Review Topics

Chapter Seven

• Know all definitions & concepts associated with flow networks
• Know how to perform the Ford-Fulkerson algorithm (FFA)
• Know how to use the FFA to calculate max flows and min cuts
• Know how to construct residual graphs
• Know how to calculate capacities of cuts and the value of a network flow based on any cut.
• Know the version of the FFA that runs in O(mC) steps, what that means, how to explain it, and how to show it is true. Know what m and C represent in the formula O(mC)
• Know the relationship between flows and cuts.
• Know the second version of the FFA that "chooses good augmenting paths," and know the bound on the number of steps the algorithm requires - the bound that was proved in the text: O(m²logC).
• Know what m and C represent in the bound O(m²logC).
• Know how to explain the Δ parameter of the second version of the FFA and how it us used to achieve good augmenting paths.
• Understand that the facts we proved about the FFA assume that the flow networks under consideration have positive integer capacities on all edges.
• Know how to solve bipartite matching problems using the FFA.
• Know that the following problems can be solved using the FFA: Survey Design, Airline Scheduling, Image Segmentation, and Baseball Elimination.

Chapter Eight

• Know the definitions of P and NP.
• Know what a decision problem is.
• Know what an instance of a decision problem is.
• Know about measures of size of an instance of a problem.
• Know the terminology regarding decision problems.
• Know what X≤_PY and X≡_PY mean for decision problems X and Y.
• Know about the transitivity of the ≤_P relationship - i.e. X≤_PY and Y≤_PZ imply X≤_PZ.
• Know and understand that if X≤_PY and Y∈P, then X∈P
• Know and understand that if X≤_PY and X∉P, then Y∉P
• Know how the reductions we discussed were done - know the 'constructions'
• Given a description of a problem, be able to say whether it is a problem our text showed to be in P or NP.
• Know techniques for demonstrating that a problem is in P or is in NP.
• Know facts about the question of whether P = NP. What is the significance of the question? Do we know whether P ⊆ NP? Do we know whether NP ⊆ P?
• Know what NP stands for (Non-deterministically Polynomial).