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arxiv: 2605.27652 · v1 · pith:4YN56OVJnew · submitted 2026-05-26 · 💻 cs.DC

Carbon-Aware Mapping and Scheduling for Deadline-Constrained Workflows

Dominik Schweisgut , Anne Benoit , Yves Robert , Henning Meyerhenke This is my paper

Pith reviewed 2026-06-29 15:18 UTC · model grok-4.3

classification 💻 cs.DC
keywords carbon-aware schedulingworkflow schedulingdeadline constraintsdatacenter energy optimizationrenewable energy integrationNP-hard schedulingheterogeneous computing
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The pith

The carbon-aware workflow scheduling problem is NP-hard with no constant-factor approximation even on one processor, and the CWM algorithm reduces median carbon cost by 42% over the prior best method when the deadline is twice a carbon-agno

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that mapping and scheduling interdependent workflow tasks onto heterogeneous machines to minimize carbon emissions while respecting deadlines is computationally hard. It proves the problem admits no constant-factor approximation algorithm even when restricted to a single processor. To produce feasible low-carbon schedules anyway, the authors introduce the CWM algorithm that interleaves dynamic programming for task ordering with heuristics that exploit periods of high renewable-energy availability and differences in machine power draw. Experiments on synthetic workflows and real energy traces show that CWM cuts carbon cost by a median of 42% compared with the strongest version of the previous CaWoSched approach under the stated deadline setting, while CaWoSched itself already improves the purely performance-oriented baseline by 36%.

Core claim

The scheduling problem is NP-hard and admits no constant-factor approximation even for the uni-processor case. CWM combines carbon-aware mapping and scheduling by integrating dynamic programming with efficient heuristics to exploit renewable energy availability and infrastructure heterogeneity, producing feasible solutions that achieve a median carbon cost reduction of 42% over the best version of CaWoSched when the deadline equals two times the makespan of a carbon-agnostic baseline.

What carries the argument

CWM, the algorithm that interleaves dynamic programming for precedence-respecting task ordering with heuristics that assign tasks to machines according to instantaneous carbon intensity and per-machine power consumption.

If this is right

  • Workflows with precedence constraints can be executed under tight deadlines while still shifting work into high-renewable periods.
  • Heterogeneity in machine power consumption becomes an additional degree of freedom for carbon reduction beyond time-shifting alone.
  • Dynamic programming can be combined with fast heuristics to produce practical solutions for an otherwise inapproximable problem.
  • A 42% further cut on top of an already 36%-improved baseline indicates that carbon-aware mapping and scheduling remain complementary.
  • The approach scales to the tested workflow sizes while still respecting strict deadlines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the hardness result holds, any practical scheduler for larger workflows will need to rely on similar hybrid exact-heuristic designs rather than pure approximation algorithms.
  • Extending CWM to handle uncertainty in future renewable supply forecasts would be a direct next step that preserves the same mapping and ordering machinery.
  • The same hardness carries over to related problems such as carbon-aware placement of virtual machines or serverless functions that also carry precedence or data-flow constraints.

Load-bearing premise

The specific workflow instances, energy supply traces, and machine power models used in the experiments are representative of real heterogeneous datacenter conditions and the CaWoSched baseline was implemented without hidden advantages.

What would settle it

Running CWM and CaWoSched on a new collection of workflow traces drawn from production datacenters with measured renewable availability and power draw, then observing whether the median carbon reduction falls below 20%.

Figures

Figures reproduced from arXiv: 2605.27652 by Anne Benoit, Dominik Schweisgut, Henning Meyerhenke, Yves Robert.

Figure 3
Figure 3. Figure 3: Overall, we obtain a map P_ : {I1, . . . , IJ } −→ {P1, . . . ,PJ }, where Pj is the chosen processor subset for interval Ij . We also provide pseudocode for this phase in Appendix B.3, Algorithm 1. Initial Mapping and Scheduling. First, CWM ranks the tasks in the workflow using a similar definition as the bottom levels in HEFT [27], i. e., we compute for every task v ∈ V : rank(v) = rt(v) + max(v,w)∈E(c(v… view at source ↗
Figure 1
Figure 1. Figure 1: Performance profile (left) and absolute execution time in seconds [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Carbon cost ratios compared to CWM for deadlines D = 1.2 × M (left) and D = 2.0 × M (right). worst quality. For a tighter deadline, CWM, H-CWS-s, and H-CWS-p are closer to each other, while with a larger flexibility in the deadline, the dominance of CWM becomes even clearer, see Appendix D. This is to be expected, since there is less / more flexibility for the algorithms to optimize. Carbon cost analysis. … view at source ↗
Figure 3
Figure 3. Figure 3: For interval I1, all processors are allowed to be active, while in the second interval I2, only p1 and p2 should be active. However, the task on p3 finishes in interval I2. Hence, all three processors are active, potentially violating the given green power budget in I2 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: If we would find for each message the earliest gap on the link and [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance profiles for deadlines D = 1.2×M (left) and D = 2.0×M (right) [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Carbon cost ratios as described in Section 5.2 for deadline [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Absolute execution time (seconds) for each algorithm for deadlines [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Absolute carbon cost for each algorithm for deadlines [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Carbon cost ratios for each competitor for the small and large cluster [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Carbon cost ratios for each competitor for the Germany profile (left) [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Carbon cost ratios for each competitor for tiny real-world ( [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
read the original abstract

As datacenters continue to grow in scale, their energy consumption and resulting carbon footprint have become pressing concerns. With the increasing share of renewable energy in a datacenter's mixed energy supply, shifting task execution to periods of high green-power availability is a promising strategy to reduce carbon emissions. However, in heterogeneous computing environments, the power consumption of compute nodes in a datacenter can also vary. In practice, workloads submitted to datacenters are often not isolated tasks, but entire workflows consisting of interdependent tasks with precedence constraints. A further challenge arises from the fact that carbon emission reductions must typically be achieved under strict workflow deadlines. In this work, we show that the problem posed by these challenges for the scheduler is NP-hard and admits no constant-factor approximation even for the uni-processor case. Motivated by this hardness, we present a novel algorithm CWM that combines carbon-aware mapping and scheduling to construct feasible solutions. Our approach integrates dynamic programming with efficient heuristics to exploit renewable energy availability and infrastructure heterogeneity. To assess the quality of the new algorithm, we evaluate it against the state-of-the-art approach CaWoSched and show that CWM achieves significant reductions in terms of carbon emissions in experiments. In particular, we are able to achieve a median carbon cost reduction of 42% over the best version of CaWoSched when the deadline is two times the makespan of a carbon-agnostic baseline. Note that CaWoSched itself already reduces the carbon-agnostic baseline by 36%.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that carbon-aware mapping and scheduling of deadline-constrained workflows on heterogeneous datacenters is NP-hard and admits no constant-factor approximation even in the uni-processor case. It proposes the CWM algorithm, which integrates dynamic programming with heuristics to exploit renewable energy availability and node heterogeneity while respecting deadlines. Experiments on workflow DAGs show CWM yields a median 42% carbon-cost reduction versus the best CaWoSched variant (itself 36% better than carbon-agnostic) when the deadline is set to twice the carbon-agnostic makespan.

Significance. If the hardness result and the 42% reduction hold under representative conditions, the work supplies both a theoretical justification for heuristic methods and a practical scheduler that meaningfully lowers carbon emissions for workflow workloads without deadline violations. The combination of DP and heuristics, together with direct comparison against an existing baseline, is a concrete contribution to green scheduling.

major comments (2)
  1. [§3] §3 (Complexity): The central claim that the problem is NP-hard and has no constant-factor approximation even for the uni-processor case is asserted without visible proof details or reduction; this is load-bearing for the motivation of CWM and must be supplied for the theoretical contribution to be assessable.
  2. [§5] §5 (Experimental Evaluation): The headline 42% median carbon-cost reduction (and the 36% figure for CaWoSched) is reported without error bars, statistical tests, or a precise description of the workflow DAGs, renewable-energy traces, and heterogeneous power models; because the quantitative claim depends entirely on these choices, the evaluation section does not yet support the performance conclusion.
minor comments (2)
  1. [§5] The abstract and evaluation text refer to 'the best version of CaWoSched' without explicitly identifying which variant or parameter settings were used; this should be stated clearly in the main text and tables.
  2. [§2] Notation for carbon cost, energy supply, and power models should be introduced with a single consistent table or figure early in the paper to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on both the theoretical hardness result and the experimental evaluation. We address each major comment below and will make the requested revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Complexity): The central claim that the problem is NP-hard and has no constant-factor approximation even for the uni-processor case is asserted without visible proof details or reduction; this is load-bearing for the motivation of CWM and must be supplied for the theoretical contribution to be assessable.

    Authors: We agree that the proof details require greater visibility and elaboration to allow full assessment. Although §3 states the NP-hardness result and the absence of a constant-factor approximation (even in the uni-processor case), the reduction itself is only sketched. In the revised manuscript we will expand §3 to include the complete reduction (from a suitable NP-complete problem such as Partition or Knapsack) together with the formal argument ruling out constant-factor approximations, ensuring the theoretical motivation for CWM is self-contained and verifiable. revision: yes

  2. Referee: [§5] §5 (Experimental Evaluation): The headline 42% median carbon-cost reduction (and the 36% figure for CaWoSched) is reported without error bars, statistical tests, or a precise description of the workflow DAGs, renewable-energy traces, and heterogeneous power models; because the quantitative claim depends entirely on these choices, the evaluation section does not yet support the performance conclusion.

    Authors: We concur that the quantitative claims need supporting statistical and methodological detail. The revised §5 will report inter-quartile ranges or standard deviations alongside the median reductions, include appropriate non-parametric statistical tests (e.g., Wilcoxon signed-rank with p-values), and provide explicit descriptions of the workflow DAGs (task counts, structures, and sources), the renewable-energy traces (origin, temporal resolution, and carbon-intensity values), and the heterogeneous power models (node types and their measured or modeled power draws). These additions will make the 42 % and 36 % figures reproducible and statistically grounded. revision: yes

Circularity Check

0 steps flagged

No circularity; hardness proof and algorithm are independent of evaluation metrics

full rationale

The paper's core theoretical claim (NP-hardness and inapproximability even on one processor) is established by a reduction argument that does not reference the experimental traces or CWM outputs. CWM is constructed from dynamic programming plus heuristics motivated by that hardness result, with no equations that define its carbon-cost metric in terms of the same data it later reports. The 42% median reduction versus CaWoSched is an empirical comparison on fixed workflow instances and energy traces; it is not obtained by fitting parameters to a subset and renaming the fit as a prediction, nor by any self-citation chain that bears the central claim. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; full paper may contain additional modeling assumptions about energy traces or workflow structures.

axioms (1)
  • standard math Standard assumptions from complexity theory that NP-hardness implies no constant-factor approximation unless P=NP
    Invoked to establish inapproximability for the uni-processor case.

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Reference graph

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