networks
Robust to failure, fragile to attack
It is 2000, and the internet's operators have a comfortable statistic: routers fail randomly every day and the network barely notices. A new analysis punctures the comfort — in a network whose connectivity concentrates in a few heavily wired hubs, random failure and targeted attack are utterly different regimes. Quantify both: how the giant component degrades as random nodes are removed versus as the highest-degree nodes are removed deliberately, where the percolation thresholds sit, and what the degree distribution's tail decides. Then translate theory into engineering: what topology and what redundancy buy resilience against an adversary who reads the same paper. Get it wrong and the infrastructure everyone calls decentralized turns out to have a dozen load-bearing points of failure — and the adversary finds them first.
Who this problem belongs to
The two figures whose methods fit it best, out of 47 in contention.
Clauset's network science research is centered precisely on this problem's subject: rigorously distinguishing genuine scale-free, hub-concentrated network structure from statistical artifacts, and characterizing exactly how such networks degrade under random node removal versus targeted attack on high-degree hubs. His honest, skeptical methodology for power-law claims, insisting on proper statistical testing rather than eyeballing a log-log plot, is exactly the rigor this problem's percolation-threshold analysis demands. His community-detection and structural-robustness work directly informs the engineering translation this problem asks for, what topology and redundancy buy resilience against an adversary who has read the same analysis. No other career on this card maps this specifically onto the problem's exact network-robustness framing and its 2000-era research context, which is why his score sits near the maximum.
Moore's research on phase transitions in percolation and network connectivity problems, developed with statistical-physics rigor, is the direct mathematical machinery this problem's core question requires: precisely quantifying the threshold at which a network's giant component collapses under node removal, and how that threshold differs catastrophically between random failure and degree-targeted attack. His textbook treatment of percolation theory, with Mertens, gives exactly the formal vocabulary, giant component, percolation threshold, degree distribution's tail, this problem's scenario uses explicitly. He did not co-author the original scale-free-network attack-tolerance papers (Albert, Jeong, Barabasi, 2000) that this scenario directly describes. His score reflects extremely deep, technically precise, directly applicable percolation theory, just short of the problem's specific founding empirical literature.
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
47 figures are scored on this problem. Draw it in a battle to see where you land.