 
Summary: On the Complexity of Testing Hypermetric, Negative Type,
kgonal and Gap Inequalities
David Avis
Computer Science, Mcgill University and GERAD
3480 University, Montreal, Quebec, Canada H3A 2A7
avis@cs.mcgill.ca
May 28, 2003
Abstract
Hypermetric inequalities have many applications, most recently in the approxi
mate solution of maxcut problems by linear and semidenite programming. How
ever, not much is known about the separation problem for these inequalities. Pre
viously Avis and Grishukhin showed that certain special cases of the separation
problem for hypermetric inequalities are NPhard, as evidence that the separation
problem is itself hard. In this paper we show that similar results hold for inequalities
of negative type, even though the separation problem for negative type inequalities
is well known to be solvable in polynomial time. We also show similar results hold
for the more general kgonal and gap inequalities.
1 Introduction
Let b = (b 1 ; :::; b n ) be an integer vector, let k =
P
