**Models and algorithms for graph watermarking**.

D. Eppstein, M. T. Goodrich, J. Lam, N. Mamano, M. Mitzenmacher, and M. Torres.

arXiv:1605.09425.

*Proc. 19th Information Security Conference (ISC 2016)*, Honolulu, Hawaii.

Springer,*Lecture Notes in Comp. Sci.*9866 (2016), pp. 283–301.We show how to modify a small number of edges in a large social network in order to make the modified copy easy to identify, even if an adversary tries to hide the modification by permuting the vertices and flipping a much larger number of edges. The result depends on the random fluctuation of vertex degrees in such networks, and the ability to uniquely identify vertices by their adjacencies to a small number of high-degree landmark vertices. This paper won the best student paper award at ISC for its student co-authors Lam, Mamano, and Torres.

**Algorithms for stable matching and clustering in a grid**.

D. Eppstein, M. T. Goodrich, and N. Mamano.

arXiv:1704.02303

*Proc. 18th International Workshop on Combinatorial Image Analysis (IWCIA 2017)*, Plovdiv, Bulgaria, 2017.

Springer,*Lecture Notes in Comp. Sci.*10256 (2017), pp. 117–131.Motivated by redistricting, we consider geometric variants of the stable matching problem in which points (such as the pixels of a discretization of the unit square) are to be matched to a smaller number of centers such that each center has the same number of matches and no match is unstable with respect to Euclidean distances. We show how to solve such problems in polylogarithmic time per matched point, experiment with practical heuristics for solving these problems, and test methods for moving the centers to improve the shape of the matched regions.

**Defining equitable geographic districts in road networks via stable matching**.

D. Eppstein, M. T. Goodrich, D. Korkmaz, and N. Mamano.

arXiv:1706.09593

*Proc. 25th ACM SIGSPATIAL Int. Conf. Advances in Geographic Information Systems (ACM SIGSPATIAL 2017)*, Redondo Beach, California, to appear.

We cluster road networks (modeled as planar graphs, or more generally as graphs obeying a separator theorem) with a given set of cluster centers, by matching graph vertices to centers stably according to distance: no unmatched vertex and center should have smaller distances than the matched pairs for the same points. We provide a separator-based data structure for dynamic nearest neighbor queries in planar or separated graphs, which allows the optimal stable clustering to be constructed in time

*O*(*n*^{3/2}log*n*). We also experiment with heuristics for fast practical construction of this clustering.

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

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