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New Limits of Treewidth-based tractability in Optimization [article]

Yuri Faenza, Gonzalo Muñoz, Sebastian Pokutta
2019 arXiv   pre-print
The goal of this work is to contribute to the understanding of the limits of the treewidth-based tractability in optimization. Our results are as follows.  ...  Secondly, under mild assumptions, we prove that treewidth is the only graph-theoretical parameter that yields tractability a wide class of optimization problems, a fact well known in Graphical Models in  ...  Acknowledgements Research reported in this paper was partially supported by NSF CAREER award CMMI-1452463 and by the Institute for Data Valorisation (IVADO).  ... 
arXiv:1807.02551v4 fatcat:xc5pqufrvbhe5frrehjaaquu5u

Reasoning Like Human: Hierarchical Reinforcement Learning for Knowledge Graph Reasoning

Guojia Wan, Shirui Pan, Chen Gong, Chuan Zhou, Gholamreza Haffari
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
In order to deal with the situation, we propose a novel Hierarchical Reinforcement Learning framework to learn chains of reasoning from a Knowledge Graph automatically.  ...  Experimental results show that our proposed model achieves substantial improvements in ambiguous relation tasks.  ...  Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2020/263 dblp:conf/ijcai/GanianSSS20 fatcat:jmfqvv5kurcrnnbjjsepto5dye

Structural Decomposition Methods and What They are Good For

Markus Aschinger, Conrad Drescher, Georg Gottlob, Peter Jeavons, Evgenij Thorstensen, Marc Herbstritt
2011 Symposium on Theoretical Aspects of Computer Science  
As a new showcase for the latter usage, we report some recent results on the Partner Units Problem, a form of configuration problem arising in an industrial context.  ...  classes of tractable problem instances.  ...  Gottlob's work, in particular, with respect to specific topics arising in the context of the co-operation with Siemens Austria and the University of Klagenfurt, was also partially funded by the FFG Fit-IT  ... 
doi:10.4230/lipics.stacs.2011.12 dblp:conf/stacs/AschingerDGJT11 fatcat:uvrfw5qqvbgvjczxy64jh7hyne

Challenges for Efficient Query Evaluation on Structured Probabilistic Data [chapter]

Antoine Amarilli, Silviu Maniu, Mikaël Monet
2016 Lecture Notes in Computer Science  
However, a new approach for this problem has recently been proposed, based on structural decompositions of input databases, following, e.g., tree decompositions.  ...  generalize to arbitrary queries: it may even be the case that some queries cannot be rewritten to the summary facts while remaining in the same language.  ...  Hence, a practical system using the structural approach must compute tree decompositions more efficiently, even if this limits us to non-optimal decompositions.  ... 
doi:10.1007/978-3-319-45856-4_22 fatcat:5yramxr62feb7ju5ubl7olomrm

Challenges for Efficient Query Evaluation on Structured Probabilistic Data [article]

Antoine Amarilli, Silviu Maniu, Mikaël Monet
2016 arXiv   pre-print
However, a new approach for this problem has recently been proposed, based on structural decompositions of input databases, following, e.g., tree decompositions.  ...  Hence, a practical system using the structural approach must compute tree decompositions more efficiently, even if this limits us to non-optimal decompositions.  ...  Moreover, in [3] , it is shown that bounding the instance treewidth is necessary to ensure the tractability of PQE, because some queries are hard on any unbounded-treewidth instance family (under some  ... 
arXiv:1607.05538v1 fatcat:mfmr5c6lvrg3vgvk6qdngsfw5e

ToTo: An open database for computation, storage and retrieval of tree decompositions

Rim van Wersch, Steven Kelk
2017 Discrete Applied Mathematics  
Many NP-hard problems on graphs become tractable on graphs of low treewidth, but the corresponding algorithms require access to a tree decomposition of the graph of low (ideally, minimum) width.  ...  Unfortunately computation of treewidth is itself NP-hard and a wide variety of exact, heuristic and approximation algorithms have been proposed for this problem.  ...  Its importance stems from the fact that very many NP-hard optimization problems become (fixed parameter) tractable on graphs of bounded treewidth, by applying dynamic programming over low-width tree decompositions  ... 
doi:10.1016/j.dam.2016.09.023 fatcat:6jly4pw3kzfwpkqkboscxcjd64

Probabilistic Evaluation of Expressive Queries on Bounded-Treewidth Instances

Mikaël Monet
2016 Proceedings of the 2016 on SIGMOD'16 PhD Symposium - SIGMOD'16 PhD  
However, a criterion on the shape of the database has been shown in recent work to be sufficient and in some sense necessary to the tractability of this task.  ...  Databases whose treewidth is bounded by a constant k are exactly those that can be tractably queried, with respect to quantitative uncertainty estimation.  ...  As a followup to [3] and in a very recent work [4] , it has been shown that bounded-treewidth is essentially the only relevant notion for instance-based tractability of probabilistic query evaluation  ... 
doi:10.1145/2926693.2929905 dblp:conf/sigmod/Monet16 fatcat:q6srqmvjcje7pmj3ujbj5bf4n4

Approximate MRF Inference Using Bounded Treewidth Subgraphs [chapter]

Alexander Fix, Joyce Chen, Endre Boros, Ramin Zabih
2012 Lecture Notes in Computer Science  
We propose a new approach that, instead of optimizing the original graphical model, instead optimizes a tractable sub-model, defined as an energy function that uses a subset of the pairwise interactions  ...  Our Bounded Treewidth Subgraph (k-BTS) algorithm greedily computes a large weight treewidth-k subgraph of the signed graph, then solves the energy minimization problem for this subgraph by dynamic programming  ...  -While the subgraph doesn't span the entire graph, add the biggest triangle you can find, such that the base of the new triangle was already an edge in the graph.  ... 
doi:10.1007/978-3-642-33718-5_28 fatcat:ofs5ktihvvhkvoyobzgvvr7s6q

Phase Transition of Tractability in Constraint Satisfaction and Bayesian Network Inference [article]

Yong Gao
2012 arXiv   pre-print
This implies that algorithms making use of treewidth based structural knowledge only work efficiently in a limited range of random instance.  ...  In this paper we study, under the frameworks of random constraint satisfaction problems and random Bayesian networks, a typical tractable subclass characterized by the treewidth of the problems.  ...  TREEWIDTH AND TREEWIDTH BASED TRACTABILITY The concepts of treewidth and tree-decomposition on graphs generalize those of trees. The treewidth of a graph is usually defined in two equivalent ways.  ... 
arXiv:1212.2485v1 fatcat:ysu6muyuvfbp7e46544akg5d7i

A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions [chapter]

Thomas Bosman
2015 Lecture Notes in Computer Science  
Consequently, tree decomposition based algorithms have limited applicability to large scale optimization.  ...  Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems.  ...  In all cases the merging phase could use all 16 solutions, often producing a union well below the treewidth limit.  ... 
doi:10.1007/978-3-319-20086-6_30 fatcat:tz5a22p5zze6tp64g5wjoimcti

The Sum-Product Theorem: A Foundation for Learning Tractable Models [article]

Abram L. Friesen, Pedro Domingos
2016 arXiv   pre-print
We illustrate the power and generality of this approach by applying it to a new type of structured prediction problem: learning a nonconvex function that can be globally optimized in polynomial time.  ...  In any semiring, for summation to be tractable it suffices that the factors of every product have disjoint scopes. This unifies and extends many previous results in the literature.  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ONR, AFRL,  ... 
arXiv:1611.03553v1 fatcat:anbl6esnjneprbbdlybdczbzq4

Dynamic Blocking and Collapsing for Gibbs Sampling [article]

Deepak Venugopal, Vibhav Gogate
2013 arXiv   pre-print
We show that combining them is not straight-forward because collapsing (or eliminating variables) introduces new dependencies in the PGM and in computation-limited settings, this may adversely affect blocking  ...  in terms of accuracy.  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of ARO or the U.S.  ... 
arXiv:1309.6870v1 fatcat:ui25wqkmejfdnbfeohwlmbkjcy

Structurally Tractable Uncertain Data

Antoine Amarilli
2015 Proceedings of the 2015 ACM SIGMOD on PhD Symposium - SIGMOD '15 PhD Symposium  
We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation.  ...  However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard  ...  This work has been supported in part by the NormAtis project funded by the French ANR. We are grateful to the anonymous reviewers for their helpful comments.  ... 
doi:10.1145/2744680.2744690 dblp:conf/sigmod/Amarilli15 fatcat:d5pytbbcwfhk7gs367abgir3ly

Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics [chapter]

Víctor Dalmau, Phokion G. Kolaitis, Moshe Y. Vardi
2002 Lecture Notes in Computer Science  
We first show that constraint satisfaction problems on inputs of treewidth less than are definable using Datalog programs with at most variables; this provides a new explanation for the tractability of  ...  equivalent to a structure of bounded treewidth" in terms of definability in finite-variable logics.  ...  Thus, the classes À´Ì ´ µµ, ¾, constitute new large "islands of tractability" for constraint satisfaction and, moreover, their tractability is once again due to definability in Datalog.  ... 
doi:10.1007/3-540-46135-3_21 fatcat:ysssno3exfgvzkg5jl5yaa4kmi

The Complexity of Polynomial-Time Approximation

Liming Cai, Michael Fellows, David Juedes, Frances Rosamond
2007 Theory of Computing Systems  
(1 + ) of optimal, in a running time that is polynomial for every fixed value of .  ...  In 1996, Khanna and Motwani [KM96] proposed three logic-based optimization problems constrained by planar structure, and offered the hypothesis that these putatively fundamental problems might provide  ...  But there is also a limit to such "good news" -we have shown that there are problems that can be described by a collection of FOFs with minterms of size at most 4 that do not have an EPTAS unless FPT =  ... 
doi:10.1007/s00224-007-1346-y fatcat:z7x76ylombhy5i2zj5em4gt6se
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