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Sparse parameterized problems

1996
*
Annals of Pure and Applied Logic
*

This provides

doi:10.1016/0168-0072(95)00069-0
fatcat:wff4ll6e5jhdzivuxncld5nbsa
*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*...##
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On the Space Complexity of Parameterized Problems
[chapter]

2012
*
Lecture Notes in Computer Science
*

that they lie in or are

doi:10.1007/978-3-642-33293-7_20
fatcat:veuk2fqydjdudhcvepjcf6ak5y
*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*...##
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On the Structure of Parameterized Problems in NP

1995
*
Information and Computation
*

Fixed-parameter intractability

doi:10.1006/inco.1995.1156
fatcat:rmuo7ocvy5efzmyfgta4qndl3e
*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. ...##
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On the structure of parameterized problems in NP
[chapter]

1994
*
Lecture Notes in Computer Science
*

Fixed-parameter intractability

doi:10.1007/3-540-57785-8_167
fatcat:6ov7m3jppbfwvbjm2ymt4kduna
*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. ...##
###
Parameterized Complexity of Weighted Satisfiability Problems
[chapter]

2012
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-642-31612-8_26
fatcat:ortvpheqpnfuriule3ocg7ihny
*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. ...##
###
On the Parallel Parameterized Complexity of the Graph Isomorphism Problem
[article]

2017
*
arXiv
*
pre-print

In this paper, we study

arXiv:1711.08885v2
fatcat:xufsxkkaafblxo6e4p2q7h3ohe
*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*. ...##
###
On Miniaturized Problems in Parameterized Complexity Theory
[chapter]

2004
*
Lecture Notes in Computer Science
*

We introduce a general notion

doi:10.1007/978-3-540-28639-4_10
fatcat:6qiqkvwr3nar5brhxkhbneww34
*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. ...##
###
A Compendium of Parameterized Problems at Higher Levels of the Polynomial Hierarchy

2019
*
Algorithms
*

These

doi:10.3390/a12090188
fatcat:merbxfa4wjfbpcyes4lp6waf5i
*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. ...##
###
Counting Abelian Squares for a Problem in Quantum Computing
[article]

2022
*
arXiv
*
pre-print

Here I show how

arXiv:2208.02360v1
fatcat:bnpfsnyl25fjrghjlxijbi4b6y
*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 ...##
###
On the Complexity of Problems on Tree-structured Graphs
[article]

2022
*
arXiv
*
pre-print

In this paper, we introduce a new

arXiv:2206.11828v1
fatcat:rq2mmd5hgbeadiydafwomuyjuy
*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*. ...##
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Complexity of the Stable Invitations Problem

2017
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

In this work, we study

doi:10.1609/aaai.v31i1.10562
fatcat:dcxa26w2yfbohinetdvqiuoi6a
*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. ...##
###
Approximation of Natural W[P]-Complete Minimisation Problems Is Hard

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. ...

##
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Dynamic Parameterized Problems

2017
*
Algorithmica
*

In this work, we study

doi:10.1007/s00453-017-0349-6
fatcat:w42snepu6zc3helts3t4xyum6a
*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. ...##
###
Hardness Magnification for Natural Problems

2018
*
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
*

Our examples

doi:10.1109/focs.2018.00016
dblp:conf/focs/OliveiraS18
fatcat:4youvi7wjfbxzn32ttjuy4c6f4
*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. ...##
###
The Complexity of Tiling Problems
[article]

2019
*
arXiv
*
pre-print

We also pinpoint tiling

arXiv:1907.00102v2
fatcat:7rf6xiqc4zd6niwk55dlqjqri4
*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. ...
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