Question

Here is an algorithm for calling a triend on the telephone: Step Operation 1\. Dial the phone and wait for either an answer or a busy signal 2\. If the line is not busy then do Steps 3 and 4 3\. Talk as long as you want 4\. Hang up the phone, you are done 5\. Otherwise (the line is busy) 6\. Wait exactly 1 minute 7\. Go back to Step 1 and try again During execution, this algorithm could get into a situation in which, as in the deadlock problem, no useful work can ever get done. Describe the problem, explain why it occurs, and suggest how it could be solved.

Short answer

The algorithm fails if the line is always busy. Introduce a retry limit to prevent indefinite retries.

Step-by-step solution

Understanding the Problem

The problem in this scenario is similar to a deadlock, where a task cannot proceed to completion. Here, calling a friend on the phone enters an indefinite loop if the line is continually busy, meaning the caller waits 1 minute and retries repeatedly without succeeding.

Analyzing Why It Occurs

This indefinite loop occurs because the algorithm's only reaction to a busy line is to wait and retry. If the line is always busy due to some persistent condition (e.g., the friend is continuously on the phone), the algorithm never reaches the "Talk" step, resulting in no progress.

Solution Suggestion: Adding a Termination Condition

To solve the deadlock-like problem, introduce a termination condition after a certain number of attempts. For instance, the algorithm could stop trying after ten attempts and possibly notify the caller to try again later or leave a message.

Key concepts

Deadlock Problem

In the context of computer algorithms, deadlock refers to a situation where a set of operations is unable to proceed because each is waiting for the other to complete. This results in a system freeze where no progress can be made. The telephone algorithm scenario mirrors this problem, as it can become trapped in a loop without reaching a successful outcome. This occurs because the algorithm does not have provisions to progress beyond an indefinitely busy line.

In computer systems, deadlock often occurs when resources are locked in a mutual waiting situation. For instance, Process A waits for a resource held by Process B, while Process B simultaneously waits for a resource held by Process A. Neither process can proceed, creating a deadlock.

To avoid deadlocks in algorithms, it is essential to establish mechanisms that ensure resource availability or timeout protocols to exit the waiting state without undue delay. Employing techniques such as locking hierarchies or timeout procedures can help prevent deadlock situations from arising.

Termination Condition

A termination condition is a specific scenario or condition that dictates when an algorithm should stop executing. In the phone-calling algorithm, a termination condition could come into play to prevent infinite looping when a line is persistently busy.

Establishing a reasonable termination condition involves setting a threshold, such as a maximum number of attempts. If trying to connect surpasses this threshold without success, the algorithm should cease further attempts and possibly suggest alternatives, like trying again later or utilizing voicemail.

In computer algorithms, termination conditions are crucial for ensuring that a process concludes within a logical and practical time frame. It prevents the system from wasting resources on operations that are unlikely to succeed and helps maintain overall efficiency.

Indefinite Loop

An indefinite loop in computer algorithms occurs when a sequence repeatedly executes without reaching a goal or endpoint, simply restarting the process each time the end is approached. In the dialing algorithm, this happens if the friend's line is always busy, causing the algorithm to perpetually delay and try again.

Indefinite loops are problematic because they consume resources without producing results, often leading to system inefficiencies or crashes. To mitigate indefinite loops, one should introduce exit conditions or limits, ensuring the algorithm knows when to cease and report back.

As demonstrated in programming, adding a check—such as a counter that limits the number of iterations—can help prevent indefinite loops. Implementing this ensures that every loop eventually concludes, either successfully or by failing gracefully, and allows for other processes to utilize the system efficiently.