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Sparse parameterized problems

Marco Cesati, Michael R. Fellows
1996 Annals of Pure and Applied Logic  
This provides one of the few instances in parameterized complexity theory of a full analog of a major classical theorem.  ...  The proof involves not only the standard technique of left sets, but also substantial circuit combinatorics to deal with the problem of small weft, and a diagonalization to cope with potentially nonrecursive  ...  We associate to F the parameterized circuit problem This gives us the hierarchy of parameterized complexity classes FPT G W[l] G W[2] c . . . c W[P] for which there are many natural hard or complete problems  ... 
doi:10.1016/0168-0072(95)00069-0 fatcat:wff4ll6e5jhdzivuxncld5nbsa

On the Space Complexity of Parameterized Problems [chapter]

Michael Elberfeld, Christoph Stockhusen, Till Tantau
2012 Lecture Notes in Computer Science  
that they lie in or are complete for different parameterized space classes.  ...  The purpose of the present paper is to demonstrate that the study of parameterized space complexity can give new insights into the complexity of well-studied parameterized problems like the feedback vertex  ...  One might even better understand the complexity of parameterized problems whose slices are not P-hard by considering parameterized versions of classical complexity classes based on parallel and circuit  ... 
doi:10.1007/978-3-642-33293-7_20 fatcat:veuk2fqydjdudhcvepjcf6ak5y

On the Structure of Parameterized Problems in NP

L.M. Cai, J. Chen, R. Downey, M. Fellows
1995 Information and Computation  
Fixed-parameter intractability of optimization problems in NP is studied based on computational models with limited nondeterminism.  ...  Strong evidence is provided that many NP optimization problems are not fixed-parameter tractable and that the fixed-parameter intractability hierarchy (the W -hierarchy) does not collapse.  ...  Parameterized problems form a restricted subclass in the class of general problems. Therefore, we can talk about the complexity of a parameterized problem in terms of the instance size.  ... 
doi:10.1006/inco.1995.1156 fatcat:rmuo7ocvy5efzmyfgta4qndl3e

On the structure of parameterized problems in NP [chapter]

Liming Cai, Jianer Chen, Rodney Downey, Michael Fellows
1994 Lecture Notes in Computer Science  
Fixed-parameter intractability of optimization problems in NP is studied based on computational models with limited nondeterminism.  ...  Strong evidence is provided that many NP optimization problems are not fixed-parameter tractable and that the fixed-parameter intractability hierarchy (the W -hierarchy) does not collapse.  ...  Parameterized problems form a restricted subclass in the class of general problems. Therefore, we can talk about the complexity of a parameterized problem in terms of the instance size.  ... 
doi:10.1007/3-540-57785-8_167 fatcat:6ov7m3jppbfwvbjm2ymt4kduna

Parameterized Complexity of Weighted Satisfiability Problems [chapter]

Nadia Creignou, Heribert Vollmer
2012 Lecture Notes in Computer Science  
We study the parameterized complexity of these problems and initiate a systematic study of the complexity of its fragments.  ...  Only the monotone fragment has been considered so far and proven to be of same complexity as the unrestricted problems.  ...  We are grateful to Arne Meier (Hannover) and Steffen Reith (Wiesbaden) for helpful discussions.  ... 
doi:10.1007/978-3-642-31612-8_26 fatcat:ortvpheqpnfuriule3ocg7ihny

On the Parallel Parameterized Complexity of the Graph Isomorphism Problem [article]

Bireswar Das, Murali Krishna Enduri, I. Vinod Reddy
2017 arXiv   pre-print
In this paper, we study the parallel and the space complexity of the graph isomorphism problem () for several parameterizations. Let H={H_1,H_2,...  ...  The parallel parameterized complexity of parameterized by the size of a feedback vertex set remains an open problem.  ...  The class Para-C is the family of parameterized problems that are in C after a pre-computation on the parameter, where C is a complexity class.  ... 
arXiv:1711.08885v2 fatcat:xufsxkkaafblxo6e4p2q7h3ohe

On Miniaturized Problems in Parameterized Complexity Theory [chapter]

Yijia Chen, Jörg Flum
2004 Lecture Notes in Computer Science  
We introduce a general notion of miniaturization of a problem that comprises the different miniaturizations of concrete problems considered so far.  ...  Using the appropriate logical formalism, we show that the miniaturization of a definable problem in W[t] lies in W[t], too. In particular, the miniaturization of the dominating set problem is in W[2].  ...  In [4] , Downey et al. introduce the class MINI [1] as the class of parameterized problems fpt-reducible to mini-Circuit Sat.  ... 
doi:10.1007/978-3-540-28639-4_10 fatcat:6qiqkvwr3nar5brhxkhbneww34

A Compendium of Parameterized Problems at Higher Levels of the Polynomial Hierarchy

Ronald de Haan, Stefan Szeider
2019 Algorithms  
These problems are parameterized versions of problems whose complexity lies at the second level of the Polynomial Hierarchy or higher.  ...  We present a list of parameterized problems together with a complexity classification of whether they allow a fixed-parameter tractable reduction to SAT or not.  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ... 
doi:10.3390/a12090188 fatcat:merbxfa4wjfbpcyes4lp6waf5i

Counting Abelian Squares for a Problem in Quantum Computing [article]

Ryan S. Bennink
2022 arXiv   pre-print
Here I show how the expressiveness of a certain class of parameterized quantum circuits can be reduced to the problem of counting abelian squares over a large alphabet, and use the recently developed formula  ...  In a recent work I developed a formula for efficiently calculating the number of abelian squares of length t+t over an alphabet of size d, where d may be very large.  ...  In the second part I describe the problem of quantifying the expressiveness of parameterized quantum circuits; show how for a particular family of circuits it reduces to the problem of counting abelian  ... 
arXiv:2208.02360v1 fatcat:bnpfsnyl25fjrghjlxijbi4b6y

On the Complexity of Problems on Tree-structured Graphs [article]

Hans L. Bodlaender and Carla Groenland and Hugo Jacob and Marcin Pilipczuk and Michal Pilipczuk
2022 arXiv   pre-print
In this paper, we introduce a new class of parameterized problems, which we call XALP: the class of all parameterized problems that can be solved in f(k)n^O(1) time and f(k)log n space on a non-deterministic  ...  Various natural problems on 'tree-structured graphs' are complete for this class: we show that List Coloring and All-or-Nothing Flow parameterized by treewidth are XALP-complete.  ...  Introduction A central concept in complexity theory is completeness for a class of problems.  ... 
arXiv:2206.11828v1 fatcat:rq2mmd5hgbeadiydafwomuyjuy

Complexity of the Stable Invitations Problem

Hooyeon Lee, Vassilevska Williams
In this work, we study the complexity of SIP on a finer scale, through the lense of parameterized complexity.For the two solution concepts and the special cases where the number of friends and/or enemies  ...  is bounded above by a constant, we show that the problems belong to different complexity classes when parameterized by the size of solutions.For instance finding an individually rational invitation of  ...  Acknowledgements This work was funded in part by the National Science Foundation (grant IIS-1347214), AFOSR MURI, and the Kwanjeong Educational Foundation.  ... 
doi:10.1609/aaai.v31i1.10562 fatcat:dcxa26w2yfbohinetdvqiuoi6a

Approximation of Natural W[P]-Complete Minimisation Problems Is Hard

Kord Eickmeyer, Martin Grohe, Magdalena Grüber
2008 2008 23rd Annual IEEE Conference on Computational Complexity  
The decision version of the monotone circuit satisfiability problem is known to be complete for the class W[P].  ...  Our result answers a question of Alekhnovich and Razborov [2] , who proved that the weighted monotone circuit satisfiability problem has no fixed-parameter tractable 2-approximation algorithm unless every  ...  We would like to thank Dieter van Melkebeek, Peter Bro Miltersen and Alexander Razborov, as well as three anonymous referees, for helpful comments on an earlier version of this paper.  ... 
doi:10.1109/ccc.2008.24 dblp:conf/coco/EickmeyerGG08 fatcat:ofwj4d36nvednnjisx3msmzh7m

Dynamic Parameterized Problems

R. Krithika, Abhishek Sahu, Prafullkumar Tale
2017 Algorithmica  
In this work, we study the parameterized complexity of various classical graph-theoretic problems in the dynamic framework where the input graph is being updated by a sequence of edge additions and deletions  ...  ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity Dynamic Π-Deletion Parameter: k, r Input: Graphs G, G on the same vertex set, a set S ⊆ V (G) such that G − S ∈ Π and integers  ...  We are grateful to Saket Saurabh for the invaluable discussions and for providing several useful pointers that led to the writing of this paper.  ... 
doi:10.1007/s00453-017-0349-6 fatcat:w42snepu6zc3helts3t4xyum6a

Hardness Magnification for Natural Problems

Igor Carboni Oliveira, Rahul Santhanam
2018 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)  
Our examples of hardness magnification include: 1) Let MCSP[s] be the decision problem whose YES instances are truth tables of functions with circuit complexity at most s(n).  ...  We show that for several natural problems of interest, complexity lower bounds that are barely non-trivial imply super-polynomial or even exponential lower bounds in strong computational models.  ...  ACKNOWLEDGEMENTS We are grateful to Jan Krajíček, Ján Pich and Ninad Rajgopal for helpful discussions and comments.  ... 
doi:10.1109/focs.2018.00016 dblp:conf/focs/OliveiraS18 fatcat:4youvi7wjfbxzn32ttjuy4c6f4

The Complexity of Tiling Problems [article]

François Schwarzentruber
2019 arXiv   pre-print
We also pinpoint tiling problems complete for respectively LOGSPACE and NLOGSPACE.  ...  In this document, we collected the most important complexity results of tilings.  ...  Thanks to Sasha Rubin and Tristan Charrier for having given me the motivation to write this note. Especially thanks to Sasha Rubin for his comments on a previous version of that document.  ... 
arXiv:1907.00102v2 fatcat:7rf6xiqc4zd6niwk55dlqjqri4
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