A new way of using semidefinite programming with applications to linear equations mod p

• We introduce a new method of constructing approximation algorithms for combinatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a constellation of vectors in the semidefinite program. When we apply this technique to systems of linear equations mod p with at most two variables in each equation, we can show that the problem is approximable within (1 - kappa (p))p, where kappa (p)> 0 for all p. Using standard techniques we also show that it is NP-hard to approximate the problem within a constant ratio, independent of p.

Nyckelord

approximation algorithms

linear equations

lower bounds

NP-hard optimization problems

semidefinite programming

improved approximation algorithms

cut

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)