determining a lower bound price of a group of {HEAD ~ bids} of {TAIL ~ a subtree} of the search tree 
of
determining a lower bound price of a group of { HEAD ~ bids } of { TAIL ~ a subtree } of the search tree
OTH OTH OTH OTH OTH OTH OTH OTH OTH HEAD HEAD HEAD HEAD HEAD REL TAIL TAIL TAIL TAIL TAIL TAIL OTH OTH OTH OTH