An Experimental Study of Random Knapsack Problems [chapter]

Rene Beier, Berthold Vöcking
2004 Lecture Notes in Computer Science  
The size of the Pareto curve for the bicriteria version of the knapsack problem is polynomial on average. This has been shown for various random input distributions. We experimentally investigate the number of Pareto optimal knapsack fillings. Our experiments suggests that the theoretically proven upper bound of O(n 3 ) for uniform instances and O(φµn 4 ) for general probability distributions is not tight. Instead we conjecture an upper bound of O(φµn 2 ) matching a lower bound for adversarial
more » ... eights. In the second part we study advanced algorithmic techniques for the knapsack problem. We combine several ideas that have been used in theoretical studies to bound the average-case complexity of the knapsack problem. The concepts used are simple and have been known since at least 20 years, but apparently have not been used together. The result is a very competitive code that outperforms the best known implementation Combo by orders of magnitude also for harder random knapsack instances.
doi:10.1007/978-3-540-30140-0_55 fatcat:ernwloz6qfebrcbvab2znou5hu