 
Summary: Projection Merging: Reducing Redundancies in Inclusion Constraint Graphs \Lambda
Zhendong Su y
zhendong@cs.berkeley.edu
Manuel F¨ahndrich z
maf@microsoft.com
Alexander Aiken y
aiken@cs.berkeley.edu
EECS Department
University of California, Berkeley
Abstract
Inclusionbased program analyses are implemented by
adding new edges to directed graphs. In most analyses, there
are many different ways to add a transitive edge between
two nodes, namely through each different path connecting
the nodes. This path redundancy limits the scalability of
these analyses. We present projection merging, a technique
to reduce path redundancy. Combined with cycle elimina
tion [7], projection merging achieves orders of magnitude
speedup of analysis time on programs over that of using cy
cle elimination alone.
