Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 01, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Henning Thomas

Bounding Running Times via Forbidden 0-1 Matrices

In this talk I will introduce a technique from [1] that uses 0-1 matrices to bound the running time of algorithms. The picture of the technique is as follows: For an algorithm A and an instance I, a run of A on I is mapped to a 0-1 matrix M such that the number of 1's in M corresponds to the number of time steps required for this run. The idea then is to use the algorithm to derive structural properties of M, namely that it cannot contain certain (small) submatrices. With this we can bound the number of 1's in M, and thus also the running time of A.

I will illustrate the technique with the example of path compression in a union find data structure and state further results to demonstrate the strength of the technique.

[1] Pettie, Seth. Applications of Forbidden 0-1 Matrices to Search Tree and Path Compression-Based Data Structures. SODA 2010.

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