A Case Study in Complexity Estimation: Towards Parallel Branch-and-Bound over Graphical Models

We study the problem of complexity estimation in the context of parallelizing an advanced Branch and Bound-type algorithm over graphical models. The algorithm's pruning power makes load balancing, one crucial element of every distributed system, very challenging. We propose using a statistical regression model to identify and tackle disproportionally complex parallel subproblems, the cause of load imbalance, ahead of time. The proposed model is evaluated and analyzed on various levels and shown to yield robust predictions. We then demonstrate its effectiveness for load balancing in practice.

Join-graph based cost-shifting schemes

We develop several algorithms taking advantage of two common approaches for bounding MPE queries in graphical models: minibucket elimination and message-passing updates for linear programming relaxations. Both methods are quite similar, and offer useful perspectives for the other; our hybrid approaches attempt to balance the advantages of each. We demonstrate the power of our hybrid algorithms through extensive empirical evaluation. Most notably, a Branch and Bound search guided by the heuristic function calculated by one of our new algorithms has recently won first place in the PASCAL2 inference challenge.

Bounding Search Space Size via (Hyper)tree Decompositions

This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism in the problem specification and produce tighter bounds. We demonstrate on a variety of practical problem instances that we are often able to improve upon existing bounds by several orders of magnitude.