Designing Capacitated Subnetworks for Shortest Path Routing

TL;DR

This paper introduces an exact algorithm for designing capacitated subnetworks that optimize shortest path routing for energy-efficient network operation, providing the first comprehensive evaluation of solution quality.

Contribution

It develops a novel integer linear programming approach with column generation to solve the combined network design and routing problem exactly.

Findings

The proposed method yields true optimal solutions for small instances.

A simple routing fix-and-deactivate approach performs close to optimal in practice.

TOCA, a traffic-oblivious method, performs best among tested heuristics.

Abstract

In pursuit of higher energy efficiency in computer networks, one subfield of green traffic engineering aims at reducing the size of a network during times of low traffic, while still guaranteeing the ability to route all occurring demands. In this setting, we have to simultaneously solve a network design problem (choosing connections to deactivate) and a routing problem (routing paths in the active subnetwork, adhering to some routing protocol). Interestingly, there seems to be no available method to tackle the problem as a whole for the simplest (and still most commonly used) routing paradigm: shortest path routing. State-of-the-art methods either do not consider capacities, or assume that the routing paths should not change when deactivating network connections, or separate the problem into its two constituents, first solving the network design problem (using some estimators in lieu of the precise routing protocol) and only then the actual routing problem. In this paper, we present an algorithm to tackle the full combined problem exactly via a novel integer linear program, modeling dynamically changing shortest paths. To solve it, we need to devise a special-purpose column generation method. To speed up the solution process, we further propose additional provably strengthening constraints. Now having the means to yield true optimal solutions for (small) practical instances, we can for the first time give an in-depth experimental evaluation that includes the absolute quality intrinsic to the above simplifying algorithms. It turns out that the arguably simplest method--first computing a routing, fixing it, and turning off all superfluous connections--yields solutions surprisingly close to the true optimum in practice. When considering multiple different traffic demands, a recent traffic-oblivious approach (TOCA) performs best, while being comparatively straightforward to implement.