## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, January 26, 2006, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Thomas Bruderer

## Comparing Top k Lists

Motivated by several applications, we introduce various distance measures between "top k lists." Some of these distance measures are metrics, while others are not. For each of these latter distance measures: we show that it is "almost" a metric in the following two seemingly unrelated aspects: step (i) it satisfies a relaxed version of the polygonal (hence, triangle) inequality, and step (ii) there is a metric with positive constant multiples that bounds our measure above and below.This is not a coincidence---we show that these two notions of almost being a metric are the same. Based on the second notion, we define two distance measures to be equivalent if they are bounded above and below by constant multiples of each other. We thereby identify a large and robust equivalence class of distance measures. Besides the applications to the task of identifying good notions of (dis-)similarity between two top k lists, our results imply polynomial-time constant-factor approximation algorithms for the rank aggregation problem with respect to a large class of distance measures.

By Ronald Fagin, Ravi Kumar, D. Sivakumar (SODA 2003).

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