To show that ε -universal family of hash function must have ε ≥ 1 | B | − 1 | U |

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Chapter 11.3, Problem 5E

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To show that ε -universal family of hash function must have ε≥1|B|−1|U|

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Problem 3: In this problem we assume that elements are drawn from a universal set U.(i) We insert n (different) elements into an empty hash table T of length m. If m = O(n),what is the time complexity of finding the minimal element in a T?(ii) Let |U| = m2 and suppose that collision is solved by chaining. Show that for everyhash function h: U → {0, 1, . . . , m − 1} there exists a sequence of m insertions intoan empty hash table T of length m giving rise a linked list of length m.

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