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