1. Necklace with Colored Beads Cutting Problem Victor Kostyuk Advisor: Michael Capalbo

2. Problem Setup Consider a necklace (cycle) with 2n beads of k colors. There are 2a i beads of color i, and the beads are arranged on the necklace arbitrarily.

4. Goal - Efficient Cutting Alg. Is there an O(n c ) algorithm for making the least number of cuts between beads such that the resulting bead strings can be partitioned into two groups, with a i beads of color i per group?

7. Notes and Prospects Goldberg and West (1985) proved that such a partition is always possible with k+1 cuts. There is an O(n k-2 ) algorithm for finding least number of cuts, but no O(n c ) algorithm is known where c is independent of k. While such O(n c ) algorithm might not exist, an improvement on O(n k-2 ) is a possibility. Perhaps O(n c ) algorithm exits for O(k) cuts.

8. Any questions?