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Augmentative Message Passing for Traveling Salesman Problem and Graph Partitioning

The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing – for integral solutions in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a. community mining) using modularity optimization, we introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases we are able to derive simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with N3, demonstrating that augmentation is practical and efficient.

Citation

S. Ravanbakhsh, R. Rabbany, R. Greiner. "Augmentative Message Passing for Traveling Salesman Problem and Graph Partitioning". Neural Information Processing Systems (NIPS), (ed: Zoubin Ghahramani, Max Welling, Corinna Cortes, Neil D. Lawrence, Kilian Q. Weinberger), pp 289-297, December 2014.

Keywords: PGM, Message passing, TSP, factor graphs
Category: In Conference
Web Links: NIPS

BibTeX

@incollection{Ravanbakhsh+al:NIPS14,
  author = {Siamak Ravanbakhsh and Reihaneh Rabbany and Russ Greiner},
  title = {Augmentative Message Passing for Traveling Salesman Problem and
    Graph Partitioning},
  Editor = {Zoubin Ghahramani, Max Welling, Corinna Cortes, Neil D. Lawrence,
    Kilian Q. Weinberger},
  Pages = {289-297},
  booktitle = {Neural Information Processing Systems (NIPS)},
  year = 2014,
}

Last Updated: March 11, 2020
Submitted by Sabina P

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