The maximum coverage problem is that given an integer k and a list of n finite s

Question

The maximum coverage problem is that given an integer k and a list of n finite sets S 1, S2, Sn, select k sets from the n sets to have maximum size of union. This is one of the classical NP-hard problems. 1. Write a program to implement the greedy algorithm: Mark all n sets Sl, S2, Sn as unselected. Repeat k times Select one set that has the maximum number of elements not in the union the already selected sets. 2. Write a randomized implementation for the greedy algorithm. Let m be a parameter that controls the number of random samples. Mark all n sets Si, S2, ...., Sn as "unselected". The maximum coverage problem is that given an integer k and a list of n finite sets S 1, S2, Sn, select k sets from the n sets to have maximum size of union. This is one of the classical NP-hard problems. 1. Write a program to implement the greedy algorithm: Mark all n sets Sl, S2, Sn as unselected. Repeat k times Select one set that has the maximum number of elements not in the union the already selected sets. 2. Write a randomized implementation for the greedy algorithm. Let m be a parameter that controls the number of random samples. Mark all n sets Si, S2, ...., Sn as "unselected". The maximum coverage problem is that given an integer k and a list of n finite sets S 1, S2, Sn, select k sets from the n sets to have maximum size of union. This is one of the classical NP-hard problems. 1. Write a program to implement the greedy algorithm: Mark all n sets Sl, S2, Sn as unselected. Repeat k times Select one set that has the maximum number of elements not in the union the already selected sets. 2. Write a randomized implementation for the greedy algorithm. Let m be a parameter that controls the number of random samples. Mark all n sets Si, S2, ...., Sn as "unselected".

Explanation / Answer

2)

1. If low >= high, then EXIT.

2. as pivot 'x' is not a middle Pivot.

(i) decide consistently at random a number as of [low..high].

Let the arbitrarily chosen figure number be x.

(ii) Count elements in arr[low..high] that are lesser

than arr[x]. Let this count be sc.

(iii) Count rudiments in arr[low..high] that are greater

than arr[x]. Let this count be gc.

(iv) Let n = (high-low+1). If sc >= n/4 and

gc >= n/4, then x is a middle pivot.

3. Partition arr[low..high] approximately the pivot x.

4. // Recur for lesser elements

randQuickSort(arr, low, sc-1)

5. // Recur for better elements

randQuickSort(arr, high-gc+1, high)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.