**Going off-road: transversal complexity in road networks**.

D. Eppstein, M. T. Goodrich, and L. Trott.

arXiv:0909.2891.

Proc. 17th ACM SIGSPATIAL Int. Conf. Advances in Geographic Information Systems, Seattle, 2009, pp. 23–32.Shows both theoretically and experimentally that the number of times a random line crosses a road network is asymptotically upper bounded by the square root of the number of road segments.

**Extended dynamic subgraph statistics using**.*h*-index parameterized data structures

D. Eppstein, M. T. Goodrich, D. Strash, and L. Trott.

*Proc. 4th Int. Conf. on Combinatorial Optimization and Applications (COCOA 2010)*, Hawaii, 2010.

Springer,*Lecture Notes in Comp. Sci.*6508, 2010, pp. 128–141.

arXiv:1009.0783.

*Theor. Comput. Sci.*447: 44–52, 2012 (special issue for COCOA 2010).An earlier paper with Spiro at WADS 2009 provided dynamic graph algorithms for counting how many copies of each possible type of subgraph there are in a larger undirected graph, when the subgraphs have at most three vertices. This paper extends the method to directed graphs and to larger numbers of vertices per subgraph.

**Category-based routing in social networks: membership dimension and the small-world phenomenon**.

D. Eppstein, M. T. Goodrich, M. Löffler, D. Strash, and L. Trott.

*Workshop on Graph Algorithms and Applications*, Zürich, Switzerland, July 2011.

*International Conference on Computational Aspects of Social Networks (CASoN 2011)*, Salamanca, Spain, October 2011.

arXiv:1108.4675.

*Theor. Comput. Sci.*514: 96–104, 2013. (Special issue on Graph Algorithms and Applications: in Honor of Professor Giorgio Ausiello)

We investigate greedy routing schemes for social networks, in which participants know categorical information about some other participants and use it to guide message delivery by forwarding messages to neighbors that have more categories in common with the eventual destination. We define the membership dimension of such a scheme to be the maximum number of categories that any individual belongs to, a natural measure of the cognitive load of greedy routing on its participants. And we show that membership dimension is closely related to the small world phenomenon: a social network can be given a category system with polylogarithmic membership dimension that supports greedy routing if, and only if, the network has polylogarithmic diameter.

**Force-directed graph drawing using social gravity and scaling**.

M. J. Bannister, D. Eppstein, M. T. Goodrich, and L. Trott.

arXiv:1209.0748.

*20th Int. Symp. Graph Drawing*, Redmond, Washington, 2012.

Springer,*Lecture Notes in Comp. Sci.*7704, 2013, pp. 414–425.

We extend force-directed methods of graph drawing by adding a force that pulls vertices towards the center of the drawing, with a strength proportional to the centrality of the vertex. Gradually scaling up this force helps avoid the tangling that would otherwise result from its use.

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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