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Integer Programming in Parameterized Complexity: Three Miniatures [article]

Tomáš Gavenčiak and Dušan Knop and Martin Koutecký
2018 arXiv   pre-print
Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity.  ...  However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community  ...  (computational social choice; big-M coefficients to express logical connectives) [26]. 21:6 Integer Programming in Parameterized Complexity: Three Miniatures Convex IP in small dimension.  ... 
arXiv:1711.02032v3 fatcat:zzn6cumyqrcifpk7kevo5kaafm

Integer Programming in Parameterized Complexity: Three Miniatures

Tomás Gavenciak, Dusan Knop, Martin Koutecký, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity.  ...  However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community  ...  I P E C 2 0 1 8 21:4 Integer Programming in Parameterized Complexity: Three Miniatures Preliminaries For positive integers m, n with m ≤ n we set [m, n] = {m, . . . , n} and [n] = [1, n] .  ... 
doi:10.4230/lipics.ipec.2018.21 dblp:conf/iwpec/GavenciakKK18 fatcat:sem7iagkrzco7b5klxrguketre

A Basic Parameterized Complexity Primer [chapter]

Rod Downey
2012 Lecture Notes in Computer Science  
Since many of the contributed articles revolve around the concept of parameterized complexity, it seems reasonable to give the reader a (short) primer to this area.  ...  The basics from this paper will be amplified by many other articles in this Festschrift.  ...  We meet this result in Section 6. Bounded Integer Programming One technique, not discussed in [DF98, FG06] , is the use of Integer Programming in the design of FPT algorithms.  ... 
doi:10.1007/978-3-642-30891-8_9 fatcat:fpq3zvaccfcavaxomwkeh5tyby

Fixed-Parameter Complexity in AI and Nonmonotonic Reasoning [chapter]

Georg Gottlob, Francesco Scarcello, Martha Sideri
1999 Lecture Notes in Computer Science  
We study the parameterized complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable.  ...  The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems.  ...  Conclusions are given in Section 7. Parameterized complexity Parameterized complexity [14] deals with parameterized problems, i.e., problems with an associated parameter.  ... 
doi:10.1007/3-540-46767-x_1 fatcat:tui4rdaidrh6rjcvi6ybqaibgq

Fixed-parameter complexity in AI and nonmonotonic reasoning

Georg Gottlob, Francesco Scarcello, Martha Sideri
2002 Artificial Intelligence  
We study the parameterized complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable.  ...  The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems.  ...  Conclusions are given in Section 7. Parameterized complexity Parameterized complexity [14] deals with parameterized problems, i.e., problems with an associated parameter.  ... 
doi:10.1016/s0004-3702(02)00182-0 fatcat:vrfcg23nyjettjkvt2y3nne4ky

Blow-Ups, Win/Win's, and Crown Rules: Some New Directions in FPT [chapter]

Michael R. Fellows
2003 Lecture Notes in Computer Science  
This survey reviews the basic notions of parameterized complexity, and describes some new approaches to designing FPT algorithms and problem reductions for graph problems.  ...  The parameterized complexity framework is a two-dimensional framework for complexity analysis, where the first dimension is the overall imput size n.  ...  The miniaturization route to M [1]. We certainly know an algorithm to solve n-variable 3SAT in time O(2 n ). Consider the following parameterized problem.  ... 
doi:10.1007/978-3-540-39890-5_1 fatcat:jojjzpn4fffedjarzcwieynllm

Three Dimensional Dynamics of Micro Tools and Miniature Ultra-High-Speed Spindles

Bekir Bediz
2018
Application of mechanical micromachining for fabricating complex three-dimensional (3D) micro-scale features and small parts on a broad range of materials has increased significantly in the recent years  ...  modal characteristics of miniature ultra-high-speed (UHS) spindles that are used during micromachining.  ...  -Nikola Tesla Motivation In the past few decades, there has been an increasing demand for three-dimensional (3D) micro-scale complex products (see Fig. 1.1 for examples of micro-scale feature and devices  ... 
doi:10.1184/r1/6723875.v1 fatcat:ktlxcty4ofa3phmlt43tdttndq

Complex Type 4 Structure Changing Dynamics of Digital Agents: Nash Equilibria of a Game with Arms Race in Innovations

Sheri M. Markose
2016 Social Science Research Network  
The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation.  ...  The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58]  ...  three orders of magnitude.  ... 
doi:10.2139/ssrn.2900533 fatcat:hv4x3by2wffitnhok5lz5prwve

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations

Sheri M. Markose
2017 Journal of Dynamics & Games  
The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation.  ...  The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58]  ...  three orders of magnitude.  ... 
doi:10.3934/jdg.2017015 fatcat:joapkhn7kfgdzgnxm7jsil3use

On Parameterized Intractability: Hardness and Completeness

J. Chen, J. Meng
2007 Computer journal  
Moreover, the fundamentals of the structural properties in parameterized complexity theory, relationships to classical complexity theory and more recent developments in the area are also introduced.  ...  We study the theory and techniques developed in the research of parameterized intractability, emphasizing on parameterized hardness and completeness that imply (stronger) computational lower bounds for  ...  ACKNOWLEDGEMENTS Supported in part by the National Science Foundation under grants CCR-0311590 and CCF-0430683.  ... 
doi:10.1093/comjnl/bxm036 fatcat:wjrw57b5nvbfnfib3uii5tviiq

Bayesian metamodeling of complex biological systems across varying representations [article]

Barak Raveh, Liping Sun, Kate L White, Tanmoy Sanyal, Jeremy Tempkin, Dongqing Zheng, Kala Bharath Pilla, Jitin Singla, ChenXi Wang, Jihui Zha, Angdi Li, Nicholas A Graham (+3 others)
2021 bioRxiv   pre-print
To divide-and-conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models.  ...  Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity.  ...  In particular, we appreciated the discussions with Helen Berman and Peter Butler.  ... 
doi:10.1101/2021.03.29.437574 fatcat:6bcvrbyqpzdzpegbubz34bjmda

Parameterized Problems on Coincidence Graphs [chapter]

Sylvain Guillemot
2006 Lecture Notes in Computer Science  
In both cases, we show that the problems are computationally hard, though we obtain stronger hardness results in the second case.  ...  We study the complexity of several graph problems on (k, r)-representable graphs, as a function of the parameters k, r; the problems under study are Maximum Independent Set, Minimum Dominating Set and  ...  Parameterized Complexity Let A be an alphabet. A parameterized language is a set L ⊆ A * × N.  ... 
doi:10.1007/11940128_27 fatcat:uh23e23abnhhpkbfzmnvuxsejy

Confronting intractability via parameters

Rodney G. Downey, Dimitrios M. Thilikos
2011 Computer Science Review  
Almost no computational tasks in real life are specified by their size alone.  ...  One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  Such a, still non-integer, solution defines a partition of V (G) into three sets V 0 , V 1 2 , and V 1 .  ... 
doi:10.1016/j.cosrev.2011.09.002 fatcat:4efih5lobfbjdgyuu2ccbqlbbq

Confronting Intractability via Parameters [article]

Rodney G. Downey, Dimitrios M. Thilikos
2011 arXiv   pre-print
Almost no computational tasks in real life are specified by their size alone.  ...  One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  Such a, still non-integer, solution defines a partition of V (G) into three sets V 0 , V 1 2 , and V 1 .  ... 
arXiv:1106.3161v6 fatcat:6eqwtzfmunffzokn47lqyb6xwq

Robotic Control Using Hierarchical Genetic Programming [chapter]

Marcin L. Pilat, Franz Oppacher
2004 Lecture Notes in Computer Science  
and with a linear genome GP system in the domain of evolving robotic controllers for a simulated Khepera miniature robot.  ...  In this paper, we compare the performance of hierarchical GP methods (Automatically Defined Functions, Module Acquisition, Adaptive Representation through Learning) with the canonical GP Implementation  ...  We study the application of genetic programming techniques to the evolution of control programs for an autonomous miniature robot.  ... 
doi:10.1007/978-3-540-24855-2_72 fatcat:4kl6lviarvblfkgpqvk5etaabm
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