Fixed Parameter Tractability and Polynomial Time Results for the Synthesis of b-bounded Petri Nets

2019 ◽  
pp. 148-168 ◽  
Author(s):  
Ronny Tredup
Keyword(s):  
Petri Nets ◽  
Polynomial Time ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

Chapter 17. Fixed-Parameter Tractability

2021 ◽  
Author(s):  
Marko Samer ◽  
Stefan Szeider
Keyword(s):  
Polynomial Time ◽  
Parameterized Complexity ◽  
Complexity Analysis ◽  
Fixed Parameter Tractability ◽  
Graph Representations ◽  
Fine Grained ◽  
Input Size ◽  
Backdoor Sets ◽  
Fixed Parameter ◽  
Problem Instances

Parameterized complexity is a new theoretical framework that considers, in addition to the overall input size, the effects on computational complexity of a secondary measurement, the parameter. This two-dimensional viewpoint allows a fine-grained complexity analysis that takes structural properties of problem instances into account. The central notion is “fixed-parameter tractability” which refers to solvability in polynomial time for each fixed value of the parameter such that the order of the polynomial time bound is independent of the parameter. This chapter presents main concepts and recent results on the parameterized complexity of the satisfiability problem and it outlines fundamental algorithmic ideas that arise in this context. Among the parameters considered are the size of backdoor sets with respect to various tractable base classes and the treewidth of graph representations of satisfiability instances.

scholarly journals On the Computation of Fully Proportional Representation

2013 ◽  
Vol 47 ◽  
pp. 475-519 ◽  
Author(s):  
N. Betzler ◽  
A. Slinko ◽  
J. Uhlmann
Keyword(s):  
Polynomial Time ◽  
Parameterized Complexity ◽  
Proportional Representation ◽  
Fixed Parameter Tractability ◽  
Np Hard ◽  
Winner Determination ◽  
Negative Results ◽  
Polynomial Time Algorithms ◽  
Fixed Parameter

We investigate two systems of fully proportional representation suggested by Chamberlin Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

scholarly journals Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

2019 ◽  
Author(s):  
Yongjie Yang
Keyword(s):  
Polynomial Time ◽  
Control Problems ◽  
Fixed Parameter Tractability ◽  
Voting Rules ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Fixed Parameter ◽  
And Control ◽  
Manipulation And Control

We study the complexity of several manipulation and control problems for six prevalent approval based multiwinner voting rules. We show that these rules generally resist the proposed strategic types. In addition, we also give fixed-parameter tractability results for these problems with respect to several natural parameters and derive polynomial-time algorithms for certain special cases.

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.

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