Transmission Rate Problem

1
Transmission Rate Problem

• Input
• n receivers where receiver i has capacity ri
• Integer k
• Task
• Find a set of transmission rates T t1, , tk
  such that Si (ri tq) is minimized where tq is
  the largest element of T smaller than ri
• This is an actual research problem posed to me by
  a student several years ago

2
Vertex Cover

• Input
• Unweighted, undirected graph G (V,E)
• Task
• Compute a minimum sized cover C subset of V such
  that for every edge (u,v) in E, at least one of
  u,v belongs to V.

3
Scheduling with Preemptions

• Input
• A set of jobs with release times ri, processing
  times pi
• Task
• Compute a preemptive schedule of the jobs that
  minimizes the sum of the job completion times

4
Max Jobs

• Input
• A set of jobs with deadlines di and processing
  times pi
• Task
• Find a schedule of these jobs on a single machine
  that maximizes the number of jobs that complete
  by their deadlines without preemptions.
• Example
• Jobs (3, 2), (4,1), (7,6), (10,7)
• Optimal Schedule Job 1 0,2, Job 2 2,3, Job 4
  3,10