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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  ...  In this paper, we prove that the invariants hypertree-width, generalized hypertree-width, minimum number of marshals with a monotone winning strategy, and minimum number of marshals with a winning strategy  ... 
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  
Section 3 describes the Robbers and Marshals game which caracterizes hypertree-width.  ...  Hypertree Decompositions: Definition and Basics This paper reports about the recently introduced concept of hypertree decomposition and the associated notion of hypertree width.  ...  Open Problems and Future Research We believe that hypertree decompositions and hypertree width are interesting concepts deserving further investigations.  ... 
doi:10.1007/11604686_1 fatcat:32q3km744ff3pcrtrjjvhp2ffy

Tree-Related Widths of Graphs and Hypergraphs

Isolde Adler
2008 SIAM Journal on Discrete Mathematics  
We extend the definitions of hypertree-width [7] and generalised hypertree-width [8] from hypergraphs to hypergraph pairs.  ...  Besides this practical interest, hypergraph pairs serve as a tool for giving a common proof for the game theoretic characterisations of tree-width [14] and hypertree-width [8] .  ...  Thomassen for his elegant proof of compactness of tree-width and H. Scheuermann for many discussions.  ... 
doi:10.1137/050623395 fatcat:sy67w4e7jzgddnhbrep66kllri

Hypertree Decompositions: A Survey [chapter]

Georg Gottlob, Nicola Leone, Francesco Scarcello
2001 Lecture Notes in Computer Science  
This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width.  ...  Important NP hard problems become tractable if restricted to instances whose associated hypergraphs are of bounded hypertree width.  ...  Research supported by FWF (Austrian Science Funds) under the project Z29-INF (Wittgenstein Award), and by MURST under project COFIN-2000 "From Data to Information (D2I)"  ... 
doi:10.1007/3-540-44683-4_5 fatcat:e2x57x7rdbesflhlesjfs6426e

Greedy Strategies and Larger Islands of Tractability for Conjunctive Queries and Constraint Satisfaction Problems [article]

Gianluigi Greco, Francesco Scarcello
2016 arXiv   pre-print
It is shown that deciding the existence of a (non-monotone) greedy winning strategy (and compute one, if any) is tractable.  ...  Most structural decomposition methods can be characterized through hypergraph games that are variations of the Robber and Cops graph game that characterizes the notion of treewidth.  ...  holds because the notion of hypertree decomposition is characterized by the monotone Robber and Marshals game, played on H Q by a Robber and k Marshals [35] .  ... 
arXiv:1603.09617v2 fatcat:d2ai5ymeovaajh2wfeaj6bwfwa

Approximating acyclicity parameters of sparse hypergraphs [article]

Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos
2008 arXiv   pre-print
The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity.  ...  These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph.  ...  In this direction, Chekuri and Rajaraman in [4] introduced the notion of query width. Gottlob, Leone, and Scarcello [13, 14, 16] defined hypertree width and generalized hypertree width.  ... 
arXiv:0809.3646v1 fatcat:narokqvabff7xbwqioxp6jp3ny

Approximating Width Parameters of Hypergraphs with Excluded Minors

Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos
2011 SIAM Journal on Discrete Mathematics  
The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity.  ...  These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph.  ...  We are grateful to the anonymous referees for their constructive suggestions and remarks.  ... 
doi:10.1137/080743226 fatcat:heur73wfvncb5nsa67zvxu33ke

Hypertree-depth and minors in hypergraphs

Isolde Adler, Tomáš Gavenčiak, Tereza Klimošová
2012 Theoretical Computer Science  
We characterise hypergraphs of bounded hypertree-depth by the ultramonotone robber and marshals game, by vertex-hyperrankings and by centred hypercolourings.  ...  Furthermore, we show that minors in hypergraphs are 'well-behaved' with respect to hypertree-depth and other hypergraph invariants, such as generalised hypertree-depth and generalised hyperpath-width.  ...  Any hypergraph pair (G, H) satisfies The word 'ultramonotone' refers to the fact that the ultramonotone robber and marshals game is 'monotone' in the sense of [8] (robber's area monotonically shrinks  ... 
doi:10.1016/j.tcs.2012.09.007 fatcat:tc53ms3r3ng6zpe7sa75wydvcq

Heuristic Hypertree Decomposition

Thomas Korimort, Georg Gottlob
2003 Zenodo  
Recently, a new method called hypertree decomposition has been developed by Gottlob and others, that dominates in a precise sense all known methods from the literature.  ...  The quality of the solution is compared in the environment of a constraint solver developed by DaimlerChrylser, which can import strategies generated from hypertree decompositions and use them for the  ...  More precisely monotone game trees for the robber and marshals game correspond to hypertree decompositions. For details on the game theoretic approach consult [14] .  ... 
doi:10.5281/zenodo.4578376 fatcat:egyrdo3clzgnrgi5jjpbszhbhy

Query answering exploiting structural properties

Francesco Scarcello
2005 SIGMOD record  
by some fixed constant) hypertree width.  ...  We review the notion of hypertree width, a measure of the degree of cyclicity of hypergraphs that is useful for identifying and solving efficiently easy instances of hard problems, by exploiting their  ...  Acknowledgments The author sincerely thanks Georg Gottlob and Nicola Leone, who worked with him on these issues since 1999, when they jointly defined the notion of hypertree decompositions.  ... 
doi:10.1145/1084805.1084827 fatcat:enicq2ngqrbinnr2lkohxxzc7y

Generalized hypertree decompositions

Georg Gottlob, Zoltan Miklos, Thomas Schwentick
2007 Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '07  
The generalized hypertree width GHW (H) of a hypergraph H is a measure of its cyclicity.  ...  Our intractability results on generalized hypertree width motivate further research on more restrictive tractable hypergraph decomposition methods that approximate general hypertree decomposition (GHD)  ...  Acknowledgements The authors are very grateful to Isolde Adler for her comments and suggestions on earlier versions of this paper.  ... 
doi:10.1145/1265530.1265533 dblp:conf/pods/GottlobMS07 fatcat:fbi6trahpbfdzau5lmmwkl2fuy

On the complexity of combinatorial auctions

Georg Gottlob, Gianluigi Greco
2007 Proceedings of the 8th ACM conference on Electronic commerce - EC '07  
Indeed, we show that the winner determination problem is solvable in polynomial time on instances whose bidder interactions can be represented with (dual) hypergraphs having bounded hypertree width.  ...  We show that the notion of hypertree decomposition, a recently introduced measure of hypergraph cyclicity, turns out to be most useful here.  ...  Greco is supported by ICAR-CNR, and by M.I.U.R. under project TOCAI.IT.  ... 
doi:10.1145/1250910.1250934 dblp:conf/sigecom/GottlobG07 fatcat:sfhzyoy7jfhfzkm5rw47kyisou

Distance d-Domination Games [chapter]

Stephan Kreutzer, Sebastian Ordyniak
2010 Lecture Notes in Computer Science  
We are primarily interested in questions concerning the complexity and monotonicity of these games.  ...  We show that dominating games are computationally much harder than standard graph searching games where the cops only see their own vertex and establish strong non-monotonicity results for various notions  ...  We are grateful to Fedor Fomin for bringing domination games to our attention and thereby stimulating the research reported in this paper and to Fedor Fomin, Paul Hunter and Paul Dorbec for valuable discussions  ... 
doi:10.1007/978-3-642-11409-0_27 fatcat:2isaifouazdk7ljxrenimnl3ti

Tree Projections and Structural Decomposition Methods: The Power of Local Consistency and Larger Islands of Tractability [article]

Gianluigi Greco, Francesco Scarcello
2012 arXiv   pre-print
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively.  ...  These latter classes are shown to be efficiently recognizable and strictly larger than most islands of tractability known so far, both in the general case of tree projections and for specific structural  ...  holds because the notion of hypertree decomposition is characterized by the monotone Robber and Marshals game, played on H Q by a Robber and k Marshals [25] .  ... 
arXiv:1205.3321v2 fatcat:oww3cmt2ovfstmnkcmumbxwnhe

Tree Projections and Structural Decomposition Methods: Minimality and Game-Theoretic Characterization [article]

Gianluigi Greco, Francesco Scarcello
2012 arXiv   pre-print
In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones.  ...  As a special case, the Captain and Robber game can be used to characterize the generalized hypertree decomposition method, where such a game-theoretic characterization was missing and asked for.  ...  The game is the same as the one characterizing acyclicity, but with k Marshals acting simultaneously to capture the Robber: A hypergraph H has hypertree width bounded by k if, and only if, k Marshals,  ... 
arXiv:1212.2314v1 fatcat:ql7jbivowbd3rpmw4bb266zgdi
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