STAR: Steiner-Tree Approximation in Relationship Graphs

Abstract

We would like to thank Gerard de Melo for the thorough proof reading of this report and his helpful comments.

Fast approximation of steiner trees in large graphs

“…Bidirectional search) expansion strategy starting from every input node of the query. While many effective heuristics on guiding and speeding up the Breadth-First Search in this setting have been proposed (BANKS [1], Bidirectional [7], STAR [9]), their performance is still poor on very large instances of graph data. Index only: Perform extensive indexing of the graph, and after that do not use the original graph at all.…”

“…Bidirectional [7] improves on this method by adding the forward-directed traversal, reducing the number of iterators, and prioritizing nodes with low degrees for expansion. STAR [9] follows the intuition of heuristic local search. Initially, a candidate tree is constructed by similar breadthfirst expansions.…”

“…For every BFS process we keep the set of frontier nodes, that is, the nodes that are currently at the maximum distance from the source node. The BFS instances are called in a round-robbin manner (lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], and the current process makes one step in the sketch (line 9). The currently visited node v may be connected in the original graph G with the nodes visited by other processes.…”

ISReal: An Open Platform for Semantic-Based 3D Simulations in the 3D Internet

“…First, its OMS has an open plug-in (API) architecture for using any RDF/S store and semantic reasoner as appropriate and is realized with the LarKC platform 10 . The OMS query decider routes semantic queries to OMS plug-ins available for the RDF triple stores SwiftOLIM (with RDF materialization of OWL2 under OWL-Horst semantics) and AllegroGraph, the semantic OWL-DL reasoner Pellet 11 with internal Jena RDF store, and the RDF relational reasoner STAR [14]. Second, semantic query answering and service handling by the GSE is upon request only, in particular, the GSE does not actively communicate semantic updates of the global ontology to other components; this avoids communication bottleneck and supports the paradigm of perception-based knowledge for BDI agents (cf.…”

“…For example, a relational object query like "How are scene objects doorAB, doorBC and roomC related ?" is processed by STAR by reduction to the corresponding NP-hard Steiner-Tree problem for the RDF graph of the materialized global ontology followed by the polynomial computation of an approximated solution in O(nlogn) in terms of minimal RDF object property-based path [14]. The pattern-based conversion of the result by our STAR-plugin of the OMS eventually yields a more human-readable answer (rather than just a list of RDF triples) like "doorAB leads to roomB from where doorBC leads to roomC."…”