Summary: Com S 631: Lower bounds and Separation Results
Lecture 5 Scribe: Adam Case
1. Pebbling Continued
Let G = (V, E) be a DAG that can be pebbled using p pebbles. Let V1 = all vertices in
G that can be pebbled using p
pebbles and V2 = V - V1. Let G1 = (V1, E1) be the graph
induced by V1 and G2 = (V2, E2) be the graph induced by V2. In the previous lecture, we
proved two claims about graphs G1 and G2.
Claim 1. G1 requires p
- d pebbles when a game is restricted to G2.
Claim 2. G2 requires p
- d pebbles when a game is restricted to G1.
Our goal is to prove the following recurrence relation.
R(p) 2R(p/2 - d) +