The Problem
Row Reduction
The first Hungarian reduction subtracts each row's minimum from that row. This creates zeros without changing which complete assignment is cheapest. The diagram shows the reduced matrix, not an authored side table, and the zeros should be read as relative opportunities for each worker.
Row minima
The row minima are 2, 3, and 1. Why: subtracting a row constant creates at least one zero in that row. A zero after row reduction means that job is free relative to that worker's cheapest available job, not free in the original cost matrix.
Same optimizer
The cheapest assignment is unchanged. Why: every complete assignment uses exactly one entry from each row, so every assignment is shifted by the same total. If every candidate loses the same row-minimum sum, their ordering cannot change, which is the key insight that makes the reduction honest.
Candidate zeros
The highlighted zero cells mark places where a worker-job pair is cheapest relative to its row. They are candidates, not the answer yet, because a valid assignment still needs one selected cell in each row and each column.
Diagram note
Highlighted zero cells mark recomputed zeros after row reduction. The row reduction preserves the argmin exactly: it changes every complete assignment by the same amount, so the original optimum is still hiding in the reduced matrix. Pixel positions are rounded for layout; every number shown is exact.