One Color Preprocessing Improves DSATUR
Quick summary
arXiv:2609.17633v1 Announce Type: new Abstract: The Graph Coloring Problem (GCP) is NP-hard and DSATUR stands as one of the fastest heuristics for it despite producing colorings that typically use more colors than state-of-the-art coloring algorithms. We propose SSLD (Semidefinite Spectral Learning with DSATUR), which improves DSATUR by preprocessing a first good color class before letting DSATUR complete coloring the rest of the given graph. We obtain this color class from a Semidefinite Programming (SDP), similar to an SDP used to compute the Lov\'asz theta number. To the best of our knowled
Key takeaways
- arXiv:2609.17633v1 Announce Type: new Abstract: The Graph Coloring Problem (GCP) is NP-hard and DSATUR stands as one of the fastest heuristics for it despite producing colorings that typically use more colors than state-of-the-art coloring algorithms.
- We propose SSLD (Semidefinite Spectral Learning with DSATUR), which improves DSATUR by preprocessing a first good color class before letting DSATUR complete coloring the rest of the given graph.
- We obtain this color class from a Semidefinite Programming (SDP), similar to an SDP used to compute the Lov\'asz theta number.
Why it matters
“One Color Preprocessing Improves DSATUR” illustrates how changes in the AI ecosystem can affect products, workflows and user expectations together. Its lasting significance depends on measurable adoption, cost and safety outcomes.
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