Ravanbakhsh, Siamak, Rabbany, Reihaneh, Greiner, Russell

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 -- which produces 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 surprisingly 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 N^3, demonstrating that augmentation is practical and efficient.

Ravanbakhsh, Siamak, Rabbany, Reihaneh, Greiner, Russell

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 surprisingly 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 $N^3$, demonstrating that augmentation is practical and efficient.

In this paper, we show how dynamic programming techniques can be used to construct useful anytime procedures for two problems: multiplying sequences of matrices, and the Travelling Salesman Problem. Dynamic programming can be applied to a wide variety of optimization and control problems, many of them relevant to current AI research (e.g., scheduling, probabilistic reasoning, and controlling machinery). Being able to solve these kinds of problems using anytime procedures increases the range of problems to which expectation-driven iterative refinement can be applied.

Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This emphasizes the principle common to many of the algorithms appearing in that literature and clarifies their relationship to nonserial dynamic programming algorithms. We also present a general way of combining conditioning and elimination within this framework. Bounds on complexity are given for all the algorithms as a function of the problem's structure.

It may seem hard to believe, but the cast of "Dancing With the Stars: Athletes" is already in the semifinals, and before the night comes to an end, half of the teams will say their goodbyes, thanks to a shocking triple elimination. The ABC reality competition series still has six teams remaining in the competition, and with such a huge elimination looming, the teams are being put to work. They will face two rounds of competition once again, but unlike their Team Dances in Week 2, where they worked together to get higher scores, this time, their second round will involve for personal battles, with dance-offs that will secure them extra points. According to Just Jared, the public will vote live for their favorite couples via an online "Passion Meter," while the judges will also select a favorite routine. If the judges have a tie on their panel, then the couple who received the most votes from viewers will be named the winner.