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