1 research outputs found
Finding Optimal 2-Packing Sets on Arbitrary Graphs at Scale
A 2-packing set for an undirected graph is a subset such that any two vertices have no common
neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem.
We develop a new approach to solve this problem on arbitrary graphs using its
close relation to the independent set problem. Thereby, our algorithm red2pack
uses new data reduction rules specific to the 2-packing set problem as well as
a graph transformation. Our experiments show that we outperform the
state-of-the-art for arbitrary graphs with respect to solution quality and also
are able to compute solutions multiple orders of magnitude faster than
previously possible. For example, we are able to solve 63% of our graphs to
optimality in less than a second while the competitor for arbitrary graphs can
only solve 5% of the graphs in the data set to optimality even with a 10 hour
time limit. Moreover, our approach can solve a wide range of large instances
that have previously been unsolved