14,471 research outputs found
The Complexity of Finding Effectors
The NP-hard EFFECTORS problem on directed graphs is motivated by applications
in network mining, particularly concerning the analysis of probabilistic
information-propagation processes in social networks. In the corresponding
model the arcs carry probabilities and there is a probabilistic diffusion
process activating nodes by neighboring activated nodes with probabilities as
specified by the arcs. The point is to explain a given network activation state
as well as possible by using a minimum number of "effector nodes"; these are
selected before the activation process starts.
We correct, complement, and extend previous work from the data mining
community by a more thorough computational complexity analysis of EFFECTORS,
identifying both tractable and intractable cases. To this end, we also exploit
a parameterization measuring the "degree of randomness" (the number of "really"
probabilistic arcs) which might prove useful for analyzing other probabilistic
network diffusion problems as well.Comment: 28 page
Limits of Preprocessing
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a
complexity theoretic assumption, none of the considered problems can be reduced
by polynomial-time preprocessing to a problem kernel whose size is polynomial
in a structural problem parameter of the input, such as induced width or
backdoor size. Our results provide a firm theoretical boundary for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: This is a slightly longer version of a paper that appeared in the
proceedings of AAAI 201
Different Approaches to Proof Systems
The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper
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