Uncertain Graphs [DRAFT]
Propabilistic graphs may be:
where each edge is augmented with a probability value, which indicates the chance that the edge exists.
where each edge is associated with a probability distribution of weight values.
Evaluation of ST-queries is hard (#P-hard). You have to create all possible (non-probabilistic) words that correspond to the probabilistic graph and evaluate the query in each one.
To improve the efficiency sampling is employed, where possible worlds with high existential probabilities are extracted.
Can we take advantage of Ehab’s work to compute the samples?
Downloaded from: http://www.cs.hku.hk/research/techreps/document/TR-2014-09.pdf
ST-queries include reachability queries (RQ) and shortest distance queries (SDQ). These queries provide answers with probabilistic guarantees. For example, the answer of an RQ tells us the chance that \(s\) can reach \(t\); the SDQ returns the probability distribution of the distance between \(s\) and \(t\).
The main idea is to evaluate the query on \(G(q)\), a weight-distribution probabilistic graph derived from \(G\). Given a probabilistic graph \(G\) and a ST-query \(q\), PTree can generate a probabilistic graph \(G(q)\), which is typically smaller than \(G\) and has fewer possible worlds. Hence, the approach can be considered in some sense as a graph compression algorithm –- but compression of the possible worlds.
In this paper, the authors introduce PTree, a formal indexing framework for probabilistic graphs, and they further present the detailed theoretical and experimental results for three instantiations of PTree (i.e., SPQR tree, FWD, and LIN).
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