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

We introduce a new method of constructing approximation algorithms for comb inatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a const ellation of vectors in the semidefinite program. When we apply this techniq ue 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 t hat it is NP-hard to approximate the problem within a constant ratio, indep endent of p. (C) 2001 Academic Press.