Question: Suppose we use a hash function h to hash n distinct keys into an array T of length m, assuming simple uniform hashing, what is

Suppose we use a hash function h to hash n distinct keys into an array T of length m, assuming simple uniform hashing, what is the expected number of collisions? More precisely, what is the expected cardinality of {{k, l} : k ≠ l and h(k) = h(l)}?

Step by Step Solution

★★★★★

3.36 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For each pair of keys k 1 where k1 define the indicator random variabl... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

C-S-A (50).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

What is the expected number of mutant flies that must be inspected to find the first one with purple eyes? What is the expected number of purple-eyed flies that will be found if this many are...

What is the expected number of bins that remain empty when m balls are distributed into n bins uniformly at random?

What is the expected number of cases over 1 year in the city? Suppose a city is divided into eight census tracts as shown in Table 4.21. Table 4.21: Relationship between incidence of birth defects...

6 BST , AVL Trees, and Hashing [ 1 5 points ] You are given a hash table with \ ( n \ ) keys and \ ( m \ ) slots, with the simple uniform hashing assumption discussed in class ( i . e . , each key is...

4. Bloom filters. Suppose you are given a Bloom filter of size m with t hash functions (each of which can be assumed to be computed in O(1) time) and n inserted elements. Let S be the set...

1. Suppose you have a bag of 10 coins. Nine of them are fair coins, that is, if you toss any of these 9 coins the probability of getting a head, P(H) = 1/2. Similarly, probability of getting a tail,...

(III) (8 points) There are various collision resolution strategies for hash tables. Please answer the following questions under the assumption of simple uniform hashing and all keys are unique, given...

5. (20 points) In this problem we will compute the expected average size of a chain in the hash table, under the Simple Uniform Hashing assumption. The simple uniform hashing assumption states that...

: (i) What data structures are maintained by the page manager. (ii) What happens when a machine performs a read operation to a page. (iii) What happens when a machine performs a write operation to a...

llustrate different ways of connecting these components together to span a range of performance requirements. [10 marks] For each of the performance categories that you identify state today's typical...

Annuity due. Reginald is about to lease an apartment for 36 months. The landlord wants him to make the lease payments at the start of the month. The monthly payments are $1,100 per month. The...

An open loop state space system with A = B = [], C = [10] and D = 0 is given: u B muta X. B D X. A Fig. 1 A proportional block is added to this system to make closed loop system: D X K Gain C -1 -3,...

From the output of the following IOS command, what conclusion can you have based on the command's output?Select one: a . The port has the maximum number of MAC addresses that is supported by a Layer...

The electric field everywhere on the surface of a thin spherical shell of radius 0.750 m is measured to be 890 N/C and points radially toward the center of the sphere. (a) What is the net charge...

A rod 14.0 cm long is uniformly charged and has a total charge of -22.0 C. Determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its center.

(a) Find the equivalent resistance between points a and b in Figure P28.6. (b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor. 7.00 9.00 ...

The difference in potential between the accelerating plates in the electron gun of a TV picture tube is about 25 000 V. If the distance between these plates is 1.50 cm, what is the magnitude of the...

A 2.00-nF capacitor with an initial charge of 5.10 C is discharged through a 1.30-k resistor. (a) Calculate the current in the resistor 9.00 s after the resistor is connected across the terminals of...

What is a long-run average cost curve?

Suppose you're considering investing in a portfolio consisting of 3 0 % Treasury bonds and 7 0 % in an "index fund" representing all U . S . common stocks. The returns of the Treasury bonds are...

Two sisters each open IRAs in 2011 and plan to invest $3,000 per year for the next 30 years. Mary makes her first deposit on January 1, 2011, and will make all future deposits on the first day of the...

Which of the following is(are) among the responsibilities of FINRA? (1) Educating investors. (2) Fostering market transparency. (3) Writing and enforcing rules governing the activities of all...