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Enumerating minimal dominating sets in the (in)comparability graphs of bounded dimension posets [article]

Marthe Bonamy, Oscar Defrain, Piotr Micek, Lhouari Nourine
2020 arXiv   pre-print
., for comparability graphs of bounded dimension posets.  ...  It can be reduced to enumerating minimal dominating sets in a graph, in fact even to enumerating minimal dominating sets in an incomparability graph.  ...  Discussions We provided an incremental-polynomial (resp. polynomial-delay) algorithm enumerating the minimal dominating sets in the comparability (resp. incomparability) graphs of bounded dimension posets  ... 
arXiv:2004.07214v1 fatcat:5atat6z2hrbzxci2iv7kbumrfa

Maximal Antichain Lattice Algorithms for Distributed Computations [chapter]

Vijay K. Garg
2013 Lecture Notes in Computer Science  
Since the lattice may be exponential in the size of the computation, we get a significant reduction in the space complexity.  ...  For the purposes of analyzing offline traces, we also propose new enumeration algorithms to traverse the lattice.  ...  This claim follows from the facts that A ⊆ minimal(I c ), D(A) = I and U [minimal(I c )] = I c . The time complexity of ILMA is dominated by Step 2.  ... 
doi:10.1007/978-3-642-35668-1_17 fatcat:72f5jpjdfbg75em3glzoloa4ea

On H-Topological Intersection Graphs [chapter]

Steven Chaplick, Martin Töpfer, Jan Voborník, Peter Zeman
2017 Lecture Notes in Computer Science  
The minimum vertex leafage problem can be solved in n O( ) -time via a somewhat elaborate enumeration of minimal 1 tree representations of G with exactly leaves where is the leafage of G [6].  ...  Our paper is the first study of the recognition and dominating set problems of this large collection of intersection classes of graphs.  ...  In particular, the algorithm runs in n O( H ) time. E Bounded List Coloring of Co-comparability Graphs We show how to solve the problem of bounded list coloring of co-comparability graphs.  ... 
doi:10.1007/978-3-319-68705-6_13 fatcat:qtiysf6psndj7mu4bxfovgcjae

Enumeration of Enumeration Algorithms [article]

Kunihiro Wasa
2016 arXiv   pre-print
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.  ...  Reference [254] 3.2 Independent set 3.2.1 Enumeration of all maximal independent set of a hypergraph of bounded dimension Input A hypergraph H of bounded dimension.  ...  Reference [247] 2.12 Dominating set 2.12.1 Enumeration of all minimal dominating sets in a graph Input A graph G = (V, E). Output All minimal dominating sets in G.  ... 
arXiv:1605.05102v2 fatcat:bwmhesagkje5hmynqyij7jv224

On Finding Minimal Infrequent Elements in Multi-dimensional Data Defined over Partially Ordered Sets [article]

Khaled M. Elbassioni
2014 arXiv   pre-print
We study the complexity of finding all minimal infrequent elements for some interesting classes of posets.  ...  We consider databases in which each attribute takes values from a partially ordered set (poset).  ...  The precedence graph of a poset P is a directed acyclic graph with vertex set P, and set of arcs {(x, y) : y is an immediate successor of x}.  ... 
arXiv:1411.2275v1 fatcat:nhft764wevcjra4jevbpf3hrwe

Minimizing Costs of Resource Requirements in Project Networks Subject to a Fixed Completion Time

Rolf H. Möhring
1984 Operations Research  
It is even possible to characterize all smallest sets having this property (so-called minimal dominating systems). This is done in Section 2.  ...  These methods are based on algorithms recently developed in graph theory for comparability graph and interval graph recognition and orientation. The last two parts are self-contained.  ...  ACKNOWLEDGMENTS This work was supported in part by the Minister fur Wissenschaft und Forschung des Landes Nordrhein-Westfalen.  ... 
doi:10.1287/opre.32.1.89 fatcat:h7wkcbbj4bejljnnd3fnnxvo7u

The Order Dimension of Planar Maps Revisited

Stefan Felsner
2014 SIAM Journal on Discrete Mathematics  
It states that the order dimension of the incidence poset P M of vertices, edges and faces of a planar map M has dimension at most 4.  ...  Schnyder characterized planar graphs in terms of order dimension. This seminal result found several extensions.  ...  In Q G the set X is the set of minimal elements and Y is the set of maximal elements.  ... 
doi:10.1137/130945284 fatcat:bwbqjz2cbbfx7chitrqtkymeai

Cardinal invariants of closed graphs [article]

Francis Adams, Jindrich Zapletal
2020 arXiv   pre-print
In particular, we address the question when it is consistent for the bounding number to be strictly smaller than the smallest size of a set not covered by countably many compact G-anticliques.  ...  We also provide a descriptive set theoretic characterization of the class of analytic graphs with countable coloring number.  ...  The metric spaces of finite dimension behave quite differently in this respect than the infinite dimensional ones [4] . The dimension fault line appears in the following example: Example 5.6.  ... 
arXiv:1710.08075v2 fatcat:m6e7lf7uqnbevgugm7seruc5ya

On H-Topological Intersection Graphs [article]

Steven Chaplick, Martin Töpfer, Jan Voborník, Peter Zeman
2021 arXiv   pre-print
The algorithm for H-graphs adapts to an XP-time algorithm for the independent set and the independent dominating set problems on H-graphs.  ...  In fact, these results apply to classes of graphs with treewidth bounded by a function of the clique number.  ...  By Theorem 19 a the graph G is k-thin. It can be tested in O(n 3 ) time whether the graph G is s-colorable [4] .  ... 
arXiv:1608.02389v5 fatcat:xz5lppzjpjh3vgsvjtiwtwf3de

A survey of the Shi arrangement [article]

Susanna Fishel
2020 arXiv   pre-print
Shi, in 1986, proved part of this conjecture. As a byproduct, he introduced the Shi arrangement of hyperplanes and found a few of its remarkable properties.  ...  The Shi arrangement has since become a central object in algebraic combinatorics.  ...  See Athanasiadis [Ath05] or Haiman [Hai94] for more information. (4) The enumeration of bounded regions has nice results, which we have not discussed.  ... 
arXiv:1909.01257v3 fatcat:xpdn64ylbzfzvhmp7tmmkfeopa

A central partition of molecular conformational space. I. Basic structures [article]

Jacques Gabarro-Arpa
2002 arXiv   pre-print
On the basis of empirical evidence from molecular dynamics simulations, molecular conformational space can be described by means of a partition of central conical regions characterized by the dominance  ...  This work presents a geometric and combinatorial description of this structure.  ...  It can be shown that the partially ordered set (poset) L thus defined is a lattice, that is: for all pairs x , y ǫ L there is a least upper bound and a greatest lower bound.  ... 
arXiv:physics/0204035v1 fatcat:473xsirlozcdpd4iw3tfi5mvvq

Master index of volumes 81–90

1991 Discrete Mathematics  
The least point covering and domination numbers of a graph Sanchis, L.A., Maximum number of edges in connected graphs with a given domination number Sato, I., Enumeration of packed graphs (Note) Savicky  ...  Lin, C., The dimension of the Cartesian product of posets Lin, M.-C. and S. Lin, Codes with multi-level error-correcting capabilities Lin, S., see Lin, M.-C. Lindner, C.C., see Hoffman, D.G.  ... 
doi:10.1016/0012-365x(91)90131-k fatcat:gbxyeqcrdrcb7eqpruwbpkf2xy

Homological algebra of modules over posets [article]

Ezra Miller
2020 arXiv   pre-print
Tameness and its homological theory are new even in the finitely generated discrete setting of N^n-gradings, where tame is materially weaker than noetherian.  ...  Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations  ...  Comparing Theorems 6.12 and 5.19, what happened to minimality? It is not clear in what generality minimality can be characterized.  ... 
arXiv:2008.00063v2 fatcat:ze325f7r5jbyrp5zwdgrclg7ei

Efficient skyline evaluation over partially ordered domains

Shiming Zhang, Nikos Mamoulis, David W. Cheung, Ben Kao
2010 Proceedings of the VLDB Endowment  
Nevertheless these methods either use stronger notions of dominance, which generate false positives, or require expensive dominance checks.  ...  The first method uses an appropriate mapping of a partial order to a total order, inspired by the lattice theorem and an off-the-shelf skyline algorithm.  ...  This allows for efficient dominance checking between values in the domain; otherwise, traversal of the poset graph might be required.  ... 
doi:10.14778/1920841.1920996 fatcat:ejxwsc27y5bs3jlqtp2d6ajpam

The Shi arrangement and the Ish arrangement [article]

Drew Armstrong, Brendon Rhoades
2010 arXiv   pre-print
Moreover, all of these results hold in the greater generality of "deleted" Shi and Ish arrangements corresponding to an arbitrary subgraph of the complete graph.  ...  For example, the Shi and Ish arrangements share the same characteristic polynomial, the same numbers of regions, bounded regions, dominant regions, regions with c "ceilings" and d "degrees of freedom",  ...  This project arose out of an AMS sectional meeting held at Penn State in October 2009.  ... 
arXiv:1009.1655v2 fatcat:src3lz3nznh6bgznerwz2lagdi
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