Routing (Leaving Cert Applied Maths): Flashcards

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Routing
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What are routing problems in dynamic programming?

Optimisation challenges to find the best path through a network

Goal of routing problems

Maximise benefits or minimise costs over time

What approach is used in routing problems?

Backward approach - start at final stage, work to beginning

Stage in routing problems

Time periods or decision points; numbered by time remaining

State in routing problems

Possible positions/locations at each stage

Action in routing problems

Decisions/moves you can make from each state

Destination in routing problems

Where each action leads; your new state in next stage

Value in routing problems

Calculated benefit/cost of action (immediate + future)

Value calculation formula in routing

Value=Profit−Travel+OVD\text{Value} = \text{Profit} - \text{Travel} + \text{OVD}

What does OVD stand for?

Optimum Value from Destination

OVD value at final stage

Zero (no future stages to consider)

Why work backwards in routing problems?

Ensures optimal decisions by knowing exact future benefits

How to mark optimal solutions in routing tables

Use asterisks (*) to identify best choices at each stage

Three info types needed for routing problem setup

Timing constraints, benefit calculations, cost analysis

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