**Maintenance of a minimum spanning forest in a dynamic plane graph**.

D. Eppstein, G.F. Italiano, R. Tamassia, R.E. Tarjan, J. Westbrook, and M. Yung.

*1st ACM-SIAM Symp. Discrete Algorithms,*San Francisco, 1990, pp. 1–11.

*J. Algorithms*13 (1): 33–54, 1992 (special issue for 1st Symp. Discrete Algorithms).

Corrigendum,*J. Algorithms*15: 173, 1993.The complement of a minimum spanning tree is a maximum spanning tree in the dual graph. By applying this fact we can use a modified form of Sleator and Tarjan's dynamic tree data structure to update the MST in logarithmic time per update.

(BibTeX – Citations – CiteSeer – ACM DL)

**Privacy-preserving data-oblivious geometric algorithms for geographic data**.

D. Eppstein, M. T. Goodrich, and R. Tamassia.

*Proc. 18th ACM SIGSPATIAL Int. Conf. Advances in Geographic Information Systems (ACM GIS 2010)*, San Jose, California, pp. 13–22.

arXiv:1009.1904.An algorithm is data-oblivious if the memory access patterns it makes depend only on the input size and not on the actual input values; data-oblivious algorithms are an important building block of cryptographic protocols that allow algorithmic tasks to be solved by parties who each have some subset of the input data that they do not wish to reveal. We show how to solve several basic geometric problems data-obliviously, including construction of convex hulls, quadtrees, and well-separated pair decompositions, and computation of closest pairs and all nearest neighbors.

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

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