研究実績の概要 |
Our research achievements for this year are mainly focused on overcoming the difficulties foreseen at the start of this research in the computation of metrics of influence in information networks. Along with the theoretical foundations of this research, we are developing, as open-source softwares, the first libraries to solves practically those problems. Previously, two major problems were encountered that are common to all the network considered, one being the size of available data and the other the presence of cycles and strongly connected components in real life networks. Finally, the last problem to arise to practically compute those metrics in real life networks is the temporality of the transmission of knowledge.
We extended the notion of Stream Graphs ---that represents the temporality of networks using a combination of signal theory and graph theory--- to the notion of Stream Flow. With the goal to eventually apply it to our information networks, we proved classical flow notions in a stream graph context such as max-flow/min-cut duality, tractable algorithms for continuous signal functions.
With the aim to improve the computation of classical algorithm to explore graphs and search spaces, we work on general technique to reduce dimension (i.e. the number of variables and/or constraints) for general constraint optimisation problems (known as COP in the literature). Classical linear constraints are reduced accurately through the use of the Johnson-Lindenstrauss lemma (JLL). General constraints are reduced in a similar fashion after being formulated as a SAT problem.
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今後の研究の推進方策 |
Finalization and evaluation of afore-mentioned achievements, if not already available and publications of the associated library as open-source software: flow of knowledge on PDAG and general acyclic networks; general black-box algorithm for compressed data structure such as stacks, deques, lists and graphs; stream graph and flow algorithms (including visualisation tools).
Completion of the Network Interdiction framework for classical network flow using various optimization techniques adapted to small and large networks. Extension of this framework to the flow of knowledge in information networks with the aim of discover weak links and possible fake news, in particular in dynamic environment.
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