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### Linear kernels for k-tuple and liar's domination in bounded genus graphs [article]

Arijit Bishnu, Arijit Ghosh, Subhabrata Paul
2014 arXiv   pre-print
Given a graph G, the decision versions of k-Tuple Domination Problem and the Liar's Domination Problem are to check whether there exists a k-tuple dominating set and a liar's dominating set of G of a given  ...  In this paper, we study the parameterized complexity of these problems.  ...  Also assume that k = k + 3n. In [Sla09] , it is proved that G has a dominating set of cardinality at most k if and only if G has a liar's dominating set of cardinality at most k = k + 3n.  ...

### Linear kernels fork-tuple and liar's domination in bounded genus graphs

Arijit Bishnu, Arijit Ghosh, Subhabrata Paul
2017 Discrete Applied Mathematics
a k-tuple dominating set and a liar's dominating set of G of a given cardinality, respectively.  ...  A set D ⊆ V is called a k-tuple dominating set of a graph G = (V, Given a graph G, the decision versions of k-Tuple Domination Problem and the Liar's Domination Problem are to check whether there exists  ...  Also assume that k = k + 3n. In [Sla09] , it is proved that G has a dominating set of cardinality at most k if and only if G has a liar's dominating set of cardinality at most k = k + 3n.  ...

### Algorithm and Hardness results on Liar's Dominating Set and k-tuple Dominating Set [article]

Sandip Banerjee, Sujoy Bhore
2019 arXiv   pre-print
In this paper, we study two variants of the classical dominating set problem: k-tuple dominating set (k-DS) problem and Liar's dominating set (LDS) problem, and obtain several algorithmic and hardness  ...  On the hardness side, we show a Ω (n^2) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar's dominating set problem as well as for the k-tuple dominating set problem  ...  Acknowledgements The authors would like to thank Rajesh Chitnis and M. S. Ramanujan for interesting discussions during various stages of the research.  ...

### Balanced Independent and Dominating Sets on Colored Interval Graphs [article]

Sujoy Bhore, Jan-Henrik Haunert, Fabian Klute, Guangping Li, Martin Nöllenburg
2020 arXiv   pre-print
For the BIS problem on interval graphs, we design two FPT algorithms, one parameterized by (f,k) and the other by the vertex cover number of G.  ...  We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely f-Balanced Independent Set (f-BIS) and f-Balanced Dominating Set (f-BDS).  ...  Conclusions In this paper, we have studied the f -Balanced Independent and Dominating set problem for proper interval graphs.  ...

### New Algorithms for Weighted k-Domination and Total k-Domination Problems in Proper Interval Graphs [article]

Nina Chiarelli, Tatiana Romina Hartinger, Valeria Alejandra Leoni, Maria Inés Lopez Pujato, Martin Milanič
2018 arXiv   pre-print
A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set.  ...  problems) and undirected path graphs (in the case of total k-domination).  ...  The parameterized complexity of domination-type problems and application to linear codes. In Theory and applications of models of computation, volume 8402 of Lecture Notes in Comput.  ...

### OpenSpiel: A Framework for Reinforcement Learning in Games [article]

Marc Lanctot, Edward Lockhart, Jean-Baptiste Lespiau, Vinicius Zambaldi, Satyaki Upadhyay, Julien Pérolat, Sriram Srinivasan, Finbarr Timbers, Karl Tuyls, Shayegan Omidshafiei, Daniel Hennes, Dustin Morrill (+15 others)
2020 arXiv   pre-print
This document serves both as an overview of the code base and an introduction to the terminology, core concepts, and algorithms across the fields of reinforcement learning, computational game theory, and  ...  OpenSpiel is a collection of environments and algorithms for research in general reinforcement learning and search/planning in games.  ...  move games, and Leduc poker and Liar's dice for imperfect information games.  ...

### A Knowledge-Based Framework for Belief Change Part I: Foundations [chapter]

Nir Friedman, Joseph Y. Halpern
1994 Theoretical Aspects of Reasoning About Knowledge
We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief.  ...  This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin [HF89] for modeling knowledge in multi-agent  ...  Acknowledgements The authors are grateful to Craig Boutilier, Ronen Brafman, Steve Cousins, Ron Fagin, Moises Goldszmidt and particularly Daphne Koller and Moshe Vardi, for comments on drafts of this paper  ...

### Syntactic Analysis [chapter]

2005 Mathematical Models for Speech Technology
An action α i , is a 4-tuple (see Table 8 .1), α i = α i (X, U j , K, U k ), (8.6) where X ∈ V * (usually X ∈ V ), U j is the present configuration of the task model, K is a response code, and U k is  ...  Both processes were considered to be parameterized in λ and the problem was to determine λ from the observables.  ...

### Essays in Macroeconomics and Corporate Finance

Jonathan E. Goldberg
2011 Social Science Research Network
Aiyagari (1994) uses a variety of parameterizations; for the parameterization of the worker's problem that is similar to mine, Aiygari (1994) finds a wedge of 0.41 percentage points.  ...  bond, but Vayanos and Vila (2009) ignore this P to simplify their already-complex continuous-time analysis.  ...  Appendix A: Proofs Proof of Proposition 4 In period 1, the arbitrageur purchases h units of long-term debt and finances this purchase by selling hP in short-term debt.  ...

### Artificial Intelligence: Research Impact on Key Industries; the Upper-Rhine Artificial Intelligence Symposium (UR-AI 2020) [article]

Andreas Christ, Franz Quint
2020 arXiv   pre-print
management) and the University of Applied Sciences and Arts Northwestern Switzerland.  ...  , and Offenburg, the Baden-Wuerttemberg Cooperative State University Loerrach, the French university network Alsace Tech (comprised of 14 'grandes \'ecoles' in the fields of engineering, architecture and  ...  Main sponsor: esentri AG, Ettlingen Acknowledgement This research and development project is funded by the German Federal Ministry of Education and Research (BMBF) and the European Social Fund (ESF)  ...