McSplitDAL). we propose a family of Branch-and-
Bound algorithms called McSplitX+PR.
The original McSplit algorithm uses a node de-
gree heuristic to select the vertices of the graphs dur-
ing the recursive search. McSplitRL and its deriva-
tives use rewards obtained through Reinforcement
Learning, but still enforce the node degree to break
ties. We propose the McSplitX+PR algorithm family,
namely McSplit+PR, McSplitLL+PR, and McSplit-
DAL+PR, to replace the original node degree heuris-
tic with the ranking produced by the PageRank algo-
rithm. PageRank, famously known as the former al-
gorithm behind the Google search engine, generates
more effective node orderings compared to the de-
gree of vertices, as it prioritizes nodes that are easier
to reach across multiple hops rather than just in the
local neighborhood, effectively differentiating them
over more categories than the original heuristic.
Using publicly available graph pairs, we con-
ducted experiments on both the McSplitX+PR and
McSplitX families. We mainly focus on finding the
best solution within a limited time to simulate real-
world scenarios. Our results indicate that all Mc-
SplitX+PR algorithms consistently outperform their
McSplitX counterparts, with McSplitDAL+PR yield-
ing the most effective solutions than the other strate-
gies.
Among the possible future works, we would
like to mention the necessity of studying the multi-
threaded versions of the above tools. In this work,
this analysis has been limited by the fact that not all
the considered tools were initially implemented with
multi-threading capabilities. Consequently, one of
our targets is to improve the above heuristics obtain-
ing uniform scalability on multi-core architectures.
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