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We propose improved exact and heuristic algorithms for solving the maximumweight clique problem, a well-known problem in graph theory with manyapplications. Our algorithms interleave successful techniques from related workwith novel data reduction rules that use local graph structure to identify andremove vertices and edges while retaining the optimal solution. We evaluate ouralgorithms on a range of synthetic and real-world graphs, and find that theyoutperform the current state of the art on most inputs. Our data reductionsalways produce smaller reduced graphs than existing data reductions alone. As aresult, our exact algorithm, MWCRedu, finds solutions orders of magnitudefaster on naturally weighted, medium-sized map labeling graphs and randomhyperbolic graphs. Our heuristic algorithm, MWCPeel, outperforms itscompetitors on these instances, but is slightly less effective on extremelydense or large instances.

Improved Exact and Heuristic Algorithms for Maximum Weight Clique