On the Power of Lasserre SDP Hierarchy

A New Hierarchy of Sdp-relaxations for Polynomial Programming

Lasserre Lower Bounds and Definability of Semidefinite Programming

For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs (SDPs) that are required to solve the problem exactly. In particular, we show that if a finite-valued constraint problem is not solved exactly by its basic li...

The Lasserre hierarchy in Approximation algorithms

The Lasserre hierarchy is a systematic procedure to strengthen a relaxation for an optimization problem by adding additional variables and SDP constraints. In the last years this hierarchy moved into the focus of researchers in approximation algorithms as the obtain relaxations have provably nice properties. In particular on the t-th level, the relaxation can be solved in time n ) and every con...

Hierarchy Lower Bounds for Decoding Random LDPC Codes

Random (dr, d,)-regular LDPC codes (where each variable is involved in d, parity checks and each parity check involves d, variables) are well-known to achieve the Shannon capacity of the binary symmetric channel (for sufficiently large d, and d,) under exponential time decoding. However, polynomial time algorithms are only known to correct a much smaller fraction of errors. One of the most powe...

LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes

Random (dv, dc)-regular LDPC codes (where each variable is involved in dv parity checks and each parity check involves dc variables) are well-known to achieve the Shannon capacity of the binary symmetric channel (for sufficiently large dv and dc) under exponential time decoding. However, polynomial time algorithms are only known to correct a much smaller fraction of errors. One of the most powe...