Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Friday, January 05, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Boris Aronov (Department of Computer and Information Science, Polytechnic Univ., Brooklyn NY)

Sparse geometric graphs with small dilation

Given a set S of N points in R^2, and an integer K such that 0<=K<N, we show that a geometric graph with vertex set S, at most N-1+K edges, and dilation O(N/(K+1)) can be computed in time O(N log N). We also construct N-point sets for which any geometric graph with N-1+K edges has dilation Omega(N/(K+1)); a slightly weaker statement holds if the points of S are required to be in convex position.

Higher dimensional analogues may also be discussed.

Here dilation of a straight-line Euclidean embedded graph is the maximum ratio between the graph distance (the Euclidean length of the shortest path) between a pair of its vertices to the Euclidean distance between them.

Joint work with Mark de Berg, Otfried Cheong, Joachim Gudmundsson, Herman Haverkort, Michiel Smid, and Antoine Vigneron.

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