Paper Info
Title
Counting Complexity for Reasoning in Abstract Argumentation
Abstract
In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.
Year
Venue
Field
2018
national conference on artificial intelligence
Dynamic programming,Discrete mathematics,Argumentation framework,Parameterized complexity,Exponential function,Computer science,Argumentation theory,Artificial intelligence,Treewidth,Machine learning,Exponential time hypothesis,Bounded function
DocType
Volume
Citations 
Journal
abs/1811.11501
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Johannes Klaus Fichte1178.69
Markus Hecher21414.65
Arne Meier312619.00