Divide and Conquer

Closest Pair IDesign and Analysis

of Algorithms I

Tim Roughgarden

The Closest Pair Problem

Tim Roughgarden

Initial Observations

Tim Roughgarden

High-Level Approach

Tim Roughgarden

The Divide and Conquer Paradigm

Tim Roughgarden

ClosestPair()

𝑂 (𝑛)𝑂 (𝑛 log𝑛)𝑂 ¿𝑂 (𝑛2)

Suppose we can correctly implement the ClosestSplitPair subrouine in time. What will be the overall running time of the Closest Pair algorithm? (Choose the smallest upper bound that applies.)

Tim Roughgarden

ClosestPair()

Tim Roughgarden

ClosestSplitPair(,)

Tim Roughgarden

Correctness Claim