If the number of clusters is small, one might conjecture that the computational complexity of localizing such a globally rigid graph could be exponential in the number of clusters, but not the number of nodes.
We note that a completely unbalanced gene tree has only one ranking, while the number of rankings can be exponential in the number of leaves when gene trees become more balanced.
The number of optimal solutions will be exponential in the number of connected components.
Since the number of such subsets of sequences can be exponential in the number of sequences, a greedy algorithm which constructs an r-sequence alignment by aligning a single sequence with an (r−1) sequence alignment is proposed.
"Resolution of nested neuronal representations can be exponential in the number of neurons". Physical review letters 109.1 20122): 018103.
Planning is in general NP-hard, indeed PSPACE-complete even in propositional planning formalisms (Bylander 1994), and plan recognition can be exponential in the number of goals to be recognized, even if all plans available for achieving the goals are known in advance (Geib 2004).
Clearly, an exhaustive search is not feasible as the complexity would be exponential in the total number of variables.
Given k input DNA sequences of length n, and a motif size m, by assuming that a motif instance should appear in each sequence we have (n − m + 1) k candidate solutions that can be built by combining all the m-mers in all the possible ways, that is, an overall number that is exponential in the number of input sequences.
An optimal policy can be found using existing methods, but these methods require time at best polynomial in the number of states in the domain, where the number of states is exponential in the number of propositions (or state variables).
The number of possible combinations is exponential in the number of PPIs.
