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On the Enumeration of Tree Decompositions

Nofar Carmeli, Batya Kenig, Benny Kimelfeld
2016 Alberto Mendelzon Workshop on Foundations of Data Management  
In this paper, we describe our ongoing effort on the task of enumerating all (or a subset of) the tree decompositions of a graph.  ...  , tree decompositions of the same width may entail highly diverging running times on the same problem instance.  ... 
dblp:conf/amw/CarmeliKK16 fatcat:gvihlvpysnb27bzh7u74ebjamm

Enumeration for spanning trees and forests of join graphs based on the combinatorial decomposition

Sung Sik U
2016 Electronic Journal of Graph Theory and Applications  
This paper discusses the enumeration for rooted spanning trees and forests of the labelled join graphs K m + H n and K m + K n,p , where H n is a graph with n isolated vertices.  ...  Acknowledgement The author thanks the referees for very careful readings and many constructive commments that greatly improve the presentation of this paper.  ...  In [1] and [3] , it has been given the enumeration of spanning trees of the complete tripartite graph K m,n,p on m, n and p vertices and the complete multipartite graph, respectively.  ... 
doi:10.5614/ejgta.2016.4.2.5 fatcat:mrn6tjoeqbfzzfx4wy6i5oc2ea

Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs [chapter]

Maryam Bahrani, Jérémie Lumbroso
2018 2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
Our goal was to study a simple family of graphs, of which the split-decomposition trees have prime nodes drawn from an enumerable (and manageable!) set of graphs.  ...  results on graphs-in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptolemaic).  ...  Acknowledgements We would like to thank the anonymous reviewers for critically reading the manuscript and making suggestions that led to significant improvements to the content and clarity of the paper  ... 
doi:10.1137/1.9781611975062.13 dblp:conf/analco/BahraniL18 fatcat:uupao4f4yfhvfkif7fpkarb7yq

Ranked Enumeration of Minimal Triangulations [article]

Noam Ravid, Dori Medini, Benny Kimelfeld
2018 arXiv   pre-print
On the theoretical side, we establish the guarantee of polynomial delay if poly-MS is assumed, or if we are interested in tree decompositions of a width bounded by a constant.  ...  We present the first algorithm for ranked enumeration of the proper (non-redundant) tree decompositions, or equivalently minimal triangulations, under a wide class of cost functions that substantially  ...  [10] embarked on the challenge of enumerating tree decompositions; that is, generating tree decompositions one by one so that an application can stop the enumeration at any time and select the decomposition  ... 
arXiv:1709.10254v2 fatcat:3cemulyijnf5ndyelm56agaitm

On the Enumeration of all Minimal Triangulations [article]

Nofar Carmeli, Batya Kenig, Benny Kimelfeld
2016 arXiv   pre-print
Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where "proper" means that the tree decomposition cannot be improved by removing or  ...  We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time.  ...  In this paper, we explore the task of enumerating all (or a subset of) the tree decompositions of a graph.  ... 
arXiv:1604.02833v1 fatcat:g32g6p4np5cenf6k56hr3ezb2i

Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs [article]

Maryam Bahrani, Jérémie Lumbroso
2017 arXiv   pre-print
Our goal was to study a simple family of graphs, of which the split-decomposition trees have prime nodes drawn from an enumerable (and manageable!) set of graphs.  ...  produce new enumerative results on graphs---in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptolemaic).  ...  Acknowledgements We would like to thank the anonymous reviewers for critically reading the manuscript and making suggestions that led to significant improvements to the content and clarity of the paper  ... 
arXiv:1711.10647v1 fatcat:zguxw3jnuvdu7gdhyw5cugd2aa

An Exact Enumeration of Distance-Hereditary Graphs [article]

Cédric Chauve and Éric Fusy and Jérémie Lumbroso
2016 arXiv   pre-print
^n---opening the perspective such graphs could be encoded on 3n bits. We also provide the exact enumeration and asymptotics of an important subclass, the 3-leaf power graphs.  ...  Our work illustrates the power of revisiting graph decomposition results through the framework of analytic combinatorics.  ...  ; the results in this paper were presented [7] at the Seventh International Conference on Graph Transformation (ICGT 2014).  ... 
arXiv:1608.01464v1 fatcat:lmepfq33rvd7pd3vpjj3d2r5uy

A Review on the Tree Edit Distance Problem and Related Path-Decomposition Algorithms [article]

Shihyen Chen
2015 arXiv   pre-print
The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a sequence of edit steps.  ...  In the literature, there are a class of algorithms based on different yet closely related path-decomposition schemes.  ...  However, depending on the shapes of the trees, the leftmost-path decomposition for some tree shapes could yield marginal benefits regarding the running time.  ... 
arXiv:1501.00611v6 fatcat:mjztl6tqenferiehgimaugnmle

An Exact Enumeration of Distance-Hereditary Graphs

Cédric Chauve, Éric Fusy, Jérémie Lumbroso
2017 2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
Our work illustrates the power of revisiting graph decomposition results through the framework of analytic combinatorics. *  ...  Distance-hereditary graphs form an important class of graphs, from the theoretical point of view, due to the fact that they are the totally decomposable graphs for the split-decomposition.  ...  in this paper were presented [8] at the Seventh International Conference on Graph Transformation (ICGT 2014).  ... 
doi:10.1137/1.9781611974775.3 dblp:conf/analco/ChauveFL17 fatcat:cum2zdrtrnfwdo7qdbs3lh5rgq

Optimal Tree Decompositions Revisited: A Simpler Linear-Time FPT Algorithm [article]

Ernst Althaus, Sarah Ziegler
2020 arXiv   pre-print
We group tree decompositions into equivalence classes depending on the current node of the given tree decomposition, such that it suffices to enumerate one tree decomposition per equivalence class and,  ...  In our description of the second algorithm, we start by explaining how all tree decompositions of subtrees defined by the nodes of the given tree decomposition can be enumerated.  ...  We then group tree decompositions into equivalence classes depending on the current node of the given tree decomposition so that it suffices to enumerate one tree decomposition per class.  ... 
arXiv:1912.09144v2 fatcat:czruwp7r35ghhk7naag3p3w7iq

Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition [article]

Maryam Bahrani, Jérémie Lumbroso
2016 arXiv   pre-print
By building on the work of Gioan and Paul (2012) and Chauve et al. (2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding  ...  We believe this methodology here shows its potential; the natural next step to develop its reach would be to study split-decomposition trees which contain certain prime nodes.  ...  Acknowledgment We would like to thank Christophe Paul, for his help in understanding the split-decomposition tree characterization of ptolemaic graphs.  ... 
arXiv:1608.01465v1 fatcat:vgdineixlrejjittjsrwjqjj2a

Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition

Maryam Bahrani, Jérémie Lumbroso
2018 Electronic Journal of Combinatorics  
the work of Gioan and Paul (2012) and Chauve et al.(2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding induced  ...  In certain cases, no enumeration was known (ptolemaic, 4-cacti); in other cases, although the enumerations were known, an abundant potential is unlocked by the grammars we provide (in terms of asymptotic  ...  Acknowledgment We would like to thank Christophe Paul, for his help in understanding the split-decomposition tree characterization of ptolemaic graphs.  ... 
doi:10.37236/6431 fatcat:mgy4hghqgbbo7pss4ekzzzbnx4

Constant Delay Enumeration with FPT-Preprocessing for Conjunctive Queries of Bounded Submodular Width

Christoph Berkholz, Nicole Schweikardt, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class Φ of Boolean CQs of bounded submodular width, the model-checking problem for Φ on the class  ...  time we can build a data structure that allows to enumerate, without repetition and with constant delay, all tuples of the query result.  ...  ) M F C S 2 0 1 9 58:6 Constant Delay Enumeration with FPT-Preprocessing Constant delay enumeration using tree decompositions We use the same notation as [22] for decompositions of queries: A tree  ... 
doi:10.4230/lipics.mfcs.2019.58 dblp:conf/mfcs/BerkholzS19 fatcat:mymzb4fe7zapla6aa7wwn3726a

Last Car Decomposition of Planar Maps [article]

Alice Contat
2022 arXiv   pre-print
The proof is inspired by the Lackner--Panholzer last car decomposition of parking trees (arXiv:1504.04972) and consists in applying a similar decomposition to the peeling trees of planar maps.  ...  We give new equations which characterize the generating functions of planar quadrangulations and planar triangulations, with zero, one or two boundaries.  ...  Our work concentrates on peeling trees but uses another method to enumerate them which is based on Lackner-Panholzer last car decomposition of parking trees [15] .  ... 
arXiv:2205.10285v1 fatcat:jnspheqporgxtofx2g74djs22e

Book Review: Combinatorial enumeration

Ira Gessel
1985 Bulletin of the American Mathematical Society  
Goulden and Jackson's book is a comprehensive account of the decomposition-based approach to enumeration.  ...  Thus if T is the set of rooted binary plane trees and R is the set containing only a single tree with one vertex, we have a bijection T -R « R X T X T.  ... 
doi:10.1090/s0273-0979-1985-15385-6 fatcat:hjrxervkhjehdameeenknu2siy
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