Section: New Results

Efficient multi-constraint graph partitioning algorithms

Although several tools provide multi-constraint graph partitioning features, this problem had not been thoroughly investigated. In the context of the PhD of Rémi Barat, several significant results were achieved regarding the multi-constraint graph partitioning problem.

Firstly, a theoretical analysis of the solution space of the mono-criterion, balanced graph bipartitioning problem showed that this space is strongly connected. Hence, local optimization algorithms may indeed succeed in finding paths to better solutions, from some existing solution. A conjecture on the multi-criteria case has been derived. These findings reversed our view on partitioning: while most tools try to find a possibly unbalanced partition of small cut, and then try to rebalance it, it is in fact possible to compute a balanced partition of arbitrary cut, and then to improve the cut.

Secondly, a thorough investigation of the multilevel framework, and of its implementations in several existing tools, allowed us to define the characteristics of an effective coarsening method, both in the mono-criterion and multi-criteria case. Also, new multi-criteria graph algorithms were designed for the initial partitioning and local optimization phases of the multilevel framework [43]. A new data structure has been devised, which speeds-up the computation of balanced partitions in the multi-criteria case.

Thirdly, all of the aforementioned algorithms were implemented in a prototype version of Scotch .