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Acyclic Orders, Partition Schemes and CSPs: Unified Hardness Proofs and Improved Algorithms

Peter Jonsson, Victor Lagerkvist, George Osipov
2021 Artificial Intelligence  
We first consider partition schemes that contain an acyclic order and where the constraint language contains all unions of the basic relations; such CSPs are frequently occurring in e.g. temporal and spatial  ...  present a novel improved algorithm for RCC-8 and related formalisms.  ...  Acknowledgements This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.  ... 
doi:10.1016/j.artint.2021.103505 fatcat:vil7zf66i5hmlhqmffubhdfzf4

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations  ...  of algorithmic techniques.  ...  Our results unify and significantly extend the previously known cases, and yield a range of new and improved FPT algorithms, including an O (|Σ| 2k )-time algorithm for node-deletion Unique Label Cover  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

A General Scheme for Multiple Lower Bound Computation in Constraint Optimization [chapter]

Rina Dechter, Kalev Kask, Javier Larrosa
2001 Lecture Notes in Computer Science  
Preliminary experiments on Max-CSP show that using MBTE(z) to guide dynamic variable and value orderings in branch and bound yields a dramatic reduction in the search space and, for some classes of problems  ...  , this reduction is highly costeffective producing significant time savings and is competitive against specialized algorithms for Max-CSP.  ...  Our scheme is built on top of cluster-tree elimination (CTE), a tree-based decomposition schema which unifies several approaches for automated reasoning tasks.  ... 
doi:10.1007/3-540-45578-7_24 fatcat:ceyt6aefrjdilkza6pcrag4rom

Tractable Structures for Constraint Satisfaction Problems [chapter]

Rina Dechter
2006 Foundations of Artificial Intelligence  
yielding a solution. algorithm JTC followed by ACYCLIC-SOLVING provide a procedure for solving the CSP problem.  ...  and improved average performance.  ... 
doi:10.1016/s1574-6526(06)80011-8 fatcat:xgdvlfau6ranlnalqg6rxjxip4

Unifying tree decompositions for reasoning in graphical models

Kalev Kask, Rina Dechter, Javier Larrosa, Avi Dechter
2005 Artificial Intelligence  
The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the cliquetree algorithm  ...  Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can provide a speed-up of n over BE for various  ...  , are all instances of our unified scheme.  ... 
doi:10.1016/j.artint.2005.04.004 fatcat:bi5goekuzrccpdzsf3evjv5jv4

A general scheme for automatic generation of search heuristics from specification dependencies☆☆Preliminary versions of this paper were presented in [15,16,18]. This work was supported in part by NSF grant IIS-0086529 and by MURI ONR award N00014-00-1-0617

Kalev Kask, Rina Dechter
2001 Artificial Intelligence  
Their performance is compared on two optimization tasks: the Max-CSP task defined on deterministic databases and the Most Probable Explanation task defined on probabilistic databases.  ...  The heuristics are extracted from a parameterized approximation scheme called Mini-Bucket elimination that allows controlled trade-off between computation and accuracy.  ...  As an optimization version of Constraint Satisfaction, Max-CSP is NP-hard. A number of complete and incomplete algorithms have been developed for Max-CSP.  ... 
doi:10.1016/s0004-3702(01)00107-2 fatcat:qs7bfjxjqbapjas7vpnsa2qs6u

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms [article]

Georg Gottlob, Gianlugi Greco, Francesco Scarcello
2017 arXiv   pre-print
Finally, parallel algorithms for such optimization problems are proposed and analyzed.  ...  Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs).  ...  Acknowledgments Georg Gottlob's work was supported by the EPSRC Programme Grant EP/M025268/ "VADA: Value Added Data Systems -Principles and Architecture".  ... 
arXiv:1711.05216v1 fatcat:33kxkf756bc57e3rfrpkka5cri

Width Parameters Beyond Tree-width and their Applications

P. Hlineny, S.-i. Oum, D. Seese, G. Gottlob
2007 Computer journal  
In this contribution, we demonstrate how 'width' parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the  ...  These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms.  ...  Seese for improving his German English, and J. Dermietzel for his help with generating some of the figures.  ... 
doi:10.1093/comjnl/bxm052 fatcat:n4nbasuvubc5lkajkskqk22fey

Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems

Yuichi Yoshida, Yuan Zhou
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
We consider approximation schemes for the maximum constraint satisfaction problems and the maximum assignment problems.  ...  In this paper, we give a unified method of showing these approximation schemes based on the Sherali-Adams linear programming relaxation hierarchy.  ...  Max-CSP includes many fundamental problems such as Max-Cut and Max-SAT. In general, Max-CSP is NP-Hard, and it is even NP-Hard to approximate within a constant factor [4] .  ... 
doi:10.1145/2554797.2554836 dblp:conf/innovations/YoshidaZ14 fatcat:s5jn2jbg7bdqznmyt6vybzatda

Constraint satisfaction problems and global cardinality constraints

Andrei A. Bulatov, Dániel Marx
2010 Communications of the ACM  
On the theoretical side researchers focus on several directions such as: the complexity of CSPs problems, efficient algorithms for CSPs, where such algorithms exist, and connections of CSPs with other  ...  A number of commercial and freeware solvers exist capable of solving a wide range of CSPs of nearly industrial scale, and methods of solving constraint problems are developing rapidly [15] .  ...  Very often 'gadgets' used in complexity proofs can be expressed as ppdefinitions, so primitive positive definitions generalize and unify gadget reductions.  ... 
doi:10.1145/1810891.1810914 fatcat:65hgxt4sm5eqbgwui2kho3nhga

Inapproximability of Treewidth and Related Problems

Y. Wu, P. Austrin, T. Pitassi, D. Liu
2014 The Journal of Artificial Intelligence Research  
In this paper, we study the approximability of a number of graph problems: Treewidth and Pathwidth of graphs, Minimum Fill-In, One-Shot Black (and Black-White) pebbling costs of directed acyclic graphs  ...  This, and other problems on these graph models are often known to be hard to solve in general, but tractable on graphs with bounded Treewidth.  ...  An improved algorithm for c-balanced separator will also improve the approximation algorithms for the other problems.  ... 
doi:10.1613/jair.4030 fatcat:zyqijghvife2zlvgkhnhpjwfcm

AND/OR Branch-and-Bound search for combinatorial optimization in graphical models

Radu Marinescu, Rina Dechter
2009 Artificial Intelligence  
In extensive empirical evaluations we demonstrate that the new AND/OR Branch-and-Bound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes  ...  We introduce a new generation of depth-first Branch-and-Bound algorithms that explore the AND/OR search tree using static and dynamic variable orderings.  ...  and by an IRCSET Embark post-doctoral fellowship.  ... 
doi:10.1016/j.artint.2009.07.003 fatcat:ygqm7xz4kjavpoquq4ja4mzyeq

A Framework for Parameterized Subexponential Algorithms for Generalized Cycle Hitting Problems on Planar Graphs [article]

Dániel Marx, Pranabendu Misra, Daniel Neuen, Prafullkumar Tale
2021 arXiv   pre-print
, Subset Feedback Vertex Set, Group Feedback Vertex Set, Subset Group Feedback Vertex Set, Vertex Multiway Cut, and Component Order Connectivity.  ...  In particular, we use or adapt known kernelization results to obtain 2^O(√(k)·polylog(k)) n^O(1) time (randomized) algorithms for Vertex Multiway Cut, Group Feedback Vertex Set, and Subset Feedback Vertex  ...  In the cases of Vertex McW-DT and Subset FVS, it is easy to replace Torso operation by Contract to Undeletable scheme. We present unified arguments for these two cases in Lemma 6.7 .  ... 
arXiv:2110.15098v1 fatcat:nimpu577gnagrlrev4xzemzlde

When is Approximate Counting for Conjunctive Queries Tractable? [article]

Marcelo Arenas, Luis Alberto Croquevielle, Rajesh Jayaram, Cristian Riveros
2020 arXiv   pre-print
scheme (QPRAS) and sampling algorithm of Gore, Jerrum, Kannan, Sweedyk, and Mahaney '97.  ...  and the first polynomial-time algorithm for sampling answers uniformly from a query in C.  ...  This will allow us to define a natural partition scheme for the sampling procedure.  ... 
arXiv:2005.10029v3 fatcat:a3ieegpqlfbaparjkpojcigvhy

Joins via Geometric Resolutions: Worst-case and Beyond [article]

Mahmoud Abo Khamis, Hung Q. Ngo, Christopher Ré, Atri Rudra
2016 arXiv   pre-print
Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins.  ...  In addition to the geometry and logic connections, our algorithm can also be thought of as backtracking search with memoization.  ...  Acknowledgments We thank Paul Beame for clarifying the relation of our notion of geometric resolution with general resolution and we thank Javiel Rojas-Ledesma for bringing Klee's measure problem to our  ... 
arXiv:1404.0703v7 fatcat:g57exkfr7fekffnfwsx77e2xsm
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