The document discusses the activity selection problem, which aims to select the maximum number of non-conflicting activities that can be executed by a single person or machine within a given time frame. It describes how each activity has a start and finish time, and activities are compatible if their time intervals do not overlap. It then provides an algorithm that sorts activities by finish time and greedily selects activities with start times later than the current finish time.

1. Activity Selection Problem
Md. Muktar Hossain
Lecturer (Provisional), CSE, VU

2. Activity Selection Problem
❖ The Activity Selection Problem is an optimization problem which deals
with the selection of non-conflicting activities that needs to be executed
by a single person or machine in a given time frame.
❖ Let's consider that you have n activities with their start and finish times,
the objective is to find solution set having maximum number of
non-conflicting activities that can be executed in a single time frame,
assuming that only one person or machine is available for execution.

13. Activity Selection Problem
Each Activity "i" has start time si and a finish time fi, where si ≤fi. If selected activity
"i" take place meanwhile the half-open time interval [si,fi). Activities i and j are
compatible if the intervals (si, fi) and [si, fi) do not overlap (i.e. i and j are
compatible if si ≥fi or si ≥fi). The activity-selection problem chosen the maximum-
size set of mutually consistent activities.

14. Algorithm Of Greedy- Activity Selector
Activity-Selection(Activity, start, finish)
Sort Activity by finish times stored in finish
Selected = {Activity[1]}
n = Activity.length
j = 1
for i = 2 to n:
if start[i] ≥ finish[j]:
Selected = Selected U {Activity[i]}
j = i
return Selected

15. Example

16. Example