List of unsolved problems in computer science

List of unsolved problems in computer science
This article is a list of notable 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.
Computational complexity
P versus NP problem
What is the relationship between BQP and NP?
NC = P problem
NP = co-NP problem
P = BPP problem
P = PSPACE problem
L = NL problem
PH = PSPACE problem
L = P problem
L = RL problem
Unique games conjecture
Is the exponential time hypothesis true?
Is the strong exponential time hypothesis (SETH) true?
Do one-way functions exist?
Is public-key cryptography possible?
Log-rank conjecture
Polynomial versus nondeterministic-polynomial time for specific algorithmic problems
Can integer factorization be done in polynomial time on a classical (non-quantum) computer?
Can the discrete logarithm be computed in polynomial time on a classical (non-quantum) computer?
Can the shortest vector of a lattice be computed in polynomial time on a classical or quantum computer?
Can clustered planar drawings be found in polynomial time?
Can the graph isomorphism problem be solved in polynomial time?
Can leaf powers and -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
The dynamic optimality conjecture: do splay trees have a bounded competitive ratio?
Can a depth-first search tree be constructed in NC?
Can the fast Fourier transform be computed in time?
What is the fastest algorithm for multiplication of two n-digit numbers?
What is the lowest possible average-case time complexity of Shellsort with a deterministic, fixed gap sequence?
Can 3SUM be solved in strongly sub-quadratic time, that is, in time for some ?
Can the edit distance between two strings of length be computed in strongly sub-quadratic time? (This is only possible if the strong exponential time hypothesis is false.)
Can X + Y sorting be done in 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 for some ?
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–Pollack conjecture on the Steiner ratio of the Euclidean plane
Programming language theory
POPLmark
Barendregt–Geuvers–Klop conjecture
Other problems
Aanderaa–Karp–Rosenberg conjecture
Černý Conjecture
Generalized star-height problem
Separating words problem
References
External links
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.
Computer Science
Computer Science