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Hardness of Token Swapping on Trees
We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is $2$) and show that no such algorithm can achieve an approximation factor less than $2$.
Motion Planning
Data Structures and Algorithms
Computational Complexity
Hanabi is NP-hard, Even for Cheaters who Look at Their Cards
On the positive side, we show that the decision version of the problem---to decide whether or not numbers from $1$ through $n$ can be played for every color---can be solved in (almost) linear time for some restricted cases.
Discrete Mathematics Computational Complexity
