Reducibility
Glossary Contents
← Ch V
Chapter VI Set Cover
Ch VII →
  1. 16 — Cover the universe
  2. 17 — Greedy in R
  3. 18 — Where to advertise
18

Where to advertise

Every reach-and-frequency model in advertising is set cover with a budget twist.

A consumer brand wants to reach 80% of US adult women aged 25–44 at least once. Each ad placement (a podcast, a primetime slot, a billboard, a TikTok creator) reaches a set of that audience, with overlap between channels. Picking the cheapest combination of placements that covers the audience is set cover. The same template runs in vaccine campaigns (each clinic location covers a population catchment area), in disaster relief (each warehouse covers a service radius), in software testing (each test case covers a set of branches — minimum-cover-by-tests is the basis of test-suite reduction tools), and in genome assembly (each read covers a stretch of the genome). The greedy heuristic is the working horse; nobody waits for the IP solver in the marketing meeting.

In plain terms

If you want your ad to reach as many different people as possible, but each ad slot has overlapping audiences, you have a set cover problem. The greedy answer — keep buying the slot that adds the most new people — is also (provably) close to the best you can do.

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End of Chapter VI
Chapter VII Feedback Node Set →
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19 Break every cycle →