ATRO: Alternating Topology & Routing Optimization

• ATRO is a framework that alternates between topology and routing optimization to minimize maximum link utilization in datacenter networks.
• The system leverages the ABSM for exact one-hop topology design and traffic-engineering accelerators for efficient multi-hop routing.
• Empirical results demonstrate ATRO’s rapid convergence, scalability, and near-optimal performance compared to MILP and COUDER baselines.

Alternating Topology and Routing Optimization (ATRO) is a solver-free framework for computing logical topologies and routing in reconfigurable datacenter networks (DCNs). It is designed for two regimes: one-hop configurations, in which traffic is sent directly and the problem is purely topology optimization (TO), and multi-hop configurations, in which traffic may be split and routed through intermediate Pods (PoDs), requiring joint topology and routing optimization (TRO). Rather than solving the full mixed discrete–continuous problem monolithically, ATRO alternates between TO and routing optimization (RO), with the common objective of minimizing maximum link utilization (MLU), denoted by $u$ and also called nominal maximum link utilization (NMLU) (Mao et al., 18 Jul 2025).

1. Problem setting and formal objective

ATRO considers a datacenter network with $N$ PoDs, modeled as a directed graph $G=(V,E)$, where each ordered pair $(i,j)$ can potentially have logical links between PoDs $i$ and $j$. Each PoD $i$ has a port budget $R_i$ and a per-port link capacity $S_i$, giving pairwise link capacity

$S_{i,j}=\min(S_i,S_j).$

Traffic demand from PoD $N$0 to PoD $N$1 is denoted $N$2 (Mao et al., 18 Jul 2025).

The one-hop case fixes routing to direct paths and optimizes only the logical link multiplicities $N$3. The multi-hop case jointly optimizes $N$4 and routing fractions $N$5, where $N$6 is the fraction of traffic from $N$7 to $N$8 routed via PoD $N$9. The joint TRO formulation minimizes $G=(V,E)$0 subject to port-budget constraints, symmetry and integrality of the topology variables, nonnegativity and normalization of the routing fractions, and per-link utilization constraints. The induced load on link $G=(V,E)$1 is

$G=(V,E)$2

and the capacity condition is

$G=(V,E)$3

The topology variables remain combinatorial even in the one-hop case, while the multi-hop problem introduces nonlinear coupling between topology and traffic load through the utilization constraint, making the full problem a Mixed Integer Nonlinear Program (Mao et al., 18 Jul 2025).

This formulation places ATRO in the class of joint logical-topology and traffic-engineering methods. In the datacenter setting, the topology is logical rather than physical: the algorithm computes which logical links should be instantiated under per-PoD port constraints, then routes demand over that instantiated graph.

2. Alternating decomposition into topology and routing subproblems

ATRO decomposes TRO into two subproblems coupled through the current per-link traffic load $G=(V,E)$4. The TO subproblem solves for $G=(V,E)$5 and $G=(V,E)$6 given current traffic loads, while the RO subproblem solves for $G=(V,E)$7 and $G=(V,E)$8 given the current topology. The TO subproblem is exactly the one-hop optimization problem with fixed loads, and the RO subproblem is a linear-program-like traffic-engineering problem over a fixed logical topology (Mao et al., 18 Jul 2025).

Two structural observations motivate this decomposition. First, each alternating update step monotonically reduces MLU. When RO is solved with topology fixed, it minimizes $G=(V,E)$9 over all valid routings for that topology; when TO is solved with routing fixed, it minimizes $(i,j)$0 over all valid topologies for that load pattern. The resulting sequence of MLU values is therefore monotonic non-increasing. The paper explicitly characterizes this as block coordinate descent logic (Mao et al., 18 Jul 2025).

Second, the TO subproblem has a monotonic feasibility structure. If a utilization target $(i,j)$1 is feasible, then any larger $(i,j)$2 is also feasible, because increasing $(i,j)$3 relaxes the constraints

$(i,j)$4

This monotonicity is the basis for ATRO’s exact one-hop solver and is central to its solver-free design (Mao et al., 18 Jul 2025).

A practical consequence of the decomposition is that ATRO preserves feasibility throughout. It never relies on fractional topology solutions that must later be rounded, a difficulty explicitly associated with relaxation-based baselines such as COUDER. This suggests that the alternating structure is not merely a heuristic partition of the search space, but a way of isolating the discrete and continuous sources of hardness while retaining valid intermediate configurations.

3. Exact topology optimization via the Accelerated Binary Search Method

The TO module is solved by the Accelerated Binary Search Method (ABSM), a solver-free algorithm exploiting the monotonic feasibility structure of one-hop optimization. For a candidate utilization $(i,j)$5, the required number of logical links between each PoD pair is defined as

$(i,j)$6

The feasibility theorem states that $(i,j)$7 is feasible for TO if and only if

$(i,j)$8

This gives a closed-form feasibility oracle: compute the minimal required integer link multiplicities and check whether they fit within each PoD’s port budget (Mao et al., 18 Jul 2025).

ABSM then performs binary search on $(i,j)$9. The acceleration step is obtained by observing that if a midpoint $i$0 is feasible, the implied topology yields a tighter feasible utilization

$i$1

Instead of updating the upper bound to the midpoint itself, ABSM tightens it to $i$2, which the paper states is also feasible. The resulting iteration complexity is

$i$3

where $i$4 is an initial upper bound and $i$5 is the stopping threshold. Each iteration uses simple vectorized arithmetic over $i$6 matrices (Mao et al., 18 Jul 2025).

Because one-hop optimization reduces exactly to the TO subproblem, ABSM gives ATRO its strongest guarantee: global optimality in one-hop scenarios. This distinguishes ATRO from heuristic or rounding-based topology methods that trade exactness for speed even in the direct-routing regime.

4. Routing optimization, refinement, and solver-free design

The RO module is solved without commercial optimization solvers. ATRO uses existing traffic-engineering accelerators, specifically ASDO, and mentions HARP and other TE accelerators as alternatives. ASDO is highlighted as the default choice because it is an efficient, sequential traffic-engineering algorithm that can be hot-started from previous solutions, which is especially useful because RO is solved repeatedly as the topology changes (Mao et al., 18 Jul 2025).

ATRO also includes a refinement step after TO. This step adds unused ports to high-utilization links without violating constraints. The refinement does not increase MLU and can expand the future routing feasible space. In the multi-hop setting, this is important because TO may have multiple optimal logical topologies for the current load pattern, but some of those topologies are more restrictive than others for subsequent routing adaptation. The paper’s 3-PoD example is used to show that adding links through an intermediate PoD can unlock better multi-hop routing and reduce MLU (Mao et al., 18 Jul 2025).

The solver-free characterization of ATRO is therefore two-sided. TO is solved by ABSM rather than MILP or MINLP solvers; RO is delegated to TE accelerators rather than LP/MILP back ends. This decomposition directly addresses the paper’s claim that commercial solvers are too slow for real-time reconfiguration, while still preserving monotonic improvement in MLU and feasibility at every stage (Mao et al., 18 Jul 2025).

A common misconception is that ATRO implies a universal optimality guarantee for joint topology–routing problems. The datacenter formulation supports a stronger claim only in one-hop scenarios. In multi-hop scenarios, the method alternates between TO and RO, preserves monotonic improvement, and is evaluated empirically against exact and relaxation-based baselines rather than presented as a globally optimal MINLP solver (Mao et al., 18 Jul 2025).

5. Empirical behavior, scalability, and operating regimes

ATRO is evaluated on Meta production DCN topologies and synthetic full-mesh topologies, in both one-hop and multi-hop scenarios, using real traces and synthetic AI/background traffic. In multi-hop experiments, the baselines are MILP and COUDER. MILP is reported as optimal on small and medium networks but extremely slow or infeasible at larger scales, while COUDER is faster but less accurate and less stable. ATRO is reported to achieve near-optimal MLU and to be much faster and more stable (Mao et al., 18 Jul 2025).

Setting	Baselines	Reported outcome
Multi-hop	MILP, COUDER	On Topo 128, finished all runs within about 100 seconds and outperformed COUDER in both MLU and variance
Multi-hop	COUDER	On Meta ToR, achieved comparable MLU but ran about $i$7 faster
One-hop	MILP-TO, MCF, BvN	Matched the optimal MLU of MILP-TO on all tested topologies
One-hop	MILP-TO	Completed in under 10 ms even on large instances
Scalability	MILP-TO	On Topo 256 and Topo 512, still matched MILP-TO’s optimum while MILP-TO became impractical
Convergence	—	MLU decreases monotonically; most cases converge in 1–3 iterations; over 95% of samples converge within two or three rounds

The one-hop experiments also report that ATRO produces the sparsest topologies, avoiding redundant logical links. In addition, hot-start experiments show that ATRO can improve existing solutions such as COUDER’s outputs, and the refinement module improves robustness with little overhead (Mao et al., 18 Jul 2025).

These results delimit ATRO’s strongest operating regime. In one-hop settings it is an exact fast optimizer; in multi-hop settings it is a scalable alternating framework that empirically approaches optimal or strong baseline performance while retaining stable runtime behavior. This suggests that the main contribution is not a single new routing primitive, but a structural reformulation of reconfigurable DCN control that separates exact logical-link sizing from accelerated traffic engineering.

6. Broader literature and conceptual boundaries

The broader literature contains several ATRO-like decompositions, but they differ in what counts as “topology” and in whether the alternation is formal, heuristic, or only conceptual. In integrated access and backhaul (IAB) networks, a genetic-algorithm planner optimizes SBS placement and non-IAB backhaul distribution offline, while routing is treated separately as an online mechanism for bypassing temporal blockages; the central message is that well-planned topology dominates performance gains, with routing acting as a lightweight corrective layer (Madapatha et al., 2021). In wireless sensor networks, ERTO jointly optimizes transmission power and relay node degree through multi-objective Pareto analysis, then performs opportunistic routing on the resulting local topology (Li et al., 2017). In next-hop robustness, the tree-augmentation formulation orients additional edges so as to maximize the number of nodes with outdegree two or more while preserving acyclicity, thereby proactively installing alternate next hops (Borradaile et al., 2014). In routing-driven topology recovery, continuous Dynamic Monge–Kantorovich dynamics are followed by pre-extraction and redundancy filtering, so routing is optimized first and topology is then inferred and pruned (Baptista et al., 2020).

More recent work broadens the pattern further. Virtual Multi-Topology Routing derives silent virtual topologies from a limited set of real topologies via multipliers and then routes QoS-constrained demands over those virtual planes, reducing control-plane overhead and improving robustness to QoS changes (Huin et al., 2024). Pipe routing for UAV networks couples route selection inside a local “pipe” with topology control that manipulates mobility around that route region to prevent pipe thinning (Devaraju et al., 2024). In multi-hop edge inference, an alternating framework updates partition placement and congestion-aware forwarding because communication and computation delays are jointly load-dependent (Zhang et al., 28 Apr 2026). In dynamic cloud networks, a topology-aware graph reinforcement learning system combines Structure-Aware State Encoding (SASE) with a Policy-Adaptive Graph Update (PAGU) mechanism; it is described as ATRO-like in spirit, but not as a formally separated alternating optimization algorithm (Wang et al., 5 Sep 2025).

This literature indicates that ATRO is both a specific datacenter algorithm and a broader decomposition motif. In the specific 2025 DCN sense, it denotes a solver-free alternation between exact topology sizing and accelerated routing optimization (Mao et al., 18 Jul 2025). In the wider literature, the same conceptual pattern appears whenever routing decisions and structural decisions are strongly interdependent, but the structural variable may be logical-link multiplicity, node placement, power-controlled neighborhood formation, virtual topology synthesis, graph extraction, or execution-site placement.