Tuesday, 15:45 - 16:10 h, Room: H 3012


Dorit Hochbaum
Flow-based algorithms that solve clustering problems related to graph expander, normalized cut and conductance better than the spectral method


We address challenging problems in clustering, partitioning and imaging including the normalized cut
problem, graph expander, Cheeger constant problem and conductance problem. These have traditionally
been solved using the "spectral technique''. These problems are formulated here as a quadratic
ratio (Rayleigh) with discrete constraints and a single sum constraint. The spectral method solves
a relaxation that omits the discreteness constraints. A new relaxation, that omits the sum
constraint, is shown to be solvable in strongly polynomial time. It is shown, via an experimental
study, that the bipartition achieved by the combinatorial algorithm often improve dramatically in
terms of the objective value of the respective NP-hard problem, as well as in terms of the visual
quality of the segmentation, compared to the spectral method in image segmentation and image
denoising instances.


Talk 2 of the contributed session Tue.3.H 3012
"LP relaxations" [...]
Cluster 2
"Combinatorial optimization" [...]


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