# Expected Performance and Worst Case Scenario Analysis of the Divide-and-Conquer Method for the 0-1 Knapsack Problem

arXiv: https://arxiv.org/abs/2008.04124 · HTML: https://mlsanity.com/paper/2008.04124/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching](https://mlsanity.com/paper/2305.12352/) (2023)

## Abstract (arXiv)

In this paper we furnish quality certificates for the Divide-and-Conquer method solving the 0-1 Knapsack Problem: the worst case scenario and estimates for the expected performance. The probabilistic setting is given and the main random variables are defined for the analysis of the expected performance. The efficiency is rigorously approximated for one iteration of the method then, these values are used to derive analytic estimates for the performance of a general Divide-and-Conquer tree. All the theoretical results are verified with statistically suited numerical experiments for a wider illustration of the method.