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
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.
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
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]