Solving Billion-Scale Knapsack Problems

TL;DR

This paper introduces a distributed algorithmic approach to solve billion-scale knapsack problems efficiently, enabling near-optimal solutions at unprecedented scale using standard distributed computing frameworks.

Contribution

It presents a novel distributed method for solving large-scale knapsack problems, achieving near-optimal solutions at a billion-scale with practical implementation.

Findings

Able to solve KPs with 1 billion variables and constraints within 1 hour

Implemented using off-the-shelf distributed frameworks like MPI, Hadoop, Spark

Deployed in production at Ant Financial with significant business impact

Abstract

Knapsack problems (KPs) are common in industry, but solving KPs is known to be NP-hard and has been tractable only at a relatively small scale. This paper examines KPs in a slightly generalized form and shows that they can be solved nearly optimally at scale via distributed algorithms. The proposed approach can be implemented fairly easily with off-the-shelf distributed computing frameworks (e.g. MPI, Hadoop, Spark). As an example, our implementation leads to one of the most efficient KP solvers known to date -- capable to solve KPs at an unprecedented scale (e.g., KPs with 1 billion decision variables and 1 billion constraints can be solved within 1 hour). The system has been deployed to production and called on a daily basis, yielding significant business impacts at Ant Financial.