Weighted Chairman Assignment and Flow-Time Scheduling

Siyue Liu; Victor Reis

Weighted Chairman Assignment and Flow-Time Scheduling

Siyue Liu ,
Victor Reis

ITCS 2026 | November 2025 , pp. 98:1-98:15

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Given positive integers $m, n$ , a fractional assignment $x \in [0, 1] m \times n$ and weights $d \in ℝ_{& g t; 0}^{n}$ , we show that there exists an assignment $y in \{0,1\}^{m times n}$ so that for every $i \in [m]$ and $t \in [n]$ , $Big|sum_{j in [t]} d_j (x_{ij} – y_{ij}) Big| This generalizes a result of Tijdeman (1973) on the unweighted version, known as the chairman assignment problem. This also confirms a special case of the single-source unsplittable flow conjecture with arc-wise lower and upper bounds due to Morell and Skutella (IPCO 2020). As an application, we consider a scheduling problem where jobs have release times and machines have closing times, and a job can only be scheduled on a machine if it is released before the machine closes. We give a 3-approximation algorithm for maximum flow-time minimization. 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