Scheduling and Digraphs
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1 Scheduling and Digraphs Lecture 35 Sections 8.1, 8.2 Robb T. Koether Hampden-Sydney College Mon, Nov 21, 2016 Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
2 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
3 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
4 Introduction To plan a meeting with several invited speakers involves a number of tasks: (A) Locate appropriate speakers. (B) Invite them to speak. (C) Send out announcements of the meeting. (D) Build a website to register attendees. (E) Plan a banquet menu. (F) Retain a caterer. (G) Determine the registration fee. (H) Reserve a room for the banquet. (I) Update website with info. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
5 Introduction Some of these tasks can be done simultaneously. Locate appropriate speakers. Plan a banquet menu. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
6 Introduction Some of these tasks can be done simultaneously. Locate appropriate speakers. Plan a banquet menu. Some must be done in sequence. Plan a banquet menu. Determine the registration fee. Build a website to register attendees. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
7 Introduction Some of these tasks can be done simultaneously. Locate appropriate speakers. Plan a banquet menu. Some must be done in sequence. Plan a banquet menu. Determine the registration fee. Build a website to register attendees. If we know how long each task will take and if we know the dependencies, then we can figure out how long the entire project will take. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
8 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
9 Definitions Definition (Task) A task is a unit of work that cannot be broken down into smaller units. Definition (Processor) A processor is a person or a machine that carries out a task. Because a task cannot be broken down into parts, each task must be done by a single processor. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
10 Definitions Definition (Processing Times) The processing time of a task is the time necessary to complete the task. Definition (Precedence Relations) Given two tasks, a precedence relation states that one of them must be completed before the other one can be started. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
11 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
12 Example Assume the following processor times. (A) Locate appropriate speakers 3 days. (B) Invite them to speak (and get confirmation) 4 days. (C) Send out announcements of the meeting 1 day. (D) Build a website to register attendees 3 days. (E) Plan a banquet menu 1 day. (F) Retain a caterer 2 days. (G) Determine the registration fee 1 day. (H) Reserve a room for the banquet 1 day. (I) Update website with info 1 day. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
13 Example We have the following times and precedence relations. Task Time Precedent Tasks (A) Locate speakers 3 (B) Confirm speakers 4 A (C) Send announcements 1 B, D, E, G (D) Build website 3 (E) Plan menu 1 F (F) Retain caterer 2 (G) Registration fee 1 F (H) Banquet room 1 (I) Update website 1 B, D, E, G Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
14 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
15 Definitions Definition (Digraph) A digraph is a directed graph. That is, each edge is given a direction, indicated by an arrowhead. A B E F C D Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
16 Example A B Start D F E C I End H G This digraph shows the precedence relations of our example. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
17 Example A B Start D F E C I End H G This digraph shows the precedence relations of our example. Note the two additional vertices Start and End. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
18 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
19 Project Digraphs Definition (Project Digraph) A project digraph is a digraph that displays the precedence relations among the tasks of a project as well as the process times for each task, and START and END vertices. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
20 Example Example (Project Digraph) A(6) F(3) D(2) Start(0) B(5) G(3) End(0) C(7) E(5) H(4) The diagram shows the precedence relations. Some of the precedence relations are implied by the graph. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
21 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
22 Priority Lists Definition (Priority List) A priority list is a list of the tasks of a project, listed in the order in which we prefer to execute them. Definition (Priority List Model) The priority list model uses a priority list to schedule the tasks. Whenever a processor is available, the model chooses the next task in the list that is ready to be processed. (To be ready, all precedent tasks must have been completed.) If there are M tasks, then there are M! possible priority lists. It is not practical to try them all. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
23 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Suppose the priority list is A, B, C, D, E and that there are only 2 processors. What is the resulting schedule? Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
24 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 Processor Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
25 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 Processor 2 A(6) Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
26 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 Processor 2 A(6) B(5) Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
27 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 Processor 2 A(6) B(5) C(7) Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
28 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 A(6) D(2) Processor 2 B(5) C(7) Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
29 Example Example (Priority-List Scheduling) A(6) D(2) Start(0) B(5) End(0) C(7) E(5) Processor 1 A(6) D(2) Idle E(5) Processor 2 B(5) C(7) Idle Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
30 Example Example (Priority-List Scheduling) What if there had been 3 processors? What if the priority list had been A, C, D, E, B? What if the priority list had been E, D, C, B, A? Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
31 Another Example Example (Priority-List Scheduling) Task Precedent Tasks Time (A) Locate speakers 5 (B) Confirm speakers C, D 2 (C) Send announcements 4 (D) Build website 6 (E) Plan menu A, C, F 3 (F) Retain caterer A, B 1 (G) Registration fee F 4 Schedule the tasks with priority list A, B, C, D, E, F, G with 2 processors. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
32 Outline 1 Introduction 2 Definitions 3 Example 4 Digraphs 5 Project Digraphs 6 Priority Lists 7 Assignment Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
33 Assignment Assignment Chapter 8 Exercises 4, 12, 13, 14, 16, 19, 20. Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, / 25
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