Author

Lachlan Bridges

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Preprint Sep 2026

Gaussian Vertex-Face Balance in Random Convex Polyhedra with Fixed Edge Count

Choose uniformly among the combinatorial types of convex three-dimensional polyhedra with a fixed admissible number $e$ of edges, and let $V_e$ be the number of vertices. This resolves a fixed-edge limit-distribution question posed by R\"udinger: if $\beta_e=V_e/(e+2)$, then $\sqrt e(\beta_e-1/2)\Rightarrow N(0,1/32)$,...

Lachlan Bridges · 0 citations

Preprint Sep 2026

Single-Machine Scheduling with Interval Predictions and Costly Preemption

We study the single-machine total-completion-time problem $1||\sum C_j$ when processing times are unknown but each job comes with a reported interval. Jobs are initially processed in nondecreasing order of reported upper bound. If a job is still unfinished after receiving that much service, the reported upper bound has...

Lachlan Bridges · 0 citations