▁K ▁such ▁that , ▁for ▁any ▁pair ▁of ▁intervals , ▁the ▁difference ▁of ▁values ▁between ▁them ▁is ▁at ▁most ▁K ▁times ▁the ▁length ▁of ▁their ▁symmetric ▁difference ▁. ▁ ▁If ▁all ▁value ▁measures ▁are ▁Li ps ch itz - continu ous , ▁then ▁the ▁two ▁approximation ▁definitions ▁are ▁related . ▁Let ▁. ▁Then , ▁every ▁partition ▁in ▁an ▁env y - free ▁ δ - multi - partition ▁is ▁ ε - env y - free . ▁Hence , ▁D eng ▁et ▁al .' s ▁results ▁prove ▁that , ▁if ▁all ▁partners ▁have ▁Li ps ch itz - continu ous ▁valu ations , ▁an ▁ ε - env y - free ▁partition ▁can ▁be ▁found ▁with ▁ ▁queries . ▁ ▁Off line ▁calculation ▁is ▁a ▁second ▁work - around ▁that ▁finds ▁a ▁totally - env y - free ▁division ▁but ▁only ▁for ▁a ▁restricted ▁class ▁of ▁valu ations . ▁If ▁all ▁value ▁measures ▁are ▁polynomials ▁of ▁degree ▁at ▁most ▁d , ▁there ▁is ▁an ▁algorithm ▁which ▁is ▁polynomial ▁in ▁n ▁and ▁d . ▁Given ▁d , ▁the ▁algorithm ▁asks ▁the ▁agents ▁ ▁d + 1 ▁evaluation ▁queries , ▁which ▁give ▁d + 1 ▁points ▁in ▁the ▁graph ▁of ▁the ▁value ▁measure . ▁It ▁is ▁known ▁that ▁d + 1 ▁points ▁are ▁sufficient ▁to ▁interpol ate ▁a ▁polynomial ▁of ▁degree ▁d . ▁Hence , ▁the ▁algorithm ▁can ▁interpol ate ▁the ▁entire ▁value ▁measures ▁of ▁all ▁agents , ▁and ▁find ▁an ▁env y - free ▁division ▁off line . ▁The ▁number ▁of ▁required ▁queries ▁is