and *L is *_{} , and
the other, which is given in term of *T* and *L* alone, is _{} . We also prove that methods exist whose space complexity meets the lower
bounds. The first method to be mentioned under this context is called *DTN*
(*Decomposition Tree Numbering*), and it matches the lower bound of _{} .
Instead of presenting a labeling method that meets the lower bound of _{} , we
present a general translation between labeling methods. Assume we are given a
labeling method with a space complexity of _{} . The result of translating this method is a new labeling method
with a space complexity of _{} . In this manner we conclude that the conversion of DTN meets
the _{} lower
bound. This work extends, generalizes, and unifies the analysis of labeling
schemes presented in a number of previous works.