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queries, and in general distinguishing r-to-1 functions from 1-to-1 functions requires
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42:. The collision problem most often refers to the 2-to-1 version: given
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or 2-to-1. We are only allowed to make queries about the value of
124:{\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}}
551:"Limits on Efficient Computation in the Physical World"
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If we allow randomness, the problem is easier. By the
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Solving the 2-to-1 version deterministically requires
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459:{\displaystyle \Theta ({\sqrt {n}})}
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414:{\textstyle {\frac {n}{r}}+1}
353:{\textstyle {\frac {n}{r}}+1}
320:{\textstyle {\frac {n}{r}}+1}
280:{\textstyle {\frac {n}{r}}+1}
247:{\textstyle {\frac {n}{2}}+1}
421:queries is also necessary.
21:Collision detection problem
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519:{\displaystyle O(n^{1/3})}
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40:computational mathematics
578:Polynomial-time problems
28:r-to-1 collision problem
19:Not to be confused with
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157:{\displaystyle f(i)}
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62:even and a function
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381:{\displaystyle n/r}
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16:Theoretical problem
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526:queries to
573:Algorithms
567:Categories
534:References
425:Randomized
466:queries.
441:Θ
287:queries.
187:…
175:∈
110:…
98:→
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549:(2004).
164:for any
133:1-to-1
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554:(PDF)
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