Filters








109 Hits in 2.3 sec

Hypertree width and related hypergraph invariants

Isolde Adler, Georg Gottlob, Martin Grohe
2007 European journal of combinatorics (Print)  
We study the notion of hypertree-width of hypergraphs.  ...  We prove that, up to a constant factor, hypertree-width is the same as a number of other hypergraph invariants that resemble graph invariants such as bramble-number, branchwidth, linkedness, and the minimum  ...  Our results show that hypertree-width is a similarly robust hypergraph invariant as tree-width is for graphs.  ... 
doi:10.1016/j.ejc.2007.04.013 fatcat:nw4euvvqtncgdj4a5bubq44vrq

Hypertree Decompositions: Structure, Algorithms, and Applications [chapter]

Georg Gottlob, Martin Grohe, Nysret Musliu, Marko Samer, Francesco Scarcello
2005 Lecture Notes in Computer Science  
We review the concepts of hypertree decomposition and hypertree width from a graph theoretical perspective and report on a number of recent results related to these concepts.  ...  This is also true for other hypergraph invariants such as treewidth, cutset-width, and so on.  ...  (2) Are there other hypergraph invariants (and associated decompositions) that fulfill the three criteria given in Section 1 and that strongly generalize hypertree width?  ... 
doi:10.1007/11604686_1 fatcat:32q3km744ff3pcrtrjjvhp2ffy

Counting Homomorphisms via Hypergraph-Based Structural Restrictions [chapter]

Tommy Färnqvist
2012 Lecture Notes in Computer Science  
approaches to combinatorial optimization problems on bounded treewidth graphs, but basing the decompositions on various hypergraph width measures from the literature on plain CSPs.  ...  Feder and Vardi [9] observed that constraint satisfaction problems can be described as homomorphism problems for relational structures.  ...  Grohe and Marx [13] proposed a new hypergraph invariant, the fractional hypertree width, which generalizes both the hypertree width and fractional edge cover number.  ... 
doi:10.1007/978-3-642-32147-4_34 fatcat:ir6ffm3qzzecfo4qrudun7u6me

Constraint solving via fractional edge covers

Martin Grohe, Dániel Marx
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width.  ...  So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [2002].  ...  We propose a new hypergraph invariant, the fractional hypertree width, which generalizes both the hypertree width and fractional edge cover number in a natural way.  ... 
doi:10.1145/1109557.1109590 fatcat:pcqab7njwffuheifoggrggpxc4

Constraint Solving via Fractional Edge Covers [article]

Martin Grohe, Dániel Marx
2017 arXiv   pre-print
Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width.  ...  So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al.  ...  We propose a new hypergraph invariant, the fractional hypertree width, which generalizes both the hypertree width and fractional edge cover number in a natural way.  ... 
arXiv:1711.04506v1 fatcat:wtbfdstjwneenpycatf6hbo4s4

Constraint Solving via Fractional Edge Covers

Martin Grohe, Dániel Marx
2014 ACM Transactions on Algorithms  
Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width.  ...  So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [2002].  ...  We propose a new hypergraph invariant, the fractional hypertree width, which generalizes both the hypertree width and fractional edge cover number in a natural way.  ... 
doi:10.1145/2636918 fatcat:qovgxyi47nhntiyksgy44nvjxm

From Hypertree Width to Submodular Width and Data-dependent Structural Decompositions

Francesco Scarcello
2018 Sistemi Evoluti per Basi di Dati  
The paper shows that these techniques are useful not only for long and complex queries, but even for short and simple ones.  ...  upperbound and the running times required by actual algorithms used in practice.  ...  It is thus not surprising that there are hypergraphs where the fractional hypertree width is smaller than the (generalized) hypertree width.  ... 
dblp:conf/sebd/Scarcello18 fatcat:hnq23laq7jejhotv6e5fwiifxq

A greedy algorithm for constructing a low-width generalized hypertree decomposition

Kaoru Katayama, Tatsuro Okawara, Yuka Ito
2010 Proceedings of the 13th International Conference on Database Theory - ICDT '10  
Gottlob et al. also developed a polynomial time algorithm det-k-decomp which, given a hypergraph H and a constant k, computes a hypertree decomposition of width less than or equal to k if the hypertree-width  ...  The concepts of (generalized) hypertree decomposition and (generalized) hypertree-width were introduced by Gottlob et al.  ...  [1] explored the relationship between hypertree width and various hypergraph invariants.  ... 
doi:10.1145/1804669.1804692 dblp:conf/icdt/KatayamaOI10 fatcat:oxoj5qunijfqzo4xrindeb7gza

Complexity and Applications of Edge-Induced Vertex-Cuts [article]

Marko Samer, Stefan Szeider
2006 arXiv   pre-print
Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts.  ...  We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.  ...  Conclusion We introduced the notion of edge-induced vertex-cuts which is closely related to the concept of hypertree decomposition.  ... 
arXiv:cs/0607109v2 fatcat:flmpcbqbczfmpl3m5bhlxm74ya

NeurASP: Embracing Neural Networks into Answer Set Programming

Zhun Yang, Adam Ishay, Joohyung Lee
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation  ...  We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set  ...  Georg Gottlob is a Royal Society Research Professor and acknowledges support by the Royal Society for the present work in the context of the project "RAISON DATA" (Project reference: RP\R1\201074)  ... 
doi:10.24963/ijcai.2020/239 dblp:conf/ijcai/ChenGLP20 fatcat:m3inpryda5bphltwzyxclbvj3m

Construction of a GAI Tree with Hypergraph Decompositions

Liu Zhaowei, Liu Jinglei
2014 Sensors & Transducers  
The aim of this paper is to turn the group technology in WSN into GAI models which can represent multi-objective combinatorial optimization problems and then construct a GAI tree with hypertree decompositions  ...  More precisely, in Section 2, we introduce concepts and examples linked to the notion of GAI. In Section 3, we show how to construct a GAI tree with hypergraph decompositons.  ...  We would like to thank the pregnant and interesting discussions in SMILE group of Yantai University.  ... 
doaj:9902d4bfe98348f4b24d1206529c9c58 fatcat:u3sxeztlojfbrmeovq2f24tdr4

The Structure of Tractable Constraint Satisfaction Problems [chapter]

Martin Grohe
2006 Lecture Notes in Computer Science  
comments and corrections on an earlier draft of this paper.  ...  Acknowledgements The author is very grateful to Isolde Adler, Albert Atserias, Andrei Bulatov, Hubie Chen, Stephan Kreutzer, Andrei Krokhin, Daniel Marx, Nicole Schweikardt, and Marc Thurley for valuable  ...  Figure 1 . 1 A hypergraph H and a tree decomposition of H of width 3 Figure 2 . 2 A hypergraph H and a hypertree decomposition of H of width 2  ... 
doi:10.1007/11821069_5 fatcat:kxf72vtot5eolengxjuhlvq2m4

Semantic Width of Conjunctive Queries and Constraint Satisfaction Problems [article]

Georg Gottlob, Matthias Lanzinger, Reinhard Pichler
2018 arXiv   pre-print
Bounded answer sizes and decompositions have been shown to be tightly connected through the important notions of fractional hypertree width and, more recently, submodular width. recent papers by Barcel  ...  In this work, we connect all three of these threads by introducing a general notion of semantic width and investigating semantic versions of fractional hypertree width, adaptive width, submodular width  ...  This opens up an exciting area of applications and we aim to expand on this topic soon. Definition 9 . 9 For a hypergraph H: Generalized hypertree width of H [1, 11]: ghw(H) := ρ H -width.  ... 
arXiv:1812.04329v2 fatcat:gfqomcwlnbdnpfzaucxygu2pt4

Structural Tractability of Counting of Solutions to Conjunctive Queries [article]

Arnaud Durand, Stefan Mengel
2013 arXiv   pre-print
Furthermore, quantified star size is even fixed parameter tractable parameterized by some other width measures, while it is 1-hard for generalized hypertree width and thus unlikely to be fixed parameter  ...  To illustrate the applicability of our results, we also show that computing the quantified star size of a formula is possible in time n^O(k) for queries of generalized hypertree width k.  ...  is an algorithm that given a hypergraph H = (V, E) of generalized hypertree width k constructs a generalized hypertree decomposition of width O Let H = (V, E) be a hypergraph and S ⊆ V .  ... 
arXiv:1303.2059v1 fatcat:ahzo2x22hze45oywnj3yxeyk4y

HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings [article]

Wolfgang Fischl, Georg Gottlob, Davide M. Longo, Reinhard Pichler
2018 arXiv   pre-print
to different notions of width, noticeably, plain, generalized, and fractional hypertree width (hw, ghw, and fhw).  ...  for inserting, analysing, and retrieving hypergraphs are called for.  ...  Acknowledgements We would like to thank Angela Bonifati, Wim Martens, and Thomas Timm for sharing most of the hypergraphs with hw ≥ 2 from their work [14] and for their effort in anonymising these hypergraphs  ... 
arXiv:1811.08181v1 fatcat:n7obsrpzaverzcqdrftyhfpsgi
« Previous Showing results 1 — 15 out of 109 results