Anytime AND/OR Depth-First Search for Combinatorial Optimization

Otten, Lars; Dechter, Rina

doi:10.1007/978-3-319-10428-7_70

Cited by 23 publications

(24 citation statements)

References 8 publications

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“…Solutions of ILPs are found by solving a sequence of LPs and either adding additional constraints to the polytope (cutting plane techniques), or branching the polytope into several polytopes (branchand-bound techniques). We evaluate three state-of-the-art ILP solvers: IBM CPLEX wrapped by OpenGM2 [5] (ogm-ILP), the current best performing method in the PIC called breath-rotating and/or branch-and-bound [31] (BRAOBB), and the AStar-Method (ogm-ASTAR) [11]. To reduce the large memory requirements which come along with the vectorization of the objective for the LP, we also consider the multicut-representation introduced by Kappes et al [19].…”

Section: Inference Methodsmentioning

confidence: 99%

A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems

Kappes

Andres

Hamprecht

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

148

143

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Seven years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems.While these insights remain generally useful today, the phenominal success of random field models means that the kinds of inference problems we solve have changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of 24 state-of-art techniques on a corpus of 2,300 energy minimization instances from 20 diverse computer vision applications. To ensure reproducibility, we evaluate all methods in the OpenGM2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.

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Section: Inference Methodsmentioning

confidence: 99%

A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems

Kappes

Andres

Hamprecht

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

148

143

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“…Breadth-Rotating AND/OR Branch-and-Bound (BRAO-BB) Otten et al suggested a depth-first search branch-andbound algorithm over AND/OR search spaces using minibucket heuristics for bounding [26]. Contrary to naive depthfirst search, which processes one branch of the tree after another, BRAOBB processes all branches "simultaneously" in a round-robin style.…”

Section: Exact Optimization Methodsmentioning

confidence: 97%

“…In the last years combinatorial methods based on cuttingplane and branch-and-bound techniques have come more into focus in the computer vision community [4,16,26,10,34]. The main advantage of these methods is that they provide globally optimal integer solutions if no runtime restrictions are specified.…”

Section: Introductionmentioning

confidence: 99%

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Kappes

Speth²,

Reinelt³

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

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Discrete graphical models (also known as discrete Markov random fields) are a major conceptual tool to model the structure of optimization problems in computer vision. While in the last decade research has focused on fast approximative methods, algorithms that provide globally optimal solutions have come more into the research focus in the last years. However, large scale computer vision problems seemed to be out of reach for such methods.In this paper we introduce a promising way to bridge this gap based on partial optimality and structural properties of the underlying problem factorization. Combining these preprocessing steps, we are able to solve grids of size 2048 × 2048 in less than 90 seconds. On the hitherto unsolvable Chinese character dataset of Nowozin et al. we obtain provably optimal results in 56% of the instances and achieve competitive runtimes on other recent benchmark problems.While in the present work only generalized Potts models are considered, an extension to general graphical models seems to be feasible.

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“…We next provide an overview of a depth-first branch and bound and best-first search algorithms, that explore AND/OR search spaces (Marinescu & Dechter, 2009b, 2009aOtten & Dechter, 2011). These schemes use heuristics generated either by the mini-bucket elimination scheme (2.3.4) or through soft arc-consistency schemes (Marinescu & Dechter, 2009a, 2009bSchiex, 2000;Darwiche, Dechter, Choi, Gogate, & Otten, 2008) or their composite (Ihler, Flerova, Dechter, & Otten, 2012).…”

Section: Definitionmentioning

confidence: 99%

Searching for the M Best Solutions in Graphical Models

Flerova

Marinescu

Dechter

2016

jair

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The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A*, extending the well-known A* to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since bestfirst algorithms require extensive memory, we also extend the memory-efficient depth-first branch and bound to the m-best task.We adapt both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments confirm theory that the best-first approach is largely superior when memory is available, but depth-first branch and bound is more robust. We also show that our algorithms are competitive with related schemes recently developed for the m-best task.

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Anytime AND/OR Depth-First Search for Combinatorial Optimization

Cited by 23 publications

References 8 publications

A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems

A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Searching for the M Best Solutions in Graphical Models

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