Refined analysis yields O(1)-approximation for packing balanced star districts in planar graphs, extending to minor-free and bounded-expansion graphs, plus O(1) results for fixed-radius-k districts and minimum-weight variants.
For the approximation error, we sum the weights in sets from the children withε t1 andε t2, and then run Trimℓ,δ
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Packing Compact Subgraphs with Applications to Districting
Refined analysis yields O(1)-approximation for packing balanced star districts in planar graphs, extending to minor-free and bounded-expansion graphs, plus O(1) results for fixed-radius-k districts and minimum-weight variants.