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Author: Admin | 2025-04-28
Sub-quadratic time? (This is only possible if the strong exponential time hypothesis is false.)Can X + Y sorting be done in o(n2 log n) time?What is the fastest algorithm for matrix multiplication?Can all-pairs shortest paths be computed in strongly sub-cubic time, that is, in time O(V3−ϵ) for some ϵ>0?Can the Schwartz–Zippel lemma for polynomial identity testing be derandomized?Does linear programming admit a strongly polynomial-time algorithm? (This is problem #9 in Smale's list of problems.)How many queries are required for envy-free cake-cutting?What is the algorithmic complexity of the minimum spanning tree problem? Equivalently, what is the decision tree complexity of the MST problem? The optimal algorithm to compute MSTs is known, but it relies on decision trees, so its complexity is unknown.Gilbert–Pollak conjecture: Is the Steiner ratio of the Euclidean plane equal to ?Programming language theory[edit]Barendregt–Geuvers–Klop conjecture^ https://www.quantamagazine.org/videos/p-vs-np-the-greatest-unsolved-problem-in-computer-science/.^ "Algorithm Solves Graph Isomorphism in Record Time." *Quanta Magazine*https://www.quantamagazine.org/algorithm-solves-graph-isomorphism-in-record-time-20151214/.^ Fellows, Michael R.; Rosamond, Frances A.; Rotics, Udi; Szeider, Stefan (2009), "Clique-width is NP-complete" (PDF), SIAM Journal on Discrete Mathematics, 23 (2): 909–939, doi:10.1137/070687256, MR 2519936, S2CID 18055798, archived from the original (PDF) on 2019-02-27.^ Demaine, Erik D.; O'Rourke, Joseph (2007), "24 Geodesics: Lyusternik–Schnirelmann", Geometric folding algorithms: Linkages, origami, polyhedra, Cambridge: Cambridge University Press, pp. 372–375, doi:10.1017/CBO9780511735172, ISBN 978-0-521-71522-5, MR 2354878.^ Gassner, Elisabeth; Jünger, Michael; Percan, Merijam; Schaefer, Marcus; Schulz, Michael (2006), "Simultaneous graph embeddings with fixed edges" (PDF), Graph-Theoretic Concepts in Computer Science: 32nd International Workshop, WG 2006, Bergen, Norway, June 22-24, 2006, Revised Papers (PDF), Lecture Notes in Computer Science, vol. 4271, Berlin: Springer, pp. 325–335, doi:10.1007/11917496_29, ISBN 978-3-540-48381-6, MR 2290741.Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405.The RTA list of open problems – open problems in rewriting.The TLCA List of Open Problems – open problems in area typed lambda calculus.
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