I'm supervising 4 undergrads working on small pieces of my research project. Their role is to comb through archival materials, to identify a modest research question, and to write a long paper answering that question. One of the students dropped by my office this morning to chat about progress. Just before leaving, they said, "I've written papers before. But they were all based on things people'd already written - I knew the answer. This is so much more fun. I feel like a de…
Trump is very, very angry about a New York Times piece
that carefully documents his obvious physical decline.
Trump raged over the piece,
letting out a stream of lies about his performance in office
and even attacking the reporter who wrote the piece as ugly.
This may seem typical of Trump,
but we think it gets at something deeper.
Trump’s entire political mystique is premised on the fiction that he’s a strong, virile, formidable figure
who …
Perfect Network Resilience in Polynomial Time
Matthias Bentert, Stefan Schmid
https://arxiv.org/abs/2602.03827 https://arxiv.org/pdf/2602.03827 https://arxiv.org/html/2602.03827
arXiv:2602.03827v1 Announce Type: new
Abstract: Modern communication networks support local fast rerouting mechanisms to quickly react to link failures: nodes store a set of conditional rerouting rules which define how to forward an incoming packet in case of incident link failures. The rerouting decisions at any node $v$ must rely solely on local information available at $v$: the link from which a packet arrived at $v$, the target of the packet, and the incident link failures at $v$. Ideally, such rerouting mechanisms provide perfect resilience: any packet is routed from its source to its target as long as the two are connected in the underlying graph after the link failures. Already in their seminal paper at ACM PODC '12, Feigenbaum, Godfrey, Panda, Schapira, Shenker, and Singla showed that perfect resilience cannot always be achieved. While the design of local rerouting algorithms has received much attention since then, we still lack a detailed understanding of when perfect resilience is achievable.
This paper closes this gap and presents a complete characterization of when perfect resilience can be achieved. This characterization also allows us to design an $O(n)$-time algorithm to decide whether a given instance is perfectly resilient and an $O(nm)$-time algorithm to compute perfectly resilient rerouting rules whenever it is. Our algorithm is also attractive for the simple structure of the rerouting rules it uses, known as skipping in the literature: alternative links are chosen according to an ordered priority list (per in-port), where failed links are simply skipped. Intriguingly, our result also implies that in the context of perfect resilience, skipping rerouting rules are as powerful as more general rerouting rules. This partially answers a long-standing open question by Chiesa, Nikolaevskiy, Mitrovic, Gurtov, Madry, Schapira, and Shenker [IEEE/ACM Transactions on Networking, 2017] in the affirmative.
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