Local graph partitions for approximation and testing
Author(s)Hassidim, Avinatan; Kelner, Jonathan Adam; Nguyen, Huy N.; Onak, Krzysztof
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We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class of bounded-degree graphs. These oracles utilize only local computation to consistently answer queries about a global partition that breaks the graph into small connected components by removing only a small fraction of the edges. We illustrate the power of this technique by using it to extend and simplify a number of previous approximation and testing results for sparse graphs, as well as to provide new results that were unachievable with existing techniques. For instance:1. We give constant-time approximation algorithms for the size of the minimum vertex cover, the minimum dominating set, and the maximum independent set for any class of graphs with an excluded minor.2. We show a simple proof that any minor-closed graph property is testable in constant time in the bounded degree model.3. We prove that it is possible to approximate the distance to almost any hereditary property in any bounded degree hereditary families of graphs. Hereditary properties of interest include bipartiteness, k-colorability, and perfectness.
DepartmentMassachusetts Institute of Technology. Department of Materials Science and Engineering
50th Annual IEEE Symposium on Foundations of Computer Science, 2009. FOCS '09
Institute of Electrical and Electronics Engineers
Hassidim, A. et al. “Local Graph Partitions for Approximation and Testing.” Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on. 2009. 22-31. ©2010 Institute of Electrical and Electronics Engineers.
Final published version
INSPEC Accession Number: 11207160
constant time algorithms, approximation algorithms, separator theorem