Question

Define and explain principle of optimality in dynamic programming

Answer 1

A dynamic programming approach to sequencing problems
Michael Held, Richard M Karp
Journal of the Society for Industrial and Applied Mathematics 10 (1), 196-210, 1962
1. PROBLEM FORMULATIONS 1.1 A scheduling problem. Suppose we are givena set of jobsJ1, J2, J. which are to be executed successively on a single facility. Any given job Jk is assumed to require the services of the facility for rk units of time. With J is also associated a function c (t), giving the cost associated with completing J at time t. We assume that the facility is to be constantly in use, and that no job is to be interrupted before completion. With these assumptions, any given order of execution of the jobs (a schedule) may be represented by an ordering (il i i) of the integers from one through n, indicating that the jobs are to be executed in the order J,/, 1,, Given such a schedule, the termination time t of J is= 1 r., and

Answer 2

Answer:

One major difference between greedy algorithms anddynamic programming is that instead of first finding optimal solutions to subproblems and then making an informed choice, greedy algorithms first make a greedy choice, the choice that looks best at the time, and then solve a resulting subproblem, without bothering to ...