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A rumor suggests that P = NP, with a claimed approach to solve 3-SAT in O(n^{extremely large number}) time, which appears implausible or humorous.
Scott Aaronson reports rumors that AI companies, possibly OpenAI, have made significant progress on solving longstanding open problems in theoretical computer science but are holding off on announcements due to recent controversies.
The paper proves the k-server conjecture by demonstrating that the work function algorithm achieves a competitive ratio of k on every metric space.
The article discusses the potential short and long-term implications if the P vs NP problem is solved constructively, with organizations like OpenAI and Anthropic reportedly working on it, and invites insights from experts in mathematics and theoretical computer science.
The article explores the debate on whether computer science is fundamentally about computers, referencing historical perspectives and personal reflections to question the field's essence.
The paper introduces the sync heap, a novel data structure that decouples deletion from revealing the deleted element, enabling constant amortized time for insertions and deletions under limited inspections, and improving a textbook scheduling problem from O(n log n) to O(n).
Five researchers from Tsinghua, Stanford, and Max Planck have developed a new shortest path algorithm that beats Dijkstra's for sparse directed graphs, achieving O(m log^(2/3) n) time complexity, the first improvement since 1987.