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