Abstract dynamic programming models under commutativity conditions
SIAM Journal on Control and Optimization
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
Approximation algorithms for the metric labeling problem via a new linear programming formulation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Generating Semantic Descriptions From Drawings of Scenes With Shadows
Generating Semantic Descriptions From Drawings of Scenes With Shadows
Arc consistency for soft constraints
Artificial Intelligence
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The generalized distributive law
IEEE Transactions on Information Theory
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
The partial constraint satisfaction problem: Facets and lifting theorems
Operations Research Letters
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Inference tasks in Markov random fields (MRFs) are closely related to the constraint satisfaction problem (CSP) and its soft generalizations. In particular, MAP inference in MRF is equivalent to the weighted (maxsum) CSP. A well-known tool to tackle CSPs are arc consistency algorithms, a.k.a. relaxation labeling. A promising approach to MAP inference in MRFs is linear programming relaxation solved by sequential treereweighted message passing (TRW-S). There is a not widely known algorithm equivalent to TRW-S, max-sum diffusion, which is slower but very simple. We give two theoretical results. First, we show that arc consistency algorithms and max-sum diffusion become the same thing if formulated in an abstractalgebraic way. Thus, we argue that max-sum arc consistency algorithm or max-sum relaxation labeling is a more suitable name for max-sum diffusion. Second, we give a criterion that strictly decreases during these algorithms. It turns out that every class of equivalent problems contains a unique problem that is minimal w.r.t. this criterion.