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Neighborhood inclusions for minimal dominating sets enumeration: linear and polynomial delay algorithms in P_7-free and P_8-free chordal graphs [article]

Oscar Defrain, Lhouari Nourine
2019 arXiv   pre-print
On the enumeration of minimal dominating sets and related notions.  ...  SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-  ...  Neighborhood inclusions for minimal dominating sets enumeration all the clauses, and D the associated set of vertices in G. By construction D dominates all the c i 's.  ... 
arXiv:1805.02412v2 fatcat:yvlfpi42snbahgvcuoukzgdmj4

Below all subsets for Minimal Connected Dominating Set [article]

Daniel Lokshtanov, Michał Pilipczuk, Saket Saurabh
2016 arXiv   pre-print
For the same ε we also give an algorithm with running time 2^(1-ε)n· n^O(1) to enumerate all minimal connected dominating sets in an input graph G.  ...  A connected dominating set S is a minimal connected dominating set if no proper subset of S is also a connected dominating set.  ...  The authors gratefully thank the organizers of the workshop Enumeration Algorithms Using Structure, held in Lorentz Center in Leiden in August 2015, where this work was initiated.  ... 
arXiv:1611.00840v1 fatcat:mpy6d42od5fttkce7zod4lwi7i

Minimal Roman Dominating Functions: Extensions and Enumeration [article]

Faisal N. Abu-Khzam, Henning Fernau, Kevin Mann
2022 arXiv   pre-print
Recall that the existence of a similar enumeration result for minimal dominating sets is open for decades.  ...  We develop non-trivial enumeration algorithms for minimal Roman domination functions with polynomial delay and polynomial space.  ...  Notice that such a strategy would work not only for computing smallest dominating sets, but also for computing largest minimal dominating set, or for counting minimal solutions, or for enumerating them  ... 
arXiv:2204.04765v1 fatcat:cwrkde2ilrdypcscj4e2ethscu

Algorithmic Enumeration: Output-sensitive, Input-Sensitive, Parameterized, Approximativ (Dagstuhl Seminar 18421)

Henning Fernau, Petr. A. Golovach, Marie-France Sagot, Michael Wagner
2019 Dagstuhl Reports  
Enumeration problems require to list all wanted objects of the input as, e.g., particular subsets of the vertex or edge set of a given graph or particular satisfying assignments of logical expressions.  ...  The main challenge of the area of enumeration problems is that, contrary to decision, optimization and even counting problems, the output length of an enumeration problem is often exponential in the size  ...  Consider for example the classical concept of minimal dominating sets for graphs.  ... 
doi:10.4230/dagrep.8.10.63 dblp:journals/dagstuhl-reports/FernauGS18 fatcat:dwb3bv2onzanvgh6ucxh6atswm

Distortion Effects in Equal Area Unit Maps

Jochen Schiewe
2021 KN - Journal of Cartography and Geographic Information  
Hence, for some map use tasks where small regions are of importance, alternative map types are needed.  ...  To describe these distortions, a set of analytical measures is proposed. But it turns out that the expressiveness of these measures is rather limited.  ...  Philipp Loose, who programmed the above-mentioned tool for generating EAUMs.  ... 
doi:10.1007/s42489-021-00072-5 fatcat:qtutypmrhfcvhpijwbkrqnnwdm

Multi-objective Variable Neighborhood Search Algorithms for a Single Machine Scheduling Problem with Distinct due Windows

José Elias Claudio Arroyo, Rafael dos Santos Ottoni, Alcione de Paiva Oliveira
2011 Electronical Notes in Theoretical Computer Science  
The performance of the algorithms is tested on a set of medium and larger instances of the problem.  ...  In this paper, we compare three multi-objective algorithms based on Variable Neighborhood Search (VNS) heuristic.  ...  That is, before conducting the neighborhood search, the base solution is randomly picked from the set of non-dominated solutions for which no neighborhood search has been performed yet, and one of the  ... 
doi:10.1016/j.entcs.2011.11.022 fatcat:ix2xdcjdrve7hoz6t2vxqjrf24

Constraint-Based Local Search for Constrained Optimum Paths Problems [chapter]

Quang Dung Pham, Yves Deville, Pascal Van Hentenryck
2010 Lecture Notes in Computer Science  
The main technical contribution is a connected neighborhood based on rooted spanning trees to find high-quality solutions to COP problems.  ...  This paper proposes a constraint-based local search (CBLS) framework for COP applications, bringing the compositionality, reuse, and extensibility at the core of CBLS and CP systems.  ...  Acknowledgments We would like to thank Maria José Blesa Aguilera who has kindly provided some graphs for the experimentation.  ... 
doi:10.1007/978-3-642-13520-0_29 fatcat:5sttzdr4yrfxxo7xkl5vszhaei

Bi-objective scheduling for re-entrant hybrid flow shop with learning effect and setup times

S.M. Mousavi, I. Mahdavi, J. Rezaeian, M. Zandieh
2017 Scientia Iranica. International Journal of Science and Technology  
Computational results show that the proposed algorithm can obtain an effective and appropriate solution quality for our investigated problem.  ...  to a priori approach, the preferences for each objective are set by the decision-makers and then, one solution satisfying these preferences have to be found.  ...  This problem is solved with a multi-objective GA by using the Lorenz dominance relationship. Cho et al. [11] focused on the minimization of makespan and total tardiness in a RHFS.  ... 
doi:10.24200/sci.2017.4451 fatcat:c3q3332twjcgdfo2chmhd5d6w4

Linear separation of connected dominating sets in graphs

Nina Chiarelli, Martin Milanič
2019 Ars Mathematica Contemporanea  
dominating set problem.  ...  A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph.  ...  Since G is connected-domishold, it has at most n(n − 2) minimal connected dominating sets, by Lemma 6.4. The minimal connected dominating sets of G can be enumerated as follows.  ... 
doi:10.26493/1855-3974.1330.916 fatcat:awlczmj3jnfyhhlmhqyjywhq6u

Linear separation of connected dominating sets in graphs [article]

Nina Chiarelli, Martin Milanič
2018 arXiv   pre-print
dominating set problem.  ...  A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph.  ...  Acknowledgments The authors are grateful to an anonymous reviewer for insightful suggestions, to Endre Boros, Yves Crama, Vladimir Gurvich, Pinar Heggernes, Haiko Müller, and Vito Vitrih for helpful discussions  ... 
arXiv:1610.06539v2 fatcat:u4v42ucqtbe4rbm3vscdybkeky

Set-based multiobjective fitness landscapes

Sebastien Verel, Arnaud Liefooghe, Clarisse Dhaenens
2011 Proceedings of the 13th annual conference on Genetic and evolutionary computation - GECCO '11  
The aim is to adapt and to enhance the comprehensive design of set-based multiobjective search approaches, motivated by an a priori analysis of the corresponding set problem properties.  ...  Then, we give a general definition of set-based multiobjective fitness landscapes.  ...  A set preference relation is then usually induced over Σ, like the Pareto dominance relation extended to solution-sets.  ... 
doi:10.1145/2001576.2001681 dblp:conf/gecco/VerelLD11 fatcat:ytukkvynt5adrlbysuigizpvn4

Enumeration degrees and non-metrizable topology [article]

Takayuki Kihara and Keng Meng Ng and Arno Pauly
2020 arXiv   pre-print
The enumeration degrees of sets of natural numbers can be identified with the degrees of difficulty of enumerating neighborhood bases of points in a universal second-countable T_0-space (e.g. the ω-power  ...  Based on these observations, we utilize general topology (particularly non-metrizable topology) to establish a classification theory of enumeration degrees of sets of natural numbers.  ...  Therefore, near N N N -quasi-minimality is equivalent to N N N -quasi-minimality by definition. Now, by Lemma 7.30, if f is not ∅ ′ -computably dominated, then f : (ω ω ) co is N N N -quasi-minimal.  ... 
arXiv:1904.04107v2 fatcat:tepbiv3rvzcefeo273wwwbgvui

Sequencing and Scheduling in the Sheet Metal Shop [chapter]

B. Verlinden, D. Cattrysse, H. Crauwels, J. Duflou, D. Van
2007 Multiprocessor Scheduling, Theory and Applications  
To select a new tool (from the short list for that bend line), a number of rules are followed: • minimize the number of tool profiles to be used for producing the part; • maximize common preference for  ...  Since exhaustive enumeration requires too much computational time, a neighborhood search method is suggested.  ...  A first problem is the layout outline for the placing of the different stations on a press brake, minimizing the travel distance for the press brake operator.  ... 
doi:10.5772/5231 fatcat:lec2ommtjvdsjg6v26cwgbyb74

Connecting Terminals and 2-Disjoint Connected Subgraphs [chapter]

Jan Arne Telle, Yngve Villanger
2013 Lecture Notes in Computer Science  
In this paper we prove that there are at most |V \T | |T |−2 · 3 |V \T | 3 minimal T -connecting sets when |T | ≤ n/3 and that these can be enumerated within a polynomial factor of this bound.  ...  This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case |T | = 2.  ...  For example, in the minimum dominating set problem it is obvious that a dominating set of minimum cardinality is also an inclusion minimal dominating set.  ... 
doi:10.1007/978-3-642-45043-3_36 fatcat:x3nxk7qiwnairixirowpv75z7m

Connecting Terminals and 2-Disjoint Connected Subgraphs [article]

Jan Arne Telle, Yngve Villanger
2013 arXiv   pre-print
In this paper we prove that there are at most |V ∖ T| |T|-2· 3^|V ∖ T|/3 minimal T-connecting sets when |T| ≤ n/3 and that these can be enumerated within a polynomial factor of this bound.  ...  This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case |T|=2.  ...  For example, in the minimum dominating set problem it is obvious that a dominating set of minimum cardinality is also an inclusion minimal dominating set.  ... 
arXiv:1301.2506v1 fatcat:3vseu7u5enelxn35o6tdeglg64
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