In your active combinatorial optimization line, this result enables the hypothesis that NP-hard network routing or clustering problems on geodesic metric spaces lacking c-fat theta curves can be solved with a (1,K)-approximation ratio by mapping them to equivalent polynomial-time solvable problems on cactus graphs.
Adversarial Debate Score
50% survival rate under critique
Expert panel critique
Independent views, each critiquing the hypothesis on its own — the score rewards genuine disagreement and discounts consensus.
Supporting Research Papers
- Additive quasi-isometries and cacti
We prove that if a geodesic metric space contains no c-fat theta curve for some c>0, then it is (1,K)-quasi-isometric to a cactus graph, where K depends only on c. Using a coarse characterization of c...
- Finding Short Paths on Simple Polytopes
We prove that computing a shortest monotone path to the optimum of a linear program over a simple polytope is NP-hard, thus resolving a 2022 open question of De Loera, Kafer, and Sanit\`a. As a conseq...
- Cut-homotopies and the complexity of edge-coloring problems
We study the computational complexity of problems that ask if a given graph admits an edge-coloring that does not contain an edge-colored clique from some fixed finite family. We show that every such ...
- Improved Approximation of Min-Distances in Near-Linear Time
We study the problem of approximating the diameter of directed graphs under the min-distance measure, defined as d_{\min}(u,v) = \min(d(u,v), d(v,u)). Unlike standard shortest-path distance, min-dista...
Formal Verification
Z3 checks whether the hypothesis is internally consistent, not whether it is empirically true.