LIPIcs.APPROX-RANDOM.2014.381.pdf
- Filesize: 412 kB
- 11 pages
Document
Gap Amplification for Small-Set Expansion via Random Walks
Authors
-
Part of:
Volume:
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Randomization and Computation (RANDOM)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2014-09-04
File
Document Identifiers
Cite AsGet BibTex
Prasad Raghavendra and Tselil Schramm. Gap Amplification for Small-Set Expansion via Random Walks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 381-391, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.381
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.381
Abstract
In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness epsilon and soundness 1/2 is at least as difficult as Small-Set Expansion with completeness epsilon and soundness f(epsilon), for any function f(epsilon) which grows faster than (epsilon)^(1/2). We achieve this amplification via random walks--the output graph corresponds to taking random walks on the original graph. An interesting feature of our reduction is that unlike gap amplification via parallel repetition, the size of the instances (number of vertices) produced by the reduction remains the same.
Keywords
- Gap amplification
- Small-Set Expansion
- random walks
- graph products
- Unique Games
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads