Why it matters

Real systems face online decisions. Understanding shapes real-world algorithm design.

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The architecture

Input arrives one at a time.

Decide + commit before next arrives.

Competitive ratio: online cost / offline optimum.

Online algorithmsInput arrivessequentiallyIrrevocable decisionno rollbackCompetitive analysisvs offline optSki rental, k-server, paging all classic online problems
Online paradigm.
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How it works end to end

Ski rental: rent or buy. Classic 2-competitive.

Paging: LRU is O(k)-competitive.

k-server: move server to satisfy requests.

Applications: caching, scheduling, ad allocation.