FPT at Work: Using Fixed Parameter Tractability to Solve Larger Instances of Hard Problems

2006 ◽  
pp. 278-278
Author(s):  
Frank Dehne
Keyword(s):  
Fixed Parameter Tractability ◽  
Fixed Parameter ◽  
Hard Problems

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

2020 ◽  
Author(s):  
Robert Ganian ◽  
Tomáš Peitl ◽  
Friedrich Slivovsky ◽  
Stefan Szeider
Keyword(s):  
Structural Parameters ◽  
Knowledge Representation And Reasoning ◽  
Fixed Parameter Tractability ◽  
Complete Problem ◽  
Quantified Boolean Formulas ◽  
Fixed Parameter ◽  
Boolean Formulas ◽  
Hard Problems ◽  
Evaluation Problem ◽  
Primal Graph

We study dependency quantified Boolean formulas (DQBF), an extension of QBF in which dependencies of existential variables are listed explicitly rather than being implicit in the order of quantifiers. DQBF evaluation is a canonical NEXPTIME-complete problem, a complexity class containing many prominent problems that arise in Knowledge Representation and Reasoning. One approach for solving such hard problems is to identify and exploit structural properties captured by numerical parameters such that bounding these parameters gives rise to an efficient algorithm. This idea is captured by the notion of fixed-parameter tractability (FPT). We initiate the study of DQBF through the lens of fixed-parameter tractability and show that the evaluation problem becomes FPT under two natural parameterizations: the treewidth of the primal graph of the DQBF instance combined with a restriction on the interactions between the dependency sets, and also the treedepth of the primal graph augmented by edges representing dependency sets.

scholarly journals Fixed-parameter tractability and lower bounds for stabbing problems

2013 ◽  
Vol 46 (7) ◽  
pp. 839-860 ◽  
Author(s):  
Panos Giannopoulos ◽  
Christian Knauer ◽  
Günter Rote ◽  
Daniel Werner
Keyword(s):  
Lower Bounds ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

Fixed-parameter tractability for the tree assembly problem

2021 ◽  
Author(s):  
Feng Shi ◽  
Jie You ◽  
Zhen Zhang ◽  
Jingyi Liu ◽  
Jianxin Wang
Keyword(s):  
Fixed Parameter Tractability ◽  
Fixed Parameter ◽  
Assembly Problem

Fixed-parameter tractability and data reduction for multicut in trees

Networks ◽  
2005 ◽  
Vol 46 (3) ◽  
pp. 124-135 ◽  
Author(s):  
Jiong Guo ◽  
Rolf Niedermeier
Keyword(s):  
Data Reduction ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

scholarly journals Fixed-Parameter Tractability of Satisfying Beyond the Number of Variables

Algorithmica ◽  
2012 ◽  
Vol 68 (3) ◽  
pp. 739-757 ◽  
Author(s):  
Robert Crowston ◽  
Gregory Gutin ◽  
Mark Jones ◽  
Venkatesh Raman ◽  
Saket Saurabh ◽  
...  
Keyword(s):  
Fixed Parameter Tractability ◽  
Fixed Parameter

scholarly journals Finding Points in General Position

2017 ◽  
Vol 27 (04) ◽  
pp. 277-296 ◽  
Author(s):  
Vincent Froese ◽  
Iyad Kanj ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Lower Bound ◽  
General Position ◽  
Subset Selection ◽  
Selection Problem ◽  
Fixed Parameter Tractability ◽  
Maximum Cardinality ◽  
Exponential Time ◽  
Running Time ◽  
Fixed Parameter ◽  
Set Of Points

We study the General Position Subset Selection problem: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and present several fixed-parameter tractability results for the problem as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.

scholarly journals Adapting Stable Matchings to Evolving Preferences

2020 ◽  
Vol 34 (02) ◽  
pp. 1830-1837 ◽  
Author(s):  
Robert Bredereck ◽  
Jiehua Chen ◽  
Dušan Knop ◽  
Junjie Luo ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Computational Cost ◽  
Modern Society ◽  
Stable Matching ◽  
Stable Marriage ◽  
Fixed Parameter Tractability ◽  
Stable Matchings ◽  
Changing Environments ◽  
Fixed Parameter ◽  
Comprehensive Picture

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing “incrementalized versions” of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters “degree of change” both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter “distance between old and new stable matching”.

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