Probabilistic analysis of knapsack core algorithms

We study the average-case performance of algorithms for the binary knapsack problem. Our focus lies on the analysis of so-called core algorithms, the predominant algorithmic concept used in practice. These algorithms start with the computation of an optimal fractional solution that has only one fractional item and then they exchange items until an optimal integral solution is found. The idea is that in many cases the optimal integral solution should be close to the fractional one such that only a few items need to be exchanged. Despite the well known hardness of the knapsack problem on worst-case instances, practical studies show that knapsack core algorithms can solve large scale instances very efficiently. For example, they exhibit almost linear running time on purely random inputs. In this paper, we present the first theoretical result on the running time of core algorithms that comes close to the results observed in practical experiments. We prove an upper bound of O

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: René Beier, Berthold Vöcking
• Keywords: Algorithms, Core Algorithms, Knapsack Problem, Running Time, SODA 2004