Two things you can do with linear program
Use it to get upper bounds on solution:
- Example: at a node in tree with corresponds to including v,w in clique but excluding x, y.
- If at that point solution of LP gives bound < size of already known clique, can backtrack.
Can use it to help choose good traversal order => good solutions found fast => can backtrack earlier.
- Example: if xi=1 in linear program, might guess that vi is in integer solution as well.