Complete Cyclic Subtask Graphs for Tool-Using LLM Agents: Flexibility, Cost, and Bottlenecks in Multi-Agent Workflows

Abstract: Long-horizon tool-using tasks sometimes benefit from revisiting earlier subtasks for recovery and exploration, but added multi-agent workflow flexibility can also introduce coordination overhead and substantial inference cost. We study complete cyclic subtask graphs, a deliberately maximally flexible multi-agent architecture in which executable subtask nodes are fully connected and a unified state-analysis-and-routing agent selects transitions using natural-language criteria. This makes unrestricted revisitation explicit and directly analyzable at the subtask level. We evaluate task-specific (Spec-Cyc) and benchmark-generic (Gen-Cyc) graphs on TextCraft, ALFWorld, and Finance-Agent, with ablations over planner/executor/router strength, tool exposure (generalist vs specialized), $n$-shot successful trajectory summaries, and fault-injected random subtask perturbations. The benchmarks expose three distinct regimes. ALFWorld highlights a setting where explicit revisitation supports recovery and exploration; TextCraft, a largely prerequisite-chain domain, often favors the efficiency of simpler forward execution; and Finance-Agent remains bottlenecked by retrieval, grounding, and evidence synthesis more than by workflow flexibility alone. Shared-win token comparisons further show that the added flexibility can be substantially more expensive than a single ReAct agent. Overall, we use complete cyclic subtask graphs as a maximally flexible experimental lens for measuring when multi-agent revisitation helps, when it mainly adds coordination cost, and when external task bottlenecks dominate.

• The paper shows that complete cyclic workflows improve recovery in partially observable ALFWorld, raising success to 58.2% with Spec-Cyc versus 33.8% for ReAct, but provide little benefit in retrieval- and dependency-limited tasks.
• The paper finds that flexibility carries a major inference cost, with cyclic methods using up to 3.9 times more tokens than ReAct on shared-win ALFWorld episodes and up to 383% more on some TextCraft settings.
• The paper demonstrates that router and executor capability, general-purpose tool access, and reusable Gen-Cyc graphs strongly influence robustness, while Finance-Agent remains bottlenecked by retrieval, grounding, and evidence synthesis.

Overview

This paper studies complete cyclic subtask graphs as a deliberately maximally flexible workflow representation for tool-using LLM agents. A task is decomposed into executable subtask nodes; the edge set is fully connected (including self-loops), and each edge carries a natural-language transition criterion evaluated by a unified analyzer-and-router agent against a rolling trajectory state. The authors' stated goal is not to claim that full connectivity is optimal, but to use it as an experimental lens for measuring when explicit revisitation buys genuine recovery, when it degenerates into thrashing, and when performance is dominated by bottlenecks external to the controller (2604.22820).

Two construction regimes are compared: Spec-Cyc, which generates a task-specific graph per instance, and Gen-Cyc, which generates one benchmark-generic graph reused across instances to test whether cyclic revisitation acts as a transferable control policy. Both are evaluated against ReAct and a forward-biased dependency DAG (DepDAG) on TextCraft (depths 2–4), ALFWorld, and Finance-Agent, with ablations over planner/executor/router model tiers, tool exposure (generalist vs. specialist executors), $n$-shot successful-trajectory summaries, and control-flow fault injection.

Architecture and formalization

The task graph is a labeled directed graph $G=(T,E,C)$ with $E = T \times T$, so every subtask can transition to every other. Execution alternates between executor segments and routing decisions: within segment $m$, executor $\alpha_{i_m}$ issues up to $C_l$ tool calls; at segment boundaries the router updates structured rolling memory and selects the next node by evaluating outgoing criteria. Termination occurs on environment success or exhaustion of a global tool-call budget $C_g$. Routing cost is bounded at $O(|T|)$ criterion evaluations per segment under either per-criterion or single-call implementations.

The authors center their controlled comparisons on gpt-4o-mini, deliberately choosing weaker-tier models so that recovery effects of orchestration remain observable rather than being masked by model capability near benchmark saturation. This is a defensible methodological choice, but it means headline numbers should not be read as state-of-the-art claims.

Three regimes across benchmarks

The head-to-head comparison without $n$-shot summaries separates cleanly by benchmark structure:

Benchmark	ReAct SR	DepDAG SR	Spec-Cyc SR	Gen-Cyc SR
TextCraft-2	94.3%	58.6%	85.2%	93.9%
TextCraft-3	82.5%	17.9%	50.4%	71.5%
TextCraft-4	45.5%	0.0%	15.2%	36.4%
ALFWorld	33.8%	52.2%	58.2%	56.7%
Finance-Agent	12.4%	9.5%	14.3%	15.2%

ALFWorld is the clearest case for cyclic control: both cyclic variants exceed ReAct substantially (58.2% vs. 33.8% for Spec-Cyc), consistent with partial observability making backtracking genuinely useful. Success-conditioned visitation analysis shows successful cyclic trajectories typically leverage revisitation for error correction rather than first-pass progress alone, and an environment-state exploration study on ALFWorld confirms higher unique-state coverage relative to ReAct.

TextCraft favors simpler forward execution. ReAct dominates at every depth, and the gap widens with horizon (94.3% vs. 85.2% at depth 2; 45.5% vs. 15.2% for Spec-Cyc at depth 4). Once the prerequisite chain is identified, extra routing flexibility becomes coordination overhead — consistent with prior findings that multi-agent coordination can underperform single agents on dependency-heavy sequential tasks.

Finance-Agent is bottlenecked elsewhere. All methods sit below ~15% success, indicating that open-world retrieval, grounding, and evidence synthesis dominate over control-flow flexibility; the modest cyclic gains are contrastive rather than substantive.

Cost of flexibility

A central contribution is the shared-win token accounting. On episodes won by both methods, cyclic workflows are frequently far more expensive than ReAct: on ALFWorld shared wins against gpt-4o-mini ReAct, Spec-Cyc costs roughly 3.9× more tokens (+289.6%); on TextCraft-3 shared wins, +125%; against the stronger gpt-5-mini ReAct tier, excesses reach +296% to +383% on TextCraft. The only exception is TextCraft-2 with Gen-Cyc, which is slightly cheaper than ReAct (−5%). The paper's framing is explicit: recovery from cyclic flexibility is purchased with materially greater inference expenditure, not obtained for free.

Role allocation, specialization, and robustness

With $n$-shot summaries, role-tier sweeps show orchestration quality materially shifts behavior from looping to recovery. Strikingly, Gen-Cyc with gpt-5-mini executors reaches 100% success on all three TextCraft depths (e.g., depth 4 at 100% ± 0% with STR 3.4, versus 48.5% for the all-gpt-4o-mini configuration), and reaches 91.5% on ALFWorld — demonstrating that router/executor strength, not graph expressivity alone, drives cyclic performance.

Tool restriction is consistently harmful: specialized executors sharply reduce SR/STR on both TextCraft and Finance-Agent, with the largest degradation under Spec-Cyc (e.g., TextCraft-4 Spec-Cyc specialists drop to 0% in the weakest configuration). Gen-Cyc is markedly more robust under tool restriction, remaining the preferred cyclic regime when tools are limited. Qualitative traces attribute this to specialists dead-ending on non-gatherable intermediates while generalists at least attempt prerequisite crafting.

Under fault injection (random redirection to a different subtask with 50% probability after individual tool calls), Gen-Cyc degrades gracefully (e.g., −3.7 pp on TextCraft-2 generalist) whereas Spec-Cyc collapses (−34.2 pp on TextCraft-2, −37.8 pp on TextCraft-3). Benchmark-generic graphs thus act as a regularizing bias: their simpler, reusable criteria are less entangled with instance-specific wording and less prone to brittle high-precision transitions where the router over-trusts subtask intent over observed state.

Limitations and open questions

The paper concedes several constraints directly. Complete connectivity is an experimental device, not a recommended deployment configuration; the token results make clear it is a high-flexibility, high-cost regime. Visitations are analyzed only on successful episodes, which mixes corrective revisits with wasteful detours — the authors note this conditioning cannot separate the two. Tool-exposure ablations exclude ALFWorld because its monolithic action interface makes any "tool" partition arbitrary, so specialization findings do not transfer there. Finance-Agent uses only 35 held-out cases, limiting statistical power for its small differences. TextCraft-4 has just 11 instances and no summary-construction split. The strongest configurations approach saturation, leaving open how flexibility effects manifest once raw model capability dominates. The proposed remedy — pruning never-won transitions, recurrent loops, and contradiction signals into a sparse learned adjacency — is motivated by the unique-transition analysis but not implemented here.

Conclusion

This work treats revisitation as a first-class, instrumentable property of agent workflows by making it structurally always available. Its empirical contribution is a characterization of three regimes: cyclic revisitation helps when recovery and exploration are central (ALFWorld), adds coordination tax in prerequisite-chain domains (TextCraft), and cannot overcome retrieval and grounding bottlenecks (Finance-Agent). Router quality emerges as critical, tool-restricted specialization amplifies coordination cost, and benchmark-generic graphs often regularize better than task-specific ones. The complete cyclic graph is best read as a maximally informative starting point from which sparser, cost-aware multi-agent workflows can be derived.