In the Search of Optimal Tree Networks: Hardness and Heuristics

TL;DR

The paper addresses designing demand-aware networks with binary-tree topologies under a traffic demand model, proving the problem is NP-hard. It introduces an optimization framework based on a (1+1) evolutionary algorithm with diverse initializers (optimal binary search trees and maximum spanning trees) and mutation operators (edge switch, edge replacement, subtree swap), coupled with efficient cost calculations. Empirical results on synthetic and real workloads show an average improvement of about $10\%$ over baseline initializations, with larger gains on smaller to mid-sized networks; random mixes of mutations often perform best. The work provides a practical approach to obtaining high-quality demand-aware trees and points to future extensions to $k$-ary trees and more sophisticated crossovers.

Abstract

Demand-aware communication networks are networks whose topology is optimized toward the traffic they need to serve. These networks have recently been enabled by novel optical communication technologies and are investigated intensively in the context of datacenters. In this work, we consider networks with one of the most common topologies~ -- a binary tree. We show that finding an optimal demand-aware binary tree network is NP-hard. Then, we propose optimization algorithms that generate efficient binary tree networks on real-life and synthetic workloads.

Figures (5)

• Figure 1: The example of OLA instance and an OBT instance reduced from OLA.
• Figure 2: The edge switch operator
• Figure 3: The random edge replacement operator
• Figure 4: Optimal edge replacement: the main principle
• Figure 5: The subtree swap operator

Theorems & Definitions (2)

• Theorem 1
• proof