List of unsolved problems in computer science
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This article is a list of unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known, or when experts in the field disagree about proposed solutions.
- P versus NP problem (often written as "P = NP")
- What is the relationship between BQP and NP?
- NC = P problem
- NP = co-NP problem
- P = BPP problem
- P = PSPACE problem
- L = NL problem
- L = P problem
- L = RL problem
- Unique games conjecture
- Is the exponential time hypothesis true?
- Do one-way functions exist?
- Is public-key cryptography possible?
Polynomial versus non-polynomial time for specific algorithmic problems
Main article: NP-intermediate
- Can integer factorization be done in polynomial time?
- Is integer factorization NP-complete?
- Can clustered planar drawings be found in polynomial time?
- Can the discrete logarithm be computed in polynomial time?
- Can the graph isomorphism problem be solved in polynomial time?
- Can leaf powers and k-leaf powers be recognized in polynomial time?
- Can parity games be solved in polynomial time?
- Can the rotation distance between two binary trees be computed in polynomial time?
- Can graphs of bounded clique-width be recognized in polynomial time?
- Can one find a simple closed quasigeodesic on a convex polyhedron in polynomial time?
- Can a simultaneous embedding with fixed edges for two given graphs be found in polynomial time?
Other algorithmic problems
- What is the fastest algorithm for multiplication of two n-digit numbers?
- What is the fastest algorithm for matrix multiplication?
- Can the Schwartz–Zippel lemma for polynomial identity testing be derandomized?
- Can a depth-first search tree be constructed in NC?
- Does linear programming admit a strongly polynomial-time algorithm? This is problem #9 in Smale's list of problems.
- What is the lower bound on the complexity of fast Fourier transform algorithms? Can they be faster than Θ (N log N)?
- The dynamic optimality conjecture: do splay trees have a bounded competitive ratio?
- Can we compute the edit distance between two strings of length n in strongly sub-quadratic time, i.e., in time O(n2−ϵ) for some ϵ>0 ?
- Is there a k-competitive online algorithm for the k-server problem?
- Can X + Y sorting be done in strictly less than O(n2 log n) time?
- How many queries are required for envy-free cake-cutting?
- What is the lowest possible worst-case time complexity of Shellsort with a deterministic, fixed gap sequence?
- Aanderaa–Karp–Rosenberg conjecture
- Generalized star height problem
- Separating words problem
- Possibility of hypercomputation
- Fellows, Michael R.; Rosamond, Frances A.; Rotics, Udi; Szeider, Stefan (2009), "Clique-width is NP-complete", SIAM Journal on Discrete Mathematics, 23 (2): 909–939, doi:10.1137/070687256, MR 2519936.
- 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", Graph-Theoretic Concepts in Computer Science: 32nd International Workshop, WG 2006, Bergen, Norway, June 22-24, 2006, Revised Papers, Lecture Notes in Computer Science, 4271, Berlin: Springer, pp. 325–335, doi:10.1007/11917496_29, MR 2290741.