By David F. Gleich, Júlia Komjáthy, Nelly Litvak
This publication constitutes the complaints of the twelfth overseas Workshop on Algorithms and versions for the internet Graph, WAW 2015, held in Eindhoven, The Netherlands, in December 2015.
The 15 complete papers provided during this quantity have been conscientiously reviewed and chosen from 24 submissions. they're prepared in topical sections named: houses of enormous graph versions, dynamic techniques on huge graphs, and homes of PageRank on huge graphs.
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Additional info for Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings
It captures how “tree-like” a graph is in terms of its metric structure, and has received attention in the analysis of networks and informatics graphs. We refer the reader to [6,15,17,18], and references therein, for details on the motivating network applications. There are several ways of characterizing δ-hyperbolic metric spaces, all of which are equivalent up to constant factors [5,7,13]. Since graphs are naturally geodesic metric spaces when distance is deﬁned using shortest paths, we will use the deﬁnition based on δ-slim triangles (originally attributed to Rips [5,13]).
Algorithmically, this property is 1 Not related to the notion of expander graphs. F. Gleich et al. ): WAW 2015, LNCS 9479, pp. 29–41, 2015. 1007/978-3-319-26784-5 3 30 M. Farrell et al. extremely useful: every ﬁrst-order-deﬁnable problem is decidable in linear fpttime in these classes . For example, counting the number of appearances of a ﬁxed pattern graph as a subgraph can be computed in linear time [9,22]. We also consider δ-hyperbolicity, which restricts the structure of shortest-path distances in the graph to be tree-like.
Definition 4 (Bounded expansion). A graph class G has bounded expansion if there exists a function f such that for all r, we have ∇r (G) < f (r). Hyperbolicity, Degeneracy, and Expansion of Random Intersection Graphs 33 When introduced, bounded expansion was originally deﬁned using an equivalent characterization based on the notion of shallow minors (cf. ): H is a r-shallow minor of G if H can be obtained from G by contracting disjoint subgraphs of radius at most r. In the context of our paper, however, the topological shallow minor variant proves more useful, and we restrict our attention to this setting.