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What and Who

A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor

Reut Levi
Université Paris Diderot - Paris 7 and École Normale Supérieure, France.
AG1 Mittagsseminar (own work)
AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI  
AG Audience
English

Date, Time and Location

Monday, 9 March 2015
11:00
30 Minutes
E1 4
024
Saarbrücken

Abstract

Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles\/}.

A {\em partition oracle\/} is a procedure that, given access to the incidence lists representation of a bounded-degree graph $G= (V,E)$ and a parameter $\eps$, when queried on a vertex $v\in V$, returns the part (subset of vertices) which $v$ belongs to in a partition of all graph vertices. The partition should be such that all parts are small, each part is connected, and if the graph has certain properties, the total number of edges between parts is at most $\eps |V|$.
In this work we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in $1/\eps$, thus improving on the result of Hassidim et al. ({\em Proceedings of FOCS 2009}) who gave a partition oracle with query complexity exponential in $1/\eps$. This improvement implies corresponding improvements in the complexity of testing planarity and other properties that are characterized by excluded minors as well as sublinear-time approximation algorithms that work under the promise that the graph has an excluded minor.

Contact

Christina Fries
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Christina Fries, 02/26/2015 13:56
Christina Fries, 02/23/2015 12:08 -- Created document.