Classical and Quantum Distributed Algorithms for the Survivable Network Design Problem
CoRR(2024)
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.
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