TY - GEN

T1 - A quasi-polynomial time partition oracle for graphs with an excluded minor

AU - Levi, Reut

AU - Ron, Dana

PY - 2013

Y1 - 2013

N2 - Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient partition oracles. A partition oracle is a procedure that, given access to the incidence lists representation of a bounded-degree graph G = (V,E) and a parameter ε, when queried on a vertex v ∈ 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 ε|V|. In this work we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in 1/ε, thus improving on the result of Hassidim et al. (Proceedings of FOCS 2009) who gave a partition oracle with query complexity exponential in 1/ε. 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.

AB - Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient partition oracles. A partition oracle is a procedure that, given access to the incidence lists representation of a bounded-degree graph G = (V,E) and a parameter ε, when queried on a vertex v ∈ 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 ε|V|. In this work we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in 1/ε, thus improving on the result of Hassidim et al. (Proceedings of FOCS 2009) who gave a partition oracle with query complexity exponential in 1/ε. 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.

UR - http://www.scopus.com/inward/record.url?scp=84880271240&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-642-39206-1_60

DO - https://doi.org/10.1007/978-3-642-39206-1_60

M3 - منشور من مؤتمر

SN - 9783642392054

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 709

EP - 720

BT - Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings

T2 - 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013

Y2 - 8 July 2013 through 12 July 2013

ER -