Data structure and Algorithm Research Project
Some Open problems
• What is the fastest algorithm for multiplication of two n-digit numbers?
• What is the fastest algorithm for matrix multiplication?
• Can integer factorization be done in polynomial time?
• Can the discrete logarithm be computed in polynomial time?
• Can the graph isomorphism problem be solved in polynomial time?
• Can parity games be solved in polynomial time?
• 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)?
• Can the 3SUM problem be solved in subquadratic time?
• Dynamic optimality conjecture for splay trees
• K-server problem
Some suggested problems
Extra credit problems on HW7 are also fine.
1. 0-1 Knapsack problem —> 2D square or rectangle knapsack with rectangle objects
2. hybrid recursion model —> deriving general rule (linear + divde and conquer)
3. Parallel implementation of divide-and-conquer algorithms on binary de Bruijn networks
XiaoxiongZhong; Rajopadhye, S.; Lo, V.M.;
4. LCA problem (Lowest Common Ancestor) http://www14.informatik.tu-muenchen.de/konferenzen/Jass08/courses/1/moufatich/El_Moufatich_Paper.pdf
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