Use the decreasing time algorithm to create a priority list for the digraph from # 3, and schedu

Use the decreasing time algorithm to create a priority list...

Key Concepts

Decreasing Time Algorithm

This algorithm is used in scheduling to order tasks by their processing times, typically arranging tasks in order of decreasing duration. The idea is that allocating the longest tasks first can help balance the workload across processors, reducing the chances of having long tasks delay the overall completion time.

Priority List

A priority list is an ordered sequence of tasks determined by a specific criterion—in this case, by decreasing execution times. It serves as a guide for scheduling, simplifying decisions on which tasks to assign first to available processors, ultimately aiming to optimize the scheduling objective, such as minimizing total completion time or makespan.

Digraph

A digraph, or directed graph, represents tasks as nodes with directed edges indicating precedence relationships (dependencies) between tasks. Analyzing and scheduling tasks using a digraph requires ensuring that each task is scheduled only after all of its prerequisite tasks have been completed, thus preserving the structural constraints of the workflow.

Multiprocessor Scheduling

Multiprocessor scheduling involves assigning tasks to multiple processors in such a way that overall performance metrics, such as completion time or resource utilization, are optimized. This concept encompasses strategies to deal with concurrency, load balancing, and dependency constraints, and it becomes particularly interesting when tasks are interdependent as represented by a digraph.

Transcript

00:01 We are given a weighted graph and we are asked to use cruikuls algorithm to find a minimum spanning tree for this graph.

00:10 The weighted graph we're given is the one from exercise 3, which is a weighted graph on the vertices, a, b, c, d, e, f, g, h, and i.

00:21 We call that an exercise 3.

00:23 We're asked to use prims algorithm to find the minimum spanning tree.

00:27 So essentially, this is a very similar problem except for now we're using cruikers algorithm.

00:37 Refer on to the book for the edge weights.

00:42 Now, the first step of cruikers ' algorithm is to draw the weighted graph with none of its edges.

00:47 So we just have the vertices, a, b, c, d, e, f, g, and i.

00:52 The next step is to find the edges with the smallest weights.

00:58 So we see that the smallest weight in this graph is 1, which belongs to the edge ef.

01:06 So we'll add this edge to the graph.

01:09 The next step is look for the next smallest weight.

01:15 So the smallest weight in the remaining graph is going to be 2, which belongs to the edges ad and h .i.

01:24 So first let's add ad.

01:27 This is perfectly valid.

01:28 It doesn't cause any circuits.

01:31 And let's add hi.

01:32 This is also valid.

01:33 It does not cause any circuits.

01:39 And now the smallest weight in the remaining graph is 3.

01:44 And this belongs to the edges bd, c .f.

01:48 And eh...

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