determining a difference between a sum of {HEAD ~ the prices} of the bid that lie on a search path connected to said subtree and the current price of {TAIL ~ the best allocation} 
determining a difference between a sum of { HEAD ~ the prices } of the bid that lie on a search path connected to said subtree and the current price of { TAIL ~ the best allocation }
OTH OTH OTH OTH OTH OTH OTH HEAD HEAD HEAD HEAD HEAD HEAD OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH TAIL TAIL TAIL TAIL TAIL TAIL TAIL