TY - GEN
T1 - Sparsest Cut on quotients of the hypercube
AU - Kolla, Alexandra
AU - Lee, James R.
PY - 2011
Y1 - 2011
N2 - We present a simple construction and analysis of an Ω(log logN) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier by Devanur, Khot, Saket, and Vishnoi [STOC 2006], following an integrality gap for non-uniform demands due to Khot and Vishnoi [FOCS 2005]. These previous constructions involve a complicated SDP solution and analysis, while our gap instance, vector solution, and analysis are somewhat simpler and more intuitive. Furthermore, our approach is rather general, and provides a variety of different gap examples derived from quotients of the hypercube. It also illustrates why the lower bound is stuck at Ω(log logN), and why new ideas are needed in order to derive stronger examples.
AB - We present a simple construction and analysis of an Ω(log logN) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier by Devanur, Khot, Saket, and Vishnoi [STOC 2006], following an integrality gap for non-uniform demands due to Khot and Vishnoi [FOCS 2005]. These previous constructions involve a complicated SDP solution and analysis, while our gap instance, vector solution, and analysis are somewhat simpler and more intuitive. Furthermore, our approach is rather general, and provides a variety of different gap examples derived from quotients of the hypercube. It also illustrates why the lower bound is stuck at Ω(log logN), and why new ideas are needed in order to derive stronger examples.
KW - Integrality gap
KW - Semidefinite programming
KW - Sparsest Cut
UR - https://www.scopus.com/pages/publications/84864582027
UR - https://www.scopus.com/pages/publications/84864582027#tab=citedBy
M3 - Conference contribution
AN - SCOPUS:84864582027
SN - 9781920682989
T3 - Conferences in Research and Practice in Information Technology Series
SP - 11
EP - 21
BT - Theory of Computing 2011 - Proceedings of the 17th Computing
T2 - Theory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011
Y2 - 17 January 2011 through 20 January 2011
ER -