SSTF (Shortest Seek Time First) in Operating Systems - Time & Space Complexity

Time Complexity: SSTF (Shortest Seek Time First)

O(n)

Understanding Time Complexity

Analyzing time complexity helps us understand how the SSTF disk scheduling algorithm performs as the number of disk requests grows.

We want to know how the time to select the next request changes when there are more requests waiting.

Scenario Under Consideration

Analyze the time complexity of the following SSTF selection process.

function selectNextRequest(currentPosition, requests) {
  let shortestDistance = Infinity;
  let nextRequest = null;
  for (let i = 0; i < requests.length; i++) {
    let distance = Math.abs(requests[i] - currentPosition);
    if (distance < shortestDistance) {
      shortestDistance = distance;
      nextRequest = requests[i];
    }
  }
  return nextRequest;
}
    

This code finds the disk request closest to the current head position by checking all pending requests.

Identify Repeating Operations

Look for repeated actions that take time.

• Primary operation: Loop through all disk requests to find the closest one.
• How many times: Once per selection, looping over all requests (n times).

How Execution Grows With Input

As the number of requests increases, the time to find the closest request grows proportionally.

Input Size (n)	Approx. Operations
10	About 10 checks
100	About 100 checks
1000	About 1000 checks

Pattern observation: The number of operations grows directly with the number of requests.

Final Time Complexity

Time Complexity: O(n)

This means the time to pick the next request grows linearly as more requests are waiting.

Common Mistake

[X] Wrong: "SSTF instantly finds the closest request regardless of how many requests there are."

[OK] Correct: SSTF must check each request to find the closest one, so more requests mean more work.

Interview Connect

Understanding how SSTF scales helps you explain disk scheduling choices clearly and shows you can analyze algorithm efficiency in real systems.

Self-Check

"What if the requests were kept sorted by position? How would that affect the time complexity of finding the next request?"

Practice

1. What does SSTF (Shortest Seek Time First) disk scheduling algorithm prioritize?

easy

A. The request closest to the current head position

B. The request that arrived first

C. The request farthest from the current head position

D. Requests in a fixed circular order

Solution

1. Step 1: Understand SSTF purpose

   SSTF aims to reduce the seek time by choosing the disk request nearest to the current head position.

2. Step 2: Compare options with SSTF behavior

   Only the request closest to the current head position matches this behavior; others describe different algorithms.

3. Final Answer:

   The request closest to the current head position -> Option A

4. Quick Check:

   SSTF = closest request [OK]

Hint: Pick the request nearest to the head position [OK]

Common Mistakes:

• Confusing SSTF with FCFS (First Come First Serve)
• Thinking SSTF picks requests in arrival order
• Assuming SSTF picks the farthest request

2. Which of the following is the correct way to describe SSTF in disk scheduling?

easy

A. It processes requests in the order they arrive.

B. It selects the request with the longest waiting time first.

C. It selects the request closest to the current head position.

D. It moves the head in one direction servicing all requests.

Solution

1. Step 1: Review SSTF definition

   SSTF selects the disk request closest to the current head position to minimize seek time.

2. Step 2: Match options with SSTF behavior

   The option "It selects the request closest to the current head position." correctly describes SSTF. Other options describe different algorithms like FCFS or SCAN.

3. Final Answer:

   It selects the request closest to the current head position. -> Option C

4. Quick Check:

   SSTF = closest request selection [OK]

Hint: Remember SSTF picks nearest request, not oldest [OK]

Common Mistakes:

• Mixing SSTF with FCFS or SCAN algorithms
• Assuming SSTF picks requests by waiting time
• Confusing direction-based scheduling with SSTF

3. Given the disk head is at position 50 and requests are at positions [45, 70, 10, 55], which request will SSTF service first?

medium

A. 45

B. 70

C. 10

D. 55

Solution

1. Step 1: Calculate distances from head position 50

   Distances: 45 (5), 70 (20), 10 (40), 55 (5)

2. Step 2: Identify closest request

   Requests at 45 and 55 are both 5 units away. SSTF can pick either, but usually picks the first closest found, here 45.

3. Final Answer:

   45 -> Option A

4. Quick Check:

   Closest request = 45 [OK]

Hint: Calculate absolute distance, pick smallest [OK]

Common Mistakes:

• Choosing the farthest request by mistake
• Ignoring equal distances and picking wrong one
• Confusing SSTF with FCFS order

4. A disk head is at position 30. Requests are at [35, 25, 40, 20]. A student incorrectly picks 40 as the next request in SSTF. What is the error?

medium

A. They ignored the current head position.

B. They chose the farthest request instead of the closest.

C. They picked the request with the longest waiting time.

D. They selected requests in arrival order.

Solution

1. Step 1: Calculate distances from head position 30

   Distances: 35 (5), 25 (5), 40 (10), 20 (10)

2. Step 2: Identify correct SSTF choice

   Closest requests are 35 and 25 (5 units away). Choosing 40 (10 units) is incorrect.

3. Final Answer:

   They chose the farthest request instead of the closest. -> Option B

4. Quick Check:

   SSTF picks closest, not farthest [OK]

Hint: Always pick request with minimum distance [OK]

Common Mistakes:

• Picking requests based on arrival time
• Ignoring actual distances from head
• Confusing SSTF with other algorithms

5. A disk head starts at position 100. The request queue is [120, 89, 130, 80, 110]. Using SSTF, what is the order in which requests will be serviced?

hard

A. [110, 120, 130, 89, 80]

B. [89, 80, 110, 120, 130]

C. [110, 120, 89, 80, 130]

D. [110, 89, 80, 120, 130]

Solution

1. Step 1: Start at head position 100 and find closest request

   Distances: 120(20), 89(11), 130(30), 80(20), 110(10). Closest is 110 (10 units).

2. Step 2: Move head to 110 and repeat

   Remaining: 120(10), 89(21), 130(20), 80(30). Closest is 120 (10).

3. Step 3: Move head to 120 and repeat

   Remaining: 89(31), 130(10), 80(40). Closest is 130 (10).

4. Step 4: Move head to 130 and repeat

   Remaining: 89(41), 80(50). Closest is 89 (41).

5. Step 5: Move head to 89 and last request is 80 (9 away)

   Order: 110, 120, 130, 89, 80.

6. Final Answer:

   [110, 120, 130, 89, 80] -> Option D

7. Quick Check:

   SSTF services closest request each step [OK]

Hint: Pick closest request step-by-step from current head [OK]

Common Mistakes:

• Not updating head position after each request
• Choosing requests by arrival order
• Ignoring equal distances and picking wrong request