Dynamic discretization discovery under hard node storage constraints

TL;DR

This paper improves dynamic discretization discovery (DDD) by establishing bounds on storage relaxation for discrete problems, enhancing its effectiveness in solving constrained universal packet routing problems.

Contribution

It shows that for discrete problems, weak relaxations are unnecessary, providing bounds on storage allowances and demonstrating improved DDD performance in packet routing.

Findings

Effective DDD application to universal packet routing with storage constraints

Bounded storage relaxations improve solution quality and computational efficiency

Demonstrated advantages over traditional integer programming methods

Abstract

The recently developed dynamic discretization discovery (DDD) is a powerful method that allows many time-dependent problems to become more tractable. While DDD has been applied to a variety of problems, one particular challenge has been to deal with storage constraints without leading to a weak relaxation in each iteration. Specifically, the current approach to deal with certain hard storage constraints in continuous settings is to remove a subset of the storage constraints completely in each iteration of DDD. In this work, we show that for discrete problems, such weak relaxations are not necessary. Specifically, we find bounds on the additional storage that must be permitted in each iteration. We demonstrate our techniques in the case of the classical universal packet routing problem in the presence of bounded node storage, which can currently only be solved via integer programming. We present computational results demonstrating the effectiveness of DDD when solving universal packet routing.