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Answer Set Solving exploiting Treewidth and its Limits [article]

Markus Hecher
2019 arXiv   pre-print
Typically, a parameterized algorithm utilizing treewidth takes or computes a tree decomposition, which is an arrangement of a graph into a tree, and evaluates the problem in parts by dynamic programming  ...  Since dynamic programming on tree decomposition lands itself well to counting, we designed a framework for projected model counting, which applies to ASP, abstract argumentation and even to problems higher  ...  Background Tree Decompositions. Tree decompositions are built for a given graph and are a tree-like representation of the graph.  ... 
arXiv:1905.01688v1 fatcat:zmhwwfjhnjeudbnqharz7hse6y

Revisiting decomposition analysis of geometric constraint graphs

R. Joan-Arinyo, A. Soto-Riera, S. Vila-Marta, J. Vilaplana-Pastó
2004 Computer-Aided Design  
In this paper we first introduce the concept of deficit of a constraint graph. Then we give a new formalization of the decomposition algorithm due to Owen.  ...  Finally we apply tree decompositions to prove that the class of problems solved by the formalizations studied here and other formalizations reported in the literature is the same.  ...  Acknowledgements This research has been supported by CICYT under the project TIC2001-2099-C03-01.  ... 
doi:10.1016/s0010-4485(03)00057-5 fatcat:xgewhl53vjf2nmh7d3n2flh7va

Improving the Performance of Consistency Algorithms by Localizing and Bolstering Propagation in a Tree Decomposition

Shant Karakashian, Robert Woodward, Berthe Choueiry
2013 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Those strategies are: a) localizing the application ofthe consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation betweenclusters by adding redundant constraints  ...  In this paper,we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcingR(*,m)C and getting closer to the above tractability condition.  ...  We propose two main strategies for improving the performance of this algorithm in the context of a tree decomposition of the CSP: 1.  ... 
doi:10.1609/aaai.v27i1.8594 fatcat:defijwbz3zfknargqfcndooweq

A formal approach to the definition and the design of conceptual schemata for databased systems

Carlo Zaniolo, Michel A. Melkaoff
1982 ACM Transactions on Database Systems  
A formal approach is proposed to the definition and the design of conceptual database diagrams to be used as conceptual schemata in a system featuring a multilevel schema architecture, and as an aid for  ...  The basis for our schemata is a combined representation for two fundamental structures underlying every relation: the first defined by its minimal atomic decompositions, the second by its elementary functional  ...  In general, if such a binary tree has n internal nodes (decomposition steps) it has n + 1 terminal nodes (atomic projections).  ... 
doi:10.1145/319682.319695 fatcat:npeeylfufzagri7zyob4httcvi

Page 2797 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
The authors present a decomposition method for indefinite qua- dratic programming problems having n variables and m linear constraints.  ...  [Ding, Baoyan] (3-WTRL-B; Waterloo, ON) A decomposition method for global and local quadratic minimization. (English summary) J. Global Optim. 16 (2000), no. 2, 133-151.  ... 

Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations [chapter]

Marc Tedder, Derek Corneil, Michel Habib, Christophe Paul
2008 Lecture Notes in Computer Science  
Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization  ...  Accordingly, there has been a drive towards a practical, linear-time algorithm for the problem.  ...  this research. ⋆⋆ Michel Habib and Christophe Paul were supported by the French ANR project ANR-O6-BLAN-0148-01, Graph Decomposition and Algorithms (GRAAL). fundamental tool in algorithmic graph theory  ... 
doi:10.1007/978-3-540-70575-8_52 fatcat:xehsdbkcvbezncnedfodbfub44

ABC

John B. Smith, F. Donelson Smith
1991 Proceedings of the third annual ACM conference on Hypertext - HYPERTEXT '91  
This description includes a brief overview of the system, but emphasizes three components: a hypermedia data management system or graph server, a set of browsers for working with graph objects, and a set  ...  of applications for working with data contents of graph nodes.  ...  Second, algorithms can be developed for comparing decomposition structures to structures inherent in the system code and/or the hypertext graph structure of the artifact.  ... 
doi:10.1145/122974.122992 dblp:conf/ht/SmithS91 fatcat:7tscxkfaezb43jti2xupmnyp5a

Tree-based reparameterization framework for analysis of sum-product and related algorithms

M.J. Wainwright, T.S. Jaakkola, A.S. Willsky
2003 IEEE Transactions on Information Theory  
We present a tree-based reparameterization (TRP) framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles.  ...  Algorithms in this class can be formulated as a sequence of reparameterization updates, each of which entails refactorizing a portion of the distribution corresponding to an acyclic subgraph (i.e., a tree  ...  For acyclic graphs (i.e., trees), standard and highly efficient algorithms exist for this task.  ... 
doi:10.1109/tit.2003.810642 fatcat:ru76eua74fca3hc7zm54gv5x4a

Continuous Queries for Multi-Relational Graphs [article]

Sutanay Choudhury, Lawrence B. Holder, Abhik Ray, George Chin Jr., John T. Feo
2013 arXiv   pre-print
The algorithm is based on a novel data structure called the Subgraph Join Tree (SJ-Tree) that leverages the structural and semantic characteristics of the underlying multi-relational graph.  ...  This work is dedicated to answer the question that emerges naturally: how can we efficiently execute a continuous query on a dynamic graph?  ...  Bill Howe at the University of Washington for his suggestions that have improved this paper.  ... 
arXiv:1209.2178v2 fatcat:wusxy3r6srgubkadzkk57ii4la

Distributed Algorithms for Low Stretch Spanning Trees

Ruben Becker, Yuval Emek, Mohsen Ghaffari, Christoph Lenzen, Michael Wagner
2019 International Symposium on Distributed Computing  
Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch.  ...  Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log 3 n), where  ...  Replacing the cone growing process with this decomposition technique also results in a conceptually much simpler algorithm for constructing spanning trees of small expected stretch in standard centralized  ... 
doi:10.4230/lipics.disc.2019.4 dblp:conf/wdag/BeckerEGL19 fatcat:lpbwemj3fvfwfc4vpnbshlyoqi

A Two Layered Approach for Querying Integrated XML Sources

Felipe Victolla Silveira, Carlos A. Heuser
2007 11th International Database Engineering and Applications Symposium (IDEAS 2007)  
This paper presents a set of fragmentation operators specifically designed for our approach, as well as a query decomposition mechanism that allows a query stated at the conceptual level to be decomposed  ...  conceptually representing data sources and (2) that of mapping the local graph-like model into an XML tree-like schema.  ...  Acknowledgments This work is partially supported by CNPq (projects 473310/2004-0, and Gerindo) and FAPERGS (project ).  ... 
doi:10.1109/ideas.2007.4318083 dblp:conf/ideas/SilveiraH07 fatcat:cgdyihggzvd5hlmzcoz33tqmpi

Beyond trees: MRF inference via outer-planar decomposition

Dhruv Batra, A. C. Gallagher, Devi Parikh, Tsuhan Chen
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD).  ...  Loopy Belief Propagation (BP) and Tree-reweighted (TRW) methods). This paper presents a unifying perspective of these approximate techniques called "Decomposition Methods".  ...  We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions.  ... 
doi:10.1109/cvpr.2010.5539951 dblp:conf/cvpr/BatraGPC10 fatcat:zpodxtnqabbm7c6w5ozwgfq7qe

An Agent-based Improved Task Decomposition Model for Multiple Expert Systems

Li Yang, Xiedong Cao, Jie Li
2013 TELKOMNIKA Indonesian Journal of Electrical Engineering  
Firstly, AND/OR dependency graph for operation set is presented. Formal description of task decomposition based on With AND/OR dependency graph, is proposed.  ...  To solve task decomposition of multi-expert system, agent-based task decomposition model and algorithm based on dependency is introduced.  ...  Cooperation and Exchange Project (2012HH0004) of Sichuan Province.  ... 
doi:10.11591/telkomnika.v11i10.2539 fatcat:m2a2vsdcxrgcbpzj66lwt5hjzu

Efficient Graph Minors Theory and Parameterized Algorithms for (Planar) Disjoint Paths [article]

Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi
2020 arXiv   pre-print
Remarkably, the above algorithm for Disjoint Paths is a cornerstone of the entire Graph Minors Theory, and conceptually vital to the g(k)n^3-time algorithm for Minor Testing (given two undirected graphs  ...  Lastly, we will discuss the main ideas behind a new algorithm that combines treewidth reduction and an algebraic approach to solve Planar Disjoint Paths in time 2^k^O(1)n^O(1) (for undirected graphs).  ...  Their project introduced key definitions and concepts such as those of an excluded grid and a tree decomposition (a decomposition of a graph into a tree-like structure), along with key structural results  ... 
arXiv:2008.08373v1 fatcat:6r5lrs44nnegrcde6iakechrei

Linear kernels for (connected) dominating set on graphs with excluded topological subgraphs

Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos, Marc Herbstritt
2013 Symposium on Theoretical Aspects of Computer Science  
Our kernelization algorithm is based on a non-trivial combination of the following ingredients The structural theorem of Grohe and Marx [STOC 2012] for graphs excluding a fixed graph H as a topological  ...  In other words, we give polynomial time algorithms that, for a given H-topological-minor free graph G and a positive integer k, output an Htopological-minor free graph G on O(k) vertices such that G has  ...  We also believe that a broadening of the kernelization horizon for these two problems without the use of some tree-based structural characterization of sparsity requires completely different ideas.  ... 
doi:10.4230/lipics.stacs.2013.92 dblp:conf/stacs/FominLST13 fatcat:7xiyebshenbdrb7t6ihlnlldku
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