The best-fitheuristicfortherectangularstrippackingproblem:Anefficient implementation andtheworst-caseapproximationratio

We investigatethebest-fitheuristicalgorithmbyBurkeetal.[2004.Anewplacementheuristicforthe orthogonal stock-cuttingproblem.OperationsResearch52,655–671]fortherectangularstrippacking problem. Foritssimplicityandgoodperformance,thebest-fitheuristichasbecomeoneofthemost significant algorithmsfortherectangularstrippacking.Inthispaper,weproposeanefficientimple- mentation ofthebest-fitheuristicthatrequiresO(n) spaceandO(n log n) time,where n is thenumber of rectangles.Weprovethatthiscomplexityisoptimal,andwealsoshowthepracticalusefulnessof our implementationviacomputationalexperiments.Furthermore,wegivetheworst-caseapproximation ratio ofthebest-fitheuristic.