It is the 1990s, and a powerful pattern for hard combinatorial problems matures: when the discrete problem is NP-hard, embed it in a larger continuous one you can actually solve — a semidefinite program over matrices — solve that, then round the continuous solution back to a discrete one, losing only a bounded fraction of quality. Apply it to partitioning a graph to cut the most edges, and prove the rounding never loses more than a specific, surprising fraction of the optimum. The relaxation must be tight enough to be worth solving and the rounding must carry a proof. Get it wrong and you attack head-on and fail, or relax so loosely the answer is worthless — convex relaxation with a provable rounding is a sharp weapon against hardness.
Chose Graph diffusion kernels — right call.
Kondor's group-theoretic and equivariant machine learning work, along with his research on graph kernels, engages deeply with discrete algebraic structures on graphs, permutation groups, graph isomorphism, symmetry, giving him genuine mathematical fluency with the kind of graph structure this max-cut problem concerns. Graph kernel computation does sometimes involve convex relaxations of hard graph problems, a real methodological cousin of this problem's SDP relaxation. But his research applies this machinery to representation learning and kernel design, not to max-cut approximation or the Goemans-Williamson rounding proof specifically. His score reflects genuine graph-mathematics fluency without direct authorship of this specific technique. Risi Kondor would recognize the shape of this problem immediately from adjacent work, even without having personally published the specific technique it calls for.
Torvalds's creation of Linux and Git gave computing essential operating-system and version-control infrastructure, foundational to how modern semidefinite-programming solvers get built and deployed, but this is purely infrastructural. His own technical contributions addressed kernel architecture and distributed version control, not convex optimization or combinatorial graph algorithms; he wrote no relaxation technique, no rounding proof, no graph-partitioning method. Nothing in his coded work touches semidefinite programming, NP-hardness, or graph-cut theory directly. His score reflects the same generic 'built the substrate everyone else uses' connection shared by other systems pioneers, with essentially no direct algorithmic relevance to this problem. Linus Torvalds would have essentially nothing specific to contribute if handed this exact problem, beyond the general computational literacy shared across the field.
Battle #129 · 8/10/2026, 11:39:17 AM · this result is deterministic: the same two personas on this problem always resolve the same way.