15 problems

Let a Steiner network have terminal nodes, Steiner nodes, and entry/exit points on the boundaries of soft obstacles. After perturbing the terminal nodes, consider the positions of…

The network-reduction strategy may eliminate facilities and either abandon the associated demand nodes or reassign them to facilities that remain open. The complexity-cost savings…

Let $N$ be the number of phases, let $\mathscr{G}_f$ denote an optimal free network, and let $\mathrm{Pol}_N$ denote the regular polygonal network associated with the $N$-phase con…

Initial-discrepancy conjecture. If all the discrepancies $r_{ij}$ are initially bounded by a small multiple of $\epsilon$, then the path produced by the algorithm upon termination…

Maximum-degree phase-transition conjecture. There is a threshold $\alpha_1$ on the average degree such that below it an optimal graph has a vertex of degree $\Omega(n)$, whereas ab…

Leaf-density phase-transition conjecture. There is a threshold $\alpha_0$ on the average degree such that below it all optimal graphs have a positive proportion of leaves, whereas…

Convex lower-bound conjecture. For all $x$,

Let $n$ be the network size, and consider the complexity of (iib), namely, the number of evaluations required for convergence divided by the size of the feasible discrete neighborh…

Boundary-condition diffusion conjecture. The influence of the single-node boundary conditions under Method I takes more iteration steps to diffuse messages to the bulk of the netwo…

In atomic routing games, let $x_e^*(\tau)$ denote the toll-dependent equilibrium flow on edge $e$, and let $x_e^S$ denote the flow minimizing the social cost during the upper-level…

Let CP denote the strategy that oversees the whole alliance network and makes accept-reject decisions for all partners. Let CCS denote the strategy in which airlines share informat…

Monotonicity conjecture. This monotonicity holds for a line network under the AC power flow model. The property is known for line networks under the linearized Distflow model, and…

Pressure-gradient control conjecture. Pressure gradients, rather than sheer flow amounts, control the response of the tubular channels; consequently, the controlling variables are…

Let $T$ be the set of terminals and let the $T$-cut polyhedron be the polyhedron associated with $T$-cuts. The system consists of constraints,, and -. The compact tree formulation…

In the one-to-many file-transfer problem, let the dynamic piecewise-static solution choose an ordering of peers and allocate transmission rates across epochs, with finite downlink…