Author

A. Y. Shavit

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Preprint Sep 2026

The 11/6 supremum of the Wang-Sitters rounding scheme for graph balancing

Wang and Sitters'11/6-approximation for graph balancing is not one algorithm but a set of permitted executions: Step 1 may return any feasible solution of the relaxation and Step 3 any of the many ways to match the remaining jobs into the slots the rounding opens. We determine exactly what that latitude permits: ratios...

A. Y. Shavit · 1 citation · ⚡1

Preprint Aug 2026

A minimum witness for the 3/2 configuration-linear-program gap in two-weight graph balancing, unique at its size

In restricted assignment - makespan minimization where each job has one size and a set of allowed machines - the configuration LP is the tightest studied relaxation, and its integrality gap is open in general. On two-weight graph balancing - each job allowed on at most two machines, sizes from two values - the value is...

A. Y. Shavit · 2 citations

Preprint Sep 2026

Minimum-makespan completion and vertex selection leave the Wang-Sitters constant at 11/6

The 11/6 worst-case constant of the Wang-Sitters rounding scheme, which a companion note establishes, can naturally be attributed to the freedom in Step 3, where an arbitrary valid slot matching is permitted. We show that eliminating that freedom does not improve the constant. A minimum-makespan completion oracle still...

A. Y. Shavit · 1 citation