Classical and Quantum Distributed Algorithms for the Survivable Network Design Problem

TL;DR

This paper explores classical and quantum distributed algorithms for the survivable network design problem, providing heuristics with approximation bounds and demonstrating quantum speedups in certain computations.

Contribution

It introduces the first distributed classical and quantum algorithms for SNDP, extending classical frameworks and leveraging quantum speedups for shortest path computations.

Findings

Distributed algorithms with approximation bounds for SNDP

Quantum algorithms achieve asymptotic speedups in shortest path computations

Raises questions about classical vs. quantum model separations for large instances

Abstract

We investigate distributed classical and quantum approaches for the survivable network design problem (SNDP), sometimes called the generalized Steiner problem. These problems generalize many complex graph problems of interest, such as the traveling salesperson problem, the Steiner tree problem, and the k-connected network problem. To our knowledge, no classical or quantum algorithms for the SNDP have been formulated in the distributed settings we consider. We describe algorithms that are heuristics for the general problem but give concrete approximation bounds under specific parameterizations of the SNDP, which in particular hold for the three aforementioned problems that SNDP generalizes. We use a classical, centralized algorithmic framework first studied in (Goemans & Bertsimas 1993) and provide a distributed implementation thereof. Notably, we obtain asymptotic quantum speedups by leveraging quantum shortest path computations in this framework, generalizing recent work of (Kerger et al. 2023). These results raise the question of whether there is a separation between the classical and quantum models for application-scale instances of the problems considered.